Dynamical study and robustness for a nonlinear wastewater treatment model

In this work we deal with a wastewater treatment by using the activated sludge process. The problem is formulated as a nonlinear dynamical system. Firstly, we develop the dynamical study of the model when all parameters are well known. Hence, basic properties of invariance and dissipation are established and, under a suitable condition on parameters, a globally asymptotically stable equilibrium point occurs. Secondly, when the bacterium growth function and the substrate concentration in the feed stream are not well known, the robustness analysis provides the existence of an attractor domain to which all trajectories of the system converge. Finally, we prove that we can reduce the size (volume) of this attractor domain by increasing the recycle rate to a maximum fixed level.     

Atomic modelling of crystal/complex fluid/crystal contacts—Part II. Simulating AFM tests via the GenMol code for investigating the impact of CO2 storage on kaolinite/brine/kaolinite adhesion

GenMol^TM code is used to simulate Atomic Force Microscopy (AFM) tests at a kaolinite/brine/kaolinite contact, the confined fluid in sub-nanometre interspaces being in equilibrium with an external multi-species solution. The attraction/repulsion effort, i.e. the derivative versus the interspace aperture h of the interaction energy between both kaolinite faces, is computed versus the variable composition of the confined fluid (see for the method Part I of this work). Two external solutions are tested. Solution S1 is a neutral brine (pH=7.5) leading to a possible attraction for apertures lower than 7 Å. Solution S2 is an acidified brine (pH=3.2) leading to repulsion whatever may be the aperture h. These two AFM simulations prove the existence of a critical pH value (3.2<pH_crit<7.5) of the external solution, below which the acidification of a natural brine in a CO₂ confinement inhibits adhesion between kaolinite aggregates.     

Experimental Characterization of Porosity Structure and Transport Property Changes in Limestone Undergoing Different Dissolution Regimes

Limestone dissolution by $\hbox {CO}_2$ -rich brine induces critical changes of the pore network geometrical parameters such as the pore size distribution, the connectivity, and the tortuosity which govern the macroscopic transport properties (permeability and dispersivity) that are required to parameterize the models, simulating the injection and the fate of $\hbox {CO}_2$ . A set of four reactive core-flood experiments reproducing underground conditions ( $T = 100\,^{\circ }\hbox {C}$ and $P = 12$ MPa) has been conducted for different $\hbox {CO}_2$ partial pressures $(0.034 < P_{\mathrm{CO}_2}< 3.4\; \hbox {MPa})$ in order to study the different dissolution regimes. X-ray microtomographic images have been used to characterize the changes in the structural properties from pore scale to Darcy scale, while time-resolved pressure loss and chemical fluxes enabled the determination of the sample-scale change in porosity and permeability. The results show the growth of localized dissolution features associated with high permeability increase for the highest $P_{\mathrm{CO}_2}$ , whereas dissolution tends to be more homogeneously distributed for lower values of $P_{\mathrm{CO}_2}$ . For the latter, the higher the $P_{\mathrm{CO}_2}$ , the more the dissolution patterns display ramified structures and permeability increase. For the lowest value of $P_{\mathrm{CO}_2}$ , the preferential dissolution of the calcite cement associated with the low dissolution kinetics triggers the transport that may locally accumulate and form a microporous material that alters permeability and produces an anti-correlated porosity–permeability relationship. The combined analysis of the pore network geometry and the macroscopic measurements shows that $P_{\mathrm{CO}_2}$ regulates the tortuosity change during dissolution. Conversely, the increase of the exponent value of the observed power law permeability–porosity trend while $P_{\mathrm{CO}_2}$ increases, which appears to be strongly linked to the increase of the effective hydraulic diameter, depends on the initial rock structure.     

Is There a Representative Elementary Volume for Anomalous Dispersion?

Transport in Porous Media - The concept of the representative elementary volume (REV) is often associated with the notion of hydrodynamic dispersion and Fickian transport. However, it has been...     

Upscaling of Anomalous Pore-Scale Dispersion

Transport in Porous Media - We study the upscaling of advective pore-scale dispersion in terms of the Eulerian velocity distribution and advective tortuosity, both flow attributes, and of the...     

Investigation of the Geometrical Dispersion Regime in a Single Fracture Using Positron Emission Projection Imaging

The transport properties of a natural fracture crossing a limestone block of 36 cm × 26 cm × 60 cm is studied using positron emission projection imaging. This non-invasive technique allows to measure the spatial distribution of the activity of a radioactive solution (here irradiated-copper-EDTA solution) within the fracture. The fracture aperture is measured from the spatial distribution of the activity as the fracture is completely filled with the tracer. The experiment consists in injecting the tracer at a constant flow rate in the plane of the fracture filled with an identical non-radioactive solution. Every 10 min, a two-dimensional grey scale image of the concentration field is recorded. The heterogeneity of the tracer distribution increases with time in relation with the spatial heterogeneity of the aperture field, and favours only slightly the region of larger aperture. The correlation length of the aperture distribution is larger than the correlation length of the concentration distribution of the tracer within the sample. Consequently, the concentration distribution cannot be modelled using a classical advection–dispersion equation; the mixing process has not reached a stationary Fickian dispersion regime in the finite size domain of the experiment. Nevertheless, the transversally averaged concentration profiles evaluated along the flow direction x rescale adequately with an advective variable , where is the mean velocity and t the time. This result is explained in the context of the geometrical dispersion regime where the mixing dispersion zone grows proportionally with time. Different approaches are proposed to characterise this anomalous dispersion regime.