Identification of Hydrodynamic Dispersion Tensor by Optimization Algorithm Based LBM/CMA-ES Combination

The hydrodynamic dispersion tensor (HDT) of a porous medium is a key parameter in engineering and environmental sciences. Its knowledge allows for example, to accurately predict the propagation of a pollution front induced by a surface (or subsurface) flow. This paper proposes a new mathematical model based on inverse problem-solving techniques to identify the HDT (noted D=) of the studied porous medium. We then showed that in practice, this new model can be written in the form of an integrated optimization algorithm (IOA). The IOA is based on the numerical solution of the direct problem (which solves the convection–diffusion type transport equation) and the optimization of the error function between the simulated concentration field and that observed at the application site. The partial differential equations of the direct model were solved by high resolution of (Δx=Δy=1 m) Lattice Boltzmann Method (LBM) whose computational code is named HYDRODISP-LBM (HYDRO-DISpersion by LBM). As for the optimization step, we opted for the CMA-ES (Covariance Matrix Adaptation-Evolution Strategy) algorithm. Our choice for these two methods was motivated by their excellent performance proven in the abundant literature. The paper describes in detail the operation of the coupling of the two computer codes forming the IOA that we have named HYDRODISP-LBM/CMA-ES. Finally, the IOA was applied at the Beauvais experimental site to identify the HDT D=. The geological analyzes of this site showed that the tensor identified by the IOA is in perfect agreement with the characteristics of the geological formation of the site which are connected with the mixing processes of the latter.

Effects of passive storage on modelling hydrological function and isotope dynamics in a karst flow system in southwest China

Representing passive storage in coupled flow-isotope models can facilitate simulation of mixing and retardation effects on tracer transport in many natural systems, such as catchments or rivers. However, the effectiveness of incorporating passive storages in models of complex karst flow systems remains poorly understood. In this study, we developed a coupled flow-isotope model that conceptually represents both “fast” and “slow” flow processes in heterogeneous aquifers to represent hydrological connections between hillslopes and low-lying depression units in cockpit karst landscapes. As this model originally included a varying number of passive storages at different positions of the flow system (e.g. fast/slow flow reservoirs combined with different hillslope/depression units), the model structure and relevant parameters were optimized using a multi-objective optimization algorithm. This was used to match detailed observational data of hydrological processes and isotope concentration in the Chenqi catchment in southwest China. Results show that the optimal structure for a coupled flow-isotope model incorporated only two passive storages in fast flow and slow flow paths of the hillslope unit. Using fewer or greater numbers of passive stores in the model could lead to under- or over-mixing of isotope signatures. This optimized model structure could effectively improve simulation accuracies for outlet discharge and isotope signatures, with > 0.65 of the modified Kling-Gupta efficiency. Additionally, the optimal tracer-aided model yields reasonable parameter values and estimations of hydrological components (e.g. more than 80 % of fast flow in the total discharge). Furthermore, results imply that the solute transport is primarily controlled by advection and hydrodynamic dispersion in steep hillslope unit, which is a remarkable phenomenon in the karst flow system. The study resulted in new insights, more realistic catchment conceptualizations and improved model formulation.

Modeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures

Hydrodynamic dispersion process in relation with the geometrical properties of the porous media are studied in two sets of 6 porous media samples of porosity θ ranging from 0.1 to 0.25. These two sets of samples display distinctly different evolutions of the microstructures with porosity but share the same permeability trend with porosity. The methodology combines three approaches. First, numerical experiments are performed to measure pre-asymptotic to asymptotic dispersion from diffusion-controlled to advection-controlled regime using Time-Domain Random Walk solute transport simulations. Second, a porosity-equivalent network of bonds is extracted in order to measure the geometrical properties of the samples. Third, the results of the direct numerical simulations are interpreted as a Continuous Time Random Walk (CTRW) process controlled by the flow speed distribution and correlation. These complementary modeling approaches allow evaluating the relation between the parameters of the conceptual transport process embedded in the CTRW model, the flow field properties and the pore-scale geometrical properties. The results of the direct numerical simulations for all the 12 samples show the same scaling properties of the mean flow distribution, the first passage time distribution and the asymptotic dispersion vs. the Péclet number than those predicted by the CTRW model. It allows predicting the asymptotic dispersion coefficient D* from Pe = 1 to the largest values of Pe expected for laminar flow in natural environments (Pe≈ 4,000). D*∝Pe2−α for Pe≥Pecrit, where α can be inferred from the Eulerian flow distribution and Pecrit depends on porosity. The Eulerian flow distribution is controlled by the distribution of fractions of fluid flowing at each of the pore network nodes and thus is determined mainly by the distribution of the throat radius and the coordination number. The later scales with the number of throats per unit volume independently on the porosity. The asymptotic dispersion coefficient D* decreases when porosity increases for all Péclet values larger than 1 due to the increase with porosity of both α and the flow speed decorrelation length.

A holographic superfluid symphony

We study the hydrodynamic excitations of backreacted holographic superfluids by computing the full set of quasinormal modes (QNMs) at finite momentum and matching them to the existing hydrodynamic theory of superfluids. Additionally, we analyze the behavior of the low-energy excitations in real frequency and complex momentum, going beyond the standard QNM picture. Finally, we carry out a novel type of study of the model by computing the support of the hydrodynamic modes across the phase diagram. We achieve this by determining the support of the corresponding QNMs on the different operators in the dual theory, both in complex frequency and complex momentum space. From the support, we are able to reconstruct the hydrodynamic dispersion relations using the hydrodynamic constitutive relations. Our analysis rules out a role-reversal phenomenon between first and second sound in this model, contrary to results obtained in a weakly coupled field theory framework.

Analysis of Factors for Compacted Clay Liner Performance Considering Isothermal Adsorption

The concentration profiles and breakthrough curves of the 2 m thick compacted clay liner (CCL) given in the specification were compared, considering three different adsorption isotherms (upper convex, linear, and lower concave). In addition, the effects of transport parameters, sorption isotherms, and source concentrations on pollutant migration were analyzed. The results showed that the dimensionless breakthrough curves of different source concentrations considering the linear adsorption isotherm coincided with each other, as the partition coefficient of the linear adsorption isotherm was constant. For the lower concave isotherm, the migration of a large source concentration was slowest, because the partition coefficient of the lower concave isotherm increased with an increase in concentration. For the upper convex isotherm, the migration of a large source concentration was fastest, because the partition coefficient decreased with an increase in concentration. The effects of the nonlinear isotherms on the shape of the outflow curve were similar to the effects of a change in the hydrodynamic dispersion (Dh): the concentration front of the upper convex isotherm was narrower, which was similar to the effect of a reduction in Dh (i.e., PL), and the concentration front of the lower concave isotherm was wider and similar to the effect of an increase Dh (i.e., PL). Therefore, the diffusion and adsorption parameters were fitted separately in the study, in case the nonlinear adsorption behavior was mistakenly defined as linear adsorption.

Truncation Effect on Estimation of Transport Parameters for Slug-injection Tracer Tests

For slug-injection tracer tests, tracer concentrations below the detection limit of the measurement instrument can cause truncation of the observed data. This study investigated the truncation effect on the estimation error of parameters based on analytical solutions and the results of a laboratory-scale experiment. Spatial moment analysis was performed to estimate the measured total mass and transport parameters, including the pore velocity and the longitudinal and transverse dispersivities. Increasing the travel distance and detection limit caused the measured mass and dispersivities to be underestimated regardless of the dimensionality because hydrodynamic dispersion occurs with increasing travel distance, which smoothens the concentration front. The one- and two-dimensional cases showed that the truncation effect on the measured mass and longitudinal dispersivity depended on dimensionality. In contrast, the pore velocity showed no such dependence; the center of mass did not change as the unmeasured portion due to truncation was increased because the plume, which exhibited a Gaussian distribution, was truncated symmetrically. In the experiment, the measured mass and dispersivities likewise depended on the travel distance and detection limit, but there were large differences in the detection limit at which the dimensionless parameter reached a value of zero between the experimental results and analytical solution. This is because the initial plume in the experiment was of a finite size. Thus, experimental design factors such as the scale, device, and dimensionality should be considered to minimize the estimation error of transport parameters, excluding the pore velocity.