# Mixed Solutions of Mathematical and Numerical Methods for Reactive Mass Transport Problems of Two Different Porosity Regions in Fluid-Saturated Porous Media

Chongbin Zhao, B.E. Hobbs, A. Ord

Research output: Contribution to journalArticle

### Abstract

Reactive mass transport is a common phenomenon associated with groundwater pollution in the field of groundwater hydrology. For a reactive mass transport problem involving two different porosity regions, in which the porosity of the fluid-saturated porous medium has a constant distribution in the left region and an exponential distribution in the right region, theoretical solutions for both dimensional and dimensionless acid concentrations have been derived mathematically in the left region by using the interface condition substitution strategy. The fundamental idea behind this strategy is that the boundary condition at the entrance of the left region and the mathematical governing equation of the right region at the interface location between the left and right regions can be used to determine two independent constants involved in the theoretical solutions for the dimensional and dimensionless acid concentrations in the left region of the reactive mass transport system. Since both the acid concentration and its first derivative are known at the left boundary (i.e. the interface location) of the right region, it is possible to derive analytical expressions for the numerical solution (e.g. the finite element solution) in the right region by using the point-by-point marching strategy. The related theoretical results have demonstrated that the porosity distribution pattern in the right region of the system can have a significant influence on the dimensionless acid concentration distribution in the whole system, so that it affects not only the chemical dissolution front instability, but also the reactive mass transport process in an underground water system.
Original language English 124145 8 Journal of Hydrology 580 https://doi.org/10.1016/j.jhydrol.2019.124145 Published - Jan 2020

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mass transport
numerical method
porous medium
porosity
fluid
acid
groundwater pollution
transport process
hydrology
substitution
boundary condition
dissolution
groundwater
distribution

### Cite this

@article{18e363d0b44c4926aedd1c02ffb8ba04,
title = "Mixed Solutions of Mathematical and Numerical Methods for Reactive Mass Transport Problems of Two Different Porosity Regions in Fluid-Saturated Porous Media",
abstract = "Reactive mass transport is a common phenomenon associated with groundwater pollution in the field of groundwater hydrology. For a reactive mass transport problem involving two different porosity regions, in which the porosity of the fluid-saturated porous medium has a constant distribution in the left region and an exponential distribution in the right region, theoretical solutions for both dimensional and dimensionless acid concentrations have been derived mathematically in the left region by using the interface condition substitution strategy. The fundamental idea behind this strategy is that the boundary condition at the entrance of the left region and the mathematical governing equation of the right region at the interface location between the left and right regions can be used to determine two independent constants involved in the theoretical solutions for the dimensional and dimensionless acid concentrations in the left region of the reactive mass transport system. Since both the acid concentration and its first derivative are known at the left boundary (i.e. the interface location) of the right region, it is possible to derive analytical expressions for the numerical solution (e.g. the finite element solution) in the right region by using the point-by-point marching strategy. The related theoretical results have demonstrated that the porosity distribution pattern in the right region of the system can have a significant influence on the dimensionless acid concentration distribution in the whole system, so that it affects not only the chemical dissolution front instability, but also the reactive mass transport process in an underground water system.",
author = "Chongbin Zhao and B.E. Hobbs and A. Ord",
year = "2020",
month = "1",
doi = "10.1016/j.jhydrol.2019.124145",
language = "English",
volume = "580",
journal = "Journal of Hydrology",
issn = "0022-1694",
publisher = "Pergamon",

}

In: Journal of Hydrology, Vol. 580, 124145, 01.2020.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Mixed Solutions of Mathematical and Numerical Methods for Reactive Mass Transport Problems of Two Different Porosity Regions in Fluid-Saturated Porous Media

AU - Zhao, Chongbin

AU - Hobbs, B.E.

AU - Ord, A.

PY - 2020/1

Y1 - 2020/1

N2 - Reactive mass transport is a common phenomenon associated with groundwater pollution in the field of groundwater hydrology. For a reactive mass transport problem involving two different porosity regions, in which the porosity of the fluid-saturated porous medium has a constant distribution in the left region and an exponential distribution in the right region, theoretical solutions for both dimensional and dimensionless acid concentrations have been derived mathematically in the left region by using the interface condition substitution strategy. The fundamental idea behind this strategy is that the boundary condition at the entrance of the left region and the mathematical governing equation of the right region at the interface location between the left and right regions can be used to determine two independent constants involved in the theoretical solutions for the dimensional and dimensionless acid concentrations in the left region of the reactive mass transport system. Since both the acid concentration and its first derivative are known at the left boundary (i.e. the interface location) of the right region, it is possible to derive analytical expressions for the numerical solution (e.g. the finite element solution) in the right region by using the point-by-point marching strategy. The related theoretical results have demonstrated that the porosity distribution pattern in the right region of the system can have a significant influence on the dimensionless acid concentration distribution in the whole system, so that it affects not only the chemical dissolution front instability, but also the reactive mass transport process in an underground water system.

AB - Reactive mass transport is a common phenomenon associated with groundwater pollution in the field of groundwater hydrology. For a reactive mass transport problem involving two different porosity regions, in which the porosity of the fluid-saturated porous medium has a constant distribution in the left region and an exponential distribution in the right region, theoretical solutions for both dimensional and dimensionless acid concentrations have been derived mathematically in the left region by using the interface condition substitution strategy. The fundamental idea behind this strategy is that the boundary condition at the entrance of the left region and the mathematical governing equation of the right region at the interface location between the left and right regions can be used to determine two independent constants involved in the theoretical solutions for the dimensional and dimensionless acid concentrations in the left region of the reactive mass transport system. Since both the acid concentration and its first derivative are known at the left boundary (i.e. the interface location) of the right region, it is possible to derive analytical expressions for the numerical solution (e.g. the finite element solution) in the right region by using the point-by-point marching strategy. The related theoretical results have demonstrated that the porosity distribution pattern in the right region of the system can have a significant influence on the dimensionless acid concentration distribution in the whole system, so that it affects not only the chemical dissolution front instability, but also the reactive mass transport process in an underground water system.

UR - http://www.mendeley.com/research/mixed-solutions-mathematical-numerical-methods-reactive-mass-transport-problems-two-different-porosi

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