scholarly journals Hausdorff Fractal Derivative Model to Characterize Transport of Inorganic Arsenic in Porous Media

Water ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2353
Author(s):  
Xiaoxiao Hao ◽  
HongGuang Sun ◽  
Yong Zhang ◽  
Shiyin Li ◽  
Jia Song ◽  
...  
Keyword(s):  
Porous Media ◽  
Human Life ◽  
Inorganic Arsenic ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Migration Behavior ◽  
Arsenic Pollution ◽  
Sand Column ◽  
Fractal Derivative ◽  
Arsenic Transport

The increasing severity of arsenic pollution has progressively threatened human life and attracted much attention. One of the important topics in environmental sciences is to accurately describe the inorganic arsenic transport in heterogeneous porous media, occurring anomalous diffusion phenomenon, which ultimately benefits the control of arsenic pollution. In this paper, we re-evaluate the dataset of the inorganic arsenic transport in porous media in previous work by using a time-Hausdorff fractal model (HADE). Transport experiments of arsenic-carrying (As(V)) ferric humate complex colloids through a quartz sand column were carried out under varying dissolved organic matter (humic acid) concentrations, pH values, ionic strengths, and ferric concentrations. The results show that under our experimental settings, arsenic migration is promoted with the increase of concentrations of HA, ferric ion and sodium ion, and pH to varying degrees. The intensity of arsenic sub-diffusion behavior is opposite to that of arsenic transport. The HADE model can describe the migration behavior of arsenic well, and the value of the time fractal derivative can reflect the diffusion intensity of arsenic migration to a certain extent. By comparing the HADE model, ADE model, and time-fractional model (fADE) to the experimental data, the HADE model can significantly improve all the simulation results of capturing As(V) breakthrough curves (BTCs).

Pore-scale Mixing and the Evolution from Anomalous to Normal Hydrodynamic Dispersion

2021 ◽  
Author(s):  
Marco Dentz ◽  
Alexandre Puyguiraud ◽  
Philippe Gouze
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Molecular Diffusion ◽  
Pore Space ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Hydrodynamic Dispersion ◽  
Pore Scale ◽  
Sandstone Sample ◽  
Flow Variability

<p>Transport of dissolved substances through porous media is determined by the complexity of the pore space and diffusive mass transfer within and between pores. The interplay of diffusive pore-scale mixing and spatial flow variability are key for the understanding of transport and reaction phenomena in porous media. We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion: (i) The smoothing of intra-pore velocity contrasts, (ii) the increase of the tortuosity of particle paths, and (iii) the setting of a maximum time for particle transitions. Based on these mechanisms, we derive an upscaled approach that predicts anomalous and normal hydrodynamic dispersion based on the characteristic pore length, Eulerian velocity distribution and Péclet number. The theoretical developments are supported and validated by direct numerical flow and transport simulations in a three-dimensional digitized Berea sandstone sample obtained using X-Ray microtomography. Solute breakthrough curves, are characterized by an intermediate power-law behavior and exponential cut-off, which reflect pore-scale velocity variability and intra-pore solute mixing. Similarly, dispersion evolves from molecular diffusion at early times to asymptotic hydrodynamics dispersion via an intermediate superdiffusive regime. The theory captures the full evolution form anomalous to normal transport behavior at different Péclet numbers as well as the Péclet-dependence of asymptotic dispersion. It sheds light on hydrodynamic dispersion behaviors as a consequence of the interaction between pore-scale mixing and Eulerian flow variability. </p>

scholarly journals Experimental Research on the Thresholds of Scale-Dependent Dispersivity of Solute Transport

Lithosphere ◽  
2021 ◽  
Vol 2021 (Special 3) ◽  
Author(s):  
Ruigang Zhang ◽  
Mingxi Chu ◽  
Yong Liu ◽  
Dun Wu ◽  
Wenyong Zhang
Keyword(s):  
Porous Media ◽  
Solute Transport ◽  
Threshold Value ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Travel Distance ◽  
Asymptotic Model ◽  
Linear Scale ◽  
Advection Dispersion ◽  
Early Arrival

Abstract The conventional advection-dispersion equation (ADE) has been widely used to describe the solute transport in porous media. However, it cannot interpret the phenomena of the early arrival and long tailing in breakthrough curves (BTCs). In this study, we aim to experimentally investigate the behaviors of the solute transport in both homogeneous and heterogeneous porous media. The linear-asymptotic model (LAF solution) with scale-dependent dispersivity was used to fit the BTCs, which was compared with the results of the ADE model and the conventional truncated power-law (TPL) model. Results indicate that (1) the LAF model with linear scale-dependent dispersivity could better capture the evolution of BTCs than the ADE model; (2) dispersivity initially increases linearly with the travel distance and is stable at some limited value over a large distance, and a threshold value of the travel distance is provided to reflect the constant dispersivity; and (3) compared with the TPL model, both the LAF and ADE models can capture the behavior of solute transport as a whole. For fitting the early arrival, the LAF model is less than the TPL; however, the LAF model is more concise in mathematics and its application will be studied in the future.

Lagrangian models of reactive transport in heterogeneous porous media with uncertain properties

2011 ◽  
Vol 468 (2140) ◽  
pp. 1154-1174 ◽  
Author(s):  
G. Severino ◽  
D. M. Tartakovsky ◽  
G. Srinivasan ◽  
H. Viswanathan
Keyword(s):  
Porous Media ◽  
Reactive Transport ◽  
Three Dimensional ◽  
Chemical Properties ◽  
Parametric Uncertainty ◽  
Bimolecular Reaction ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Advective Transport ◽  
Transport Parameters

We consider multi-component reactive transport in heterogeneous porous media with uncertain hydraulic and chemical properties. This parametric uncertainty is quantified by treating relevant flow and transport parameters as random fields, which renders the governing equations stochastic. We adopt a stochastic Lagrangian framework to replace a three-dimensional advection–reaction transport equation with a one-dimensional equation for solute travel times. We derive approximate expressions for breakthrough curves and their temporal moments. To illustrate our general theory, we consider advective transport of dissolved species undergoing an irreversible bimolecular reaction.

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