Analytical power series solution for contaminant transport with hyperbolic asymptotic distance-dependent dispersivity

Chen, Jui Sheng; Ni, Chuen-Fa; Liang, Ching-Ping; Chiang, Chen Chung

doi:10.1016/j.jhydrol.2008.08.020

Cited by 53 publications

(19 citation statements)

References 16 publications

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“…Using Eqs. (16), (18) and (19), the dispersion coefficient, dispersivity and actual velocity were calculated according to the relationship between elapsed time and the effluent tracer concentration normalized by initial tracer concentration (Chen et al, 2008;Gelhar et al, 1979). The number of long samples was 23, and the length varied from 32 cm to 39.5 cm.…”

Section: Concentration In Eq (8) Is Represented By a Breakthrough Cumentioning

confidence: 99%

“…Accurate estimation of the hydraulic conductivity and effective porosity are substantial to the analysis of the magnitude of water exchange and contaminant transport between groundwater and surface water, and to solve a number of relevant geotechnical problems such as groundwater seepage from tunnel, land subsidence and landslide (Boadu 2000;Chen et al, 2008;Landon et al, 2001). Dispersivity is necessary to determine the mechanical dispersion in the process of contaminants transport through porous media, and it can be determined by a laboratory column tracer test (Singh, 2002).…”

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confidence: 99%

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The Characteristics of Hydrogeological Parameters of Unconsolidated Sediments in the Nakdong River Delta of Busan City, Korea

Khakimov¹,

Chung²,

Senapathi³

et al. 2017

Journal of Soil and Groundwater Environment

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This study dealt with the characteristics and the interrelations of hydrogeological parameters such as hydraulic conductivity, dispersivity and effective porosity of unconsolidated sediments for providing the basic data necessary for the planning of the management and preservation of groundwater quality in the Nakdong River Delta of Busan City, Korea. Groundwater quality in this area has been deteriorated due to seawater intrusion, agricultural fertilizer and pesticide, industrial wastewater, and contaminated river water. The physical properties (grain size distribution, sediment type, sorting) and aquifer parameters (hydraulic conductivity, effective porosity, longitudinal dispersivity) were determined from grain size analysis, laboratory permeability test and column tracer test. Among 36 samples, there were 18 Sand (S), 7 Gravelly Sand (gS), 5 Silty Sand (zS), 5 Muddy Sand (mS), and 1 Sandy Silt (sZ). Hydraulic conductivity was determined through a falling head test, and ranged from 9.2 × 10 −5 to 2.9 × 10 −2 cm/sec (0.08 to 25.6 m/day). From breakthrough curves, dispersivity was calculated to be 0.35~3.92 cm. Also, effective porosity and average linear velocity were obtained through the column tracer test, and their values were 0.04~0.46 and 1.06E-04~6.49E-02 cm/sec, respectively. Statistical methods were used to understand the interrelations among aquifer parameters of hydraulic conductivity, effective porosity and dispersivity. The relation between dispersivity and hydraulic conductivity or effective porosity considered the sample length, because dispersivity was affected by experimental scale. The relations between dispersivity and hydraulic conductivity or effective porosity were all in inverse proportion for all long and short samples. The reason was because dispersivity was in inverse proportion to the groundwater velocity in case of steady hydrodynamic dispersion coefficient, and groundwater velocity was in proportion to the hydraulic conductivity or effective porosity. This study also elucidated that longitudinal dispersivity was dependent on the scale of column tracer test, and all hydrogeological parameters were low to high values due to the sand quantity of sediments. It is expected that the hydrogeological parameter data of sediments will be very useful for the planning of groundwater management and preservation in the Nakdong River Delta of Busan City, Korea.

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Section: Concentration In Eq (8) Is Represented By a Breakthrough Cumentioning

confidence: 99%

mentioning

confidence: 99%

The Characteristics of Hydrogeological Parameters of Unconsolidated Sediments in the Nakdong River Delta of Busan City, Korea

Khakimov¹,

Chung²,

Senapathi³

et al. 2017

Journal of Soil and Groundwater Environment

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“…(18) can be described by power series method by Kreyszig (1999) and Chen et al (2008). Following the similar approach of Chen et al (2008) and Gao et al (2012), the solution of MPNE in the Laplace domain can be obtained as…”

Section: P K Sharma and Teodrose Atnafu Abgazementioning

confidence: 99%

“…The scale effect of the dispersion coefficient in the heterogeneous soil was much more significant comparing to that in the homogeneous soil. Chen et al (2008) used hyperbolic asymptotic distance dependent dispersivity, which initially increases with travel distance and eventually reaches an asymptotic value at long travel distance. Moreover, breakthrough curves obtained from the hyperbolic asymptotic dispersivity model are compared with those obtained from the constant dispersivity model to scrutinize the relationship of the transport parameters derived by Mishra & Parker (1990).…”

Section: Introductionmentioning

confidence: 99%

Solute transport through porous media using asymptotic dispersivity

Sharma

Abgaze

2015

Sadhana

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In this paper, multiprocess non-equilibrium transport equation has been used, which accounts for both physical and chemical non-equilibrium for reactive transport through porous media. An asymptotic distance dependent dispersivity is used to embrace the concept of scale-dependent dispersion for solute transport in heterogeneous porous media. Semi-analytical solution has been derived of the governing equations with an asymptotic distance dependent dispersivity by using Laplace transform technique and the power series method. For application of analytical model, we simulated observed experimental breakthrough curves from 1500 cm long soil column experiments conducted in the laboratory. The simulation results of breakthrough curves were found to deviate from the observed breakthrough curves for both mobile-immobile and multiprocess non-equilibrium transport with constant dispersion models. However, multiprocess non-equilibrium with an asymptotic dispersion model gives better fit of experimental breakthrough curves through long soil column and hence it is more useful for describing anomalous solute transport through heterogeneous porous media. The present model is simpler than the stochastic numerical method.

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“…Later, an equivalent substitution was used by Golz (2003) for studying convective-dispersive solute transport with constant production, first-order decay and equilibrium sorption in a porous medium. An analytical technique for solving ADE with hyperbolic asymptotic distance-dependent dispersivity was presented (Chen et al 2008), in which the solution was derived by applying the extended power series method coupled with the Laplace transform. An analytical model was presented for solute transport in rivers, including transient storage in hyporheic zones (Smedt 2007), which consists of an ADE for transport in the main channel with a sink term describing diffusive solute transfer to the hyporheic zone.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

et al. 2011

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The one-dimensional linear advection-diffusion equation is solved analytically by using the Laplace integral transform. The solute transport as well as the flow field is considered to be unsteady, both of independent patterns. The solute dispersion occurs through an inhomogeneous semi-infinite medium. Hence, velocity is considered to be an increasing function of the space variable, linearly interpolated in a finite domain in which solute dispersion behaviour is studied. Dispersion is considered to be proportional to the square of the spatial linear function. Thus, the coefficients of the advection-diffusion equation are functions of both the independent variables, but the expression for each coefficient is considered in degenerate form. These coefficients are reduced into constant coefficients with the help of a new space variable, introduced in our earlier works, and new time variables. The source of the solute is considered to be a stationary uniform point source of pulse type.

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Analytical power series solution for contaminant transport with hyperbolic asymptotic distance-dependent dispersivity

Cited by 53 publications

References 16 publications

The Characteristics of Hydrogeological Parameters of Unconsolidated Sediments in the Nakdong River Delta of Busan City, Korea

The Characteristics of Hydrogeological Parameters of Unconsolidated Sediments in the Nakdong River Delta of Busan City, Korea

Solute transport through porous media using asymptotic dispersivity

One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

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