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

Water ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 125
Author(s):  
Hassan Smaoui ◽  
Lahcen Zouhri ◽  
Sami Kaidi
Keyword(s):  
Porous Medium ◽  
Optimization Algorithm ◽  
Error Function ◽  
Concentration Field ◽  
Application Site ◽  
Hydrodynamic Dispersion ◽  
Diffusion Type ◽  
Perfect Agreement ◽  
Dispersion Tensor ◽  
Direct Model

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.

Hydrodynamic Dispersion Coefficient of Urea in Silty Loam Soil

2019 ◽  
Vol 6 (04) ◽  
Author(s):  
RAM PAL ◽  
H C SHARMA ◽  
M IMTIYAZ
Keyword(s):  
Transport Phenomenon ◽  
Porous Medium ◽  
Contaminant Transport ◽  
Dispersion Coefficient ◽  
Hydrodynamic Dispersion ◽  
Soil Columns ◽  
Soil Medium ◽  
Adverse Health Effects ◽  
Silty Loam ◽  
Loam Soil

The modern theme of agriculture is not only to increase production but also to minimize undesirable environmental effects. Leaching of surface-applied fertilizer is the major source of groundwater pollution. Nitrogenous fertilizers are the most popular among the Indian farmers, which on leaching reach the groundwater in different forms (NH4-N, NO3-N, etc). NO3-N leaches faster than other types, remains in-reactive in groundwater, moves with the velocity of groundwater and contaminates it. Contamination arises when NO3-N accumulates in groundwater and consumed in high amount by humans and animals, may result in adverse health effects. For the study of contaminant transport phenomenon in porous medium, a general convection dispersion equation is used, in which dispersion coefficient is one of the primary parameters necessary to be determined for a particular soil. Keeping it in view a study was conducted to assess different available techniques to determine the dispersion coefficient with the help of soil columns having silty loam soil as soil medium. The value of the dispersion coefficient obtained for silty loam soil, by this method was equal to 0.00576 m2.

The effect of hydrodynamic dispersion on reactive flows in porous media

2001 ◽  
Vol 12 (5) ◽  
pp. 557-569 ◽  
Author(s):  
J. CHADAM ◽  
P. ORTOLEVA ◽  
Y. QIN ◽  
R. STAMICAR
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Critical Value ◽  
Reactive Flow ◽  
Hydrodynamic Dispersion ◽  
Reaction Interface ◽  
Shape Stability ◽  
Linearized Problem ◽  
New Feature ◽  
Moving Free Boundary

The shape stability of the reaction interface for reactive flow in a porous medium is investigated. Previous work showed that the Reaction-Infiltration Instability could cause the reaction zone to lose stability when the Peclet number exceeded a critical value. The new feature of this study is to include a velocity-dependent hydrodynamic dispersion. A mathematical model for this phenomenon is given in the form of a moving free-boundary problem. The spectrum of the linearized problem is obtained, and the related analysis and numerical calculations show that the onset of the instability is not eliminated by the new dispersive terms. The details of analysis show that the instability is reduced especially by the transverse dispersion.

scholarly journals Heat and Mass Transfer with Free Convection MHD Flow Past a Vertical Plate Embedded in a Porous Medium

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Farhad Ali ◽  
Ilyas Khan ◽  
Sharidan Shafie ◽  
Norzieha Musthapa
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Free Convection ◽  
Heat And Mass Transfer ◽  
Numerical Solutions ◽  
Elementary Function ◽  
Error Function ◽  
Mhd Flow ◽  
Uniform Motion ◽  
Dimensionless Time

An analysis to investigate the combined effects of heat and mass transfer on free convection unsteady magnetohydrodynamic (MHD) flow of viscous fluid embedded in a porous medium is presented. The flow in the fluid is induced due to uniform motion of the plate. The dimensionless coupled linear partial differential equations are solved by using Laplace transform method. The solutions that have been obtained are expressed in simple forms in terms of elementary functionexp(·)and complementary error functionerfc(·). They satisfy the governing equations; all imposed initial and boundary conditions and can immediately be reduced to their limiting solutions. The influence of various embedded flow parameters such as the Hartmann number, permeability parameter, Grashof number, dimensionless time, Prandtl number, chemical reaction parameter, Schmidt number, and Soret number is analyzed graphically. Numerical solutions for skin friction, Nusselt number, and Sherwood number are also obtained in tabular forms.

Study of flow and hydrodynamic dispersion in a porous medium using pulsed–field–gradient magnetic resonance

1997 ◽  
Vol 453 (1958) ◽  
pp. 489-513 ◽  
Author(s):  
M. H. G. Amin ◽  
S. J. Gibbs ◽  
R. J. Chorley ◽  
K. S. Richards ◽  
T. A. Carpenter ◽  
...  
Keyword(s):  
Porous Medium ◽  
Magnetic Resonance ◽  
Field Gradient ◽  
Hydrodynamic Dispersion ◽  
Pulsed Field

Fast and Globally Convergent Nonlinear System Model for 3D Magnetostrictive Systems

2014 ◽  
Author(s):  
Hafez Tari ◽  
Marcelo J. Dapino
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Flux Density ◽  
Error Function ◽  
Second Order ◽  
System Model ◽  
Magnetic Flux Density ◽  
Magnetostrictive Material ◽  
Globally Convergent ◽  
Direct Model

A globally convergent and fully coupled magnetomechanical model for 3D magnetostrictive systems is presented. In magnetostrictive actuators, magnetic field and stress inputs generate magnetic flux density and strain. We refer to models that follow this scheme as direct models (no relation to the direct magnetomechanical effect). In certain design and control situations, inverse models are necessary in which the magnetic field and stress are found from specified magnetic flux density and strains. This inversion typically involves an iterative procedure, which may be prone to convergence issues. An inverse model approach is proposed for arbitrary magnetostrictive materials. The inversion requirement is a continuous and second order differentiable direct model for any chosen magnetostrictive material. The approach is globally convergent, which makes it ideal for use in finite element frameworks. The premise of the proposed iterative system model is to constitute a recursive correction formula based on second order approximations of a novel scalar error function which allows to achieve a faster convergence rate. A continuation approach is then used to achieve global convergence for arbitrary input parameters. To illustrate, Galfenol is chosen as the magnetostrictive material, and analytical derivations of the Jacobian and Hessian matrices are presented. Finally, the computational efficiency of the proposed approach is shown to compare favorably against existing models.

scholarly journals Measurement and Simulation of the Nonlocal Dispersion Tensor in Porous Media

2021 ◽  
Author(s):  
◽  
Mark Warwick Hunter
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Parameter Space ◽  
Capillary Flow ◽  
Pulse Sequence ◽  
Blood Perfusion ◽  
Model Systems ◽  
Length Scales ◽  
Dispersion Tensor ◽  
Nonlocal Dispersion

<p>Nuclear Magnetic Resonance (NMR) techniques have been used extensively to characterise dispersion and diffusion in porous media. The completely non-invasive nature of the measurements and the ability to measure opaque samples provide the makings for an excellent tool. Detailed understanding of the microstructure of porous media leads to the ability to model and predict macroscopic effects such as ground water flow, oil extraction, blood perfusion and enable understanding of industrial catalytic reactors. The range of properties that NMR is capable of measuring is extensive but one particular quantity, the nonlocal dispersion tensor has long been identified as an ideal way to characterise dispersive effects at short time and length scales. The nonlocal dispersion tensor is a quantity that is included in theory proposed by Koch and Brady (1987) to explain non-Fickian dispersive behaviour. Demonstrated here is, for the first time, a method to measure the tensor. Details of the newly developed NMR pulse sequence and the post processing technique required to extract the nonlocal dispersion tensor are given. Successful measurements have been undertaken on model systems such as capillary flow and Couette flow. This enabled direct comparison with analytically calculated quantities and excellent agreement is found, thus verifying the methodology. A complete set of nonlocal dispersion components has been identified and measured in a model porous medium, in this case a random beadpack of monosized spheres. The new measurements provide the ability to infer and characterise the nature of fluid correlations, particularly at short length scales. In parallel, a simulation suite based on a lattice Boltzmann calculation (implemented by a co-worker Dr Andrew Jackson), has been used to independently generate the same nonlocal components as measured. The simulations have also been used to guide the design of further NMR experiments, to further investigate aspects of the new parameter space that the nonlocal dispersion tensor provides and to explore parts of the parameter space that are inaccessible by NMR. Finally, the methodology was adapted to enable nonlocal dispersion measurements on a 'real' porous medium, a Bentheimer sandstone.</p>

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