Experimental and numerical simulation of ...

Experimental and numerical simulation of contaminant transport through layered soil P. K. Sharma*1, V. A. Sawant1, S. K. Shukla2 and Zubair Khan1 In this study, the solute transport through saturated multi-layer soils was studied in the laboratory using the soil column experiment. Sodium chloride was used as a conservative chemical and sodium fluoride as a reactive chemical in the experiment. During the experiment, a pulse-type boundary condition was used. An implicit finite-difference numerical analysis was also carried out to get the numerical solution of advective–dispersive transport including equilibrium sorption and first-order degradation constant for the multi-layered soil. The results of experimental breakthrough curves (BTCs) showed that the order in which the soil layers were stratified in a water-saturated profile did not influence the effluent solute concentration distribution. The results also show the effect of column Peclet number, retardation factor, and first-order degradation coefficient on BTCs for the solute transport in multi-layered soils. Keywords: Concentration profiles, Contaminant transport, Solute column experiment, Layered soil

*Corresponding author, email [email protected]

developed an analytical solution of the reactive transport equation in a finite soil column for both continuous and pulse-type solutes at the soil surface. The solution of transport equation considered reversible and irreversible solute adsorptions. The irreversible adsorption was represented by the sink/source term. van Genuchten and Wierenga (1976) developed the mobile immobile (MIM) model, which is a practical and physical approach to describe anomalous solute transport behavior in heterogeneous soil. Selim et al. (1977) used the finite-difference method to solve the convective–dispersive equation (CDE) for the solute transport in two-layered soils under steady-state flow conditions. Transport experiments were also conducted to study the movement of Mg, Ca, and H ions in water-saturated two-layered soils (Sharkey clay and acid-washed sand) under steady-state flow. Sudicky et al. (1985) and Starr et al. (1985) studied the results of experiments designed to evaluate the impact of diffusive mass transfer between layers of low and high hydraulic conductivity on solute transport. Brusseau (1991) studied the capability of multi-process non-equilibrium model to predict the transport of solute through stratified porous medium. Jury and Utermann (1992) developed a travel function to resolve the problem of solute transport through a layered soil, representing the travel time to any depth in the soil as the sum of travel times through the individual layers. They used wide columns to avoid artificially reducing the lateral mixing time. There are several options for coupling the solute concentrations at the interface between layers. Leij and van Genuchten (1995) derived solution for the advection–dispersion equation (ADE) describing solute transport during steady

ß 2014 W. S. Maney & Son Ltd Received 30 June 2013; accepted 28 August 2013 DOI 10.1179/1939787913Y.0000000014

International Journal of Geotechnical Engineering

Introduction During the past few decades, it has been experienced that many types of contaminants (tetrachloroethylene, nitrates, fluorides, etc.) can infiltrate into the ground and pollute the soil media and groundwater (Charbeneau, 2000). The fluoride wastes are generally generated by the industries dealing with aluminum, steel, glass, and fertilizer. It is observed that most groundwater contaminants are reactive in nature, and they infiltrate through the vadoze zone and reach the water-table and continue to migrate in the direction of groundwater flow. Therefore, it is essential to understand the transport process of contaminants through the subsurface porous media so that health risk can be avoided. For understanding the transport process of contaminants through the subsurface porous media, several mathematical models have been developed. Lapidus and Amundson (1952) considered equilibrium and kinetic adsorption process in a semi-infinite column. Brenner (1962) considered the case of non-reactive solute transport in a finite soil column with the boundary conditions, which allowed the solute to move by advection and dispersion across the soil surface. Shamir and Harleman (1967) proposed an analytical method and assumed that different layers were independent with regard to solute travel time. Selim and Mansell (1976)

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Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee-247667, India Discipline of Civil Engineering, Edith Cowan University, Perth, Australia

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2 Particle-size distribution curves for natural soil, sand, and silt 1 Details of one-dimensional soil column experiment

simulate the experimental BTCs for the solute transport through layered soil.

one-dimensional flow in a porous medium made up of two homogeneous layers whose interface was perpendicular to the flow direction. The interface condition for which the current solutions were derived implies that the ordering of the layers will affect the breakthrough curve (BTC) at the outlet of the medium. Wu et al. (1997) derived an analytical model for the non-linear adsorptive transport through layered soils ignoring the effects of dispersion. Zhou and Selim (2001) simulated breakthrough results of reactive solutes in a layered soil with an emphasis on a non-linear reactivity with the soil matrix. Physical and chemical properties of each soil layer were assumed to differ significantly from one another. Linear and non-linear equilibrium type, Langmuir-type retention, and nth-order and second-order kinetic adsorption processes were considered as the governing retention mechanisms. The BTCs are similar regardless of the layering arrangement or sequence. This finding is consistent for all reversible and irreversible solute-retention mechanisms considered. Naik et al. (2008) used a reliable method of obtaining BTCs of ions in soils using the transport equation. They obtained the BTCs of sodium in the presence of sulfate ions in different soils and found that effective diffusion coefficient alone cannot account for the entire attenuation or retardation factors. As the retardation of ions increases, the difference between theoretical and experimental curves increases. Liu and Si (2008) developed an analytical model of onedimensional diffusion in layered systems with a positiondependent diffusion coefficient within each layer. The orthogonal expansion technique was used to solve a onedimensional multi-layer diffusion equation in which the diffusion coefficient is expressed as a segmented linear function of positions in the porous media. Although a considerable research was focused on the single layered soil, a critical review of literature does not provide the detailed behavior of the concentration profile for the solute transport through saturated multi-layer soils. Therefore, an attempt is made in this direction using the soil column experiment in the laboratory. Sodium chloride and sodium fluoride chemicals were used as the solute tracer through the soil column. A numerical model was also developed to

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Soil column experiment The experimental set-up consists of a column, made up of an acrylic pipe with a wall thickness of 6 mm, 100 mm diameter, and 600 mm length. The cross-sectional area of pipe was 78?50 cm2. A schematic sketch of the experimental set-up of the soil column is shown in Fig. 1. Sand was collected from Bahadarabad near Haridwar, India. The natural soil and silt were collected from depths of 50 and 150 cm, respectively, below the ground surface in the campus of Indian Institute of Technology, Roorkee, India. The particle-size distribution curves of sand, silt, and natural soil are shown in Fig. 2. Other properties of these soils are reported in Table 1. Different combinations of soil were used in the soil column during the experiment. Dry soil was carefully packed in small increments into column (acrylic pipe) avoiding any soil particle-size segregation. Medium porosity fitted glass end plates were provided as a stable support at each end of the soil column. The column was filled with soil in three layers. While placing layered soils, the soil consisted of 200 mm height for each layer. First, the soil column was saturated by the tap water so that the steady-state water flow condition established. The chemical composition of the tap water is given in Table 2. Then sodium chloride solution (NaCl) with a concentration of 70 mg/l as a tracer is injected into the column as the input for 30 minutes. The porosity of the soil column matrix is estimated to be about 16%. The observed seepage velocity (V) through soil column was 1?2 cm/min. Concentrations of the tracer NaCl during the experiment was measured in the column with a constant time interval. The solute samples were collected at the outlet of the column and concentration were measured by the titration procedure. The soil contains organic and inorganic substances, so before the measurements, the soil column was washed out by water for 2 hours. The prepared solution was introduced into the soil column at a constant flux, keeping the head constant of input solution. The effluent solutions were collected in fractions of each 15 minutes into the collector. Similarly, sodium fluoride chemical was introduced at inlet

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Table 1 Properties of sand, silt, and natural soil Soil

Particle-size distribution/mm

Moisture content/%

Bulk density/g cm23

Permeability/cm min21

Sand Silt Natural soil

88% medium sandz12% fine sand 16% fine sandz84% silt (56% fine sandz38% medium sandz6% fines)

17?36 12?35 16?95

1?86 1?62 1?84

1023 1025 1024

of column. At the end of all miscible displacement experiment, the soil was carefully extruded and the volume of soil water contained in each layer was gravimetrically determined. The effluent solute concentrations were expressed as relative concentrations (C/C0), where C and C0 are solute concentration in an effluent fraction and input pulse, respectively.

Theory and governing equations In case of three-layered soils, the length of each layer is denoted by L1, L2, and L3, respectively. It is assumed that each soil layer had specific, but not necessarily the same water content, bulk density, and solute-retention properties. Only vertical steady-state water flow perpendicular to the soil layers is considered. The governing advective–dispersive transport equation considering equilibrium sorption and first-order degradation constant in the ith layer is given by Selim and Mansell (1976) .   LSi LCi L LCi LCi ri hi Di zhi ~ {q {hi li Ci Lx Lt Lt Lx Lx (1)

For linear case Si ~Kd Ci

and

LSi LCi ~Kd Lt Lt

(2)

Substituting the value of LSi/Lt from equation (2) into equation (1), after simplifying, the following expression can be obtained   ri Kd LCi L2 Ci q LCi ~Di 2 { {li Ci z1 hi Lx hi Lt Lx or LCi L2 Ci LCi (3) ~Di 2 {Vi {li Ci Lt Lx Lx where Ri ~1zrKd =hi , which is known as retardation factor and Vi ~q=hi , which is known as pore water velocity. The initial conditions used are Ri

SI ~SII ~SIII ~0 at t~0

(4a)

CI ~CII ~CIII ~0

(4b)

at t~0

(0ƒxƒLi ,i~1,2,3) where C is the concentration of solute in solution phase (M/L3), S is the amount of solute adsorbed by soil matrix (L3/M), r is the bulk density (M/L3), D is the dispersion coefficient (L2/T), q is the flow rate (L/T), l is a first-order degradation constant (T21), and t is time (T); L, M, and T represent the dimensions of length, mass, and time, respectively. The term LS/Lt on the left side of equation (1) is known as the reversible solute retention from the soil solution.

Table 2 Water quality parameters of tap water Parameters

Magnitude

Caz Ca hardness Mgz Mg hardness Total hardness Naz Kz F2 Cl2 SO422 NO222 NO322 Alkalinity TDS

47 118 17?3 72 190 20?7 2?4 2?05 19?3 16?9 0?09 10?9 215 264

The condition in equation (4) signifies that each soil layer is initially solute free. In this case, both first-type boundary condition (concentration is known) and third-type boundary condition (flux is known) are applicable to represent the inlet boundary. The difference between these two types of boundary condition was discussed by Leij and van Genuchten (1995). In this study, a first-type boundary condition for the soil surface was adopted to satisfy the principle of mass conservation. Therefore, the boundary condition at the soil surface (Layer I) is described as CI ~CII

at x~L1

CII ~CIII

at x~L1 zL2

LCIII ~0 Lx

at x~L, t§0

(5a)

(5b)

The pulse-type concentration condition is Ci (0,t)~C0 Ci (0,t)~0

for t ƒt0

(5c)

for twt0

(5d)

where C0 is the initially injected solute concentration at the inlet of the soil media (M/L3) and t0 is the pulse time (T).

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Development of numerical model It is easy to incorporate flexible boundary conditions in the numerical model as compared to the analytical solution. Hence, an implicit finite-difference numerical technique is used to get the numerical solution of advective–dispersive transport equation including equilibrium sorption and first-order degradation for solute concentration in the solution phase. Finite-difference formulation of equation (3) can be written as ! lz1 lz1 Ciz1 {2Cilz1 zCi{1 Cilz1 {Cil R { ~D Dt (Dx)2 ! lz1 lz1 Ciz1 {Ci{1 V {lCilz1 2Dx 3 Spatial solute concentration profiles predicted at different transport times in two-layered soils and compared between analytical and present numerical models (V15V2510 cm/h and D1540 cm2/h, D255 cm2/h)

(6)

where i represents the number of nodes, l and 1z1 represent the known and unknown time levels, Dx represents the grid size along the travel distance, and Dt represents the time interval.

4 Effect of a column Peclet number and b dispersion coefficient on relative concentration of solute in layered soil. c Effect of retardation factor on temporal relative concentration of layered soil column. d Effect of first-order degradation coefficient on temporal relative concentration profile

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5 Simulation of experimental breakthrough curves (BTCs) of chloride through three-layered soil a natural soilzfine sandzmedium sand, b medium sandzfine sandznatural soil, c siltzfine sandzsilt, and d fine sandzsiltzfine sand using different values of dispersion coefficient

System of linear equations is solved by using Gauss– Siedel iteration method. To reduce the numerical error, we kept the value of Courant number (Cr ~V Dt=Dx) less than or equal to 1. Spatial solute concentration profile for solute transport through two-layered soil column is shown in Fig. 3. The predicted results of concentration profiles are compared between numerical and analytical solution of Leij et al. (1991) for solute transport through layered porous media. Thus, numerical model was verified with the analytical solution.

Breakthrough curves

predicted with different values of column Peclet number as shown in Fig. 4a. It is assumed that the value of dispersion coefficient is equal in each layered soil. Input values of pore velocity, V51?2 cm min21; length of column, L560 cm; value of dispersion coefficient, D536, 7?2, and 1?44 cm2 min21 corresponding to column Peclet number Pe52, 10, and 50, respectively are used during the simulation of temporal concentration profiles. Peak of BTCs increases with an increase in the value of column Peclet number. It means the advection is higher compared to the dispersion. The peak of BTC is small in case of small value of column Peclet number. In this case, the dispersion is dominant in comparison to advection. Column Peclet number can be expressed as

Breakthrough curve represents the plotted graph between time and the measured solute concentration at the outlet of soil column. If the supplied solute source at the inlet has a constant concentration and it remains throughout the experiment, it is known as continuous solute source. If the supplied solute source is for predefined time, it has a finite pulse source. If the duration of time of the finite source is very small, it is known as instantaneous pulse source. In this section, we predicted temporal concentration profiles for different values of column Peclet number, retardation factor, dispersion coefficient, and first-order degradation coefficient. Temporal relative concentration has been

VL (7) D where Pe represents the column Peclet number, V represents the actual velocity, L represents the length of soil column, and D represents the dispersion coefficient. Breakthrough curves have been predicted with different values of dispersion coefficient as shown in Fig. 4b. If soil column has different soil layers, then the value of dispersion coefficient will be different in each soil layer. Here three different layered soil column systems are considered having different dispersion coefficients, i.e. D1,

Results and discussion

Pe ~

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6 a Simulation of experimental BTCs of fluoride through three-layered soil a natural soilzfine sandzmedium sand, b medium sandzfine sandznatural soil, c siltzfine sandzsilt, and d fine sandzsiltzfine sand using different values of retardation factor

D2, and D3, respectively. The results show that the behavior of BTC is affected because of change in the value of dispersion coefficient in the layered soil. Retardation factor represents the ratio of groundwater velocity to the contaminant velocity. For reactive solute, the peak of temporal relative concentration of solute decreases because of an increase in the value of retardation factor and retards the plume. It means it takes more time to reach at the desired location in the flow direction. It is also known that different soil has different sorption capacity of the solute. Hence, the value of retardation factor will be different for different soil as shown in Fig. 4c. Fig. 4d represents the BTCs with different values of first-order degradation coefficients. It is assumed that each soil layer has the same value of degradation coefficient. However, a higher value of degradation coefficient leads to reduce the peak of BTCs.

Simulation of experimental BTCs of chloride In this section, numerical model is used to simulate the observed experimental BTCs of chloride through threelayered soil column experiment. Experimental BTCs and simulated numerical results are discussed for chloride

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tracer through different orders of layered soil. Fig. 5a–d represents the experimental BTCs and simulated results for solute transport in three-layered soil system. It is known that the range of dispersion coefficient for individual layer soil, which is obtained from the simulation of experimental data using numerical model, depends on the type of soil. Hence for the layered soil system, different combinations of dispersion coefficient are used for the simulation of observed experimental BTC. For threelayered soil system (natural soilzfine sandzmedium sand), the values of dispersive coefficients D152?50, D251?25, and D351?00 cm2/min were used (Fig. 5a). The combination of natural soilzfine sandzmedium sand indicates that the first layer of soil in column is natural soil, second layer is fine sand, and third layer is medium sand. Similarly for soil system (medium sandzfine sandznatural soil), the value of dispersion coefficients D151, D251?25, and D352?50 cm2/min (Fig. 5b); for the (siltzfine sandzsilt) soil system, the value of dispersive coefficients D154?00, D252?80, and D354?00 cm2/min (Fig. 5c); and for the (fine sandzsiltzfine sand) soil system, the value of dispersive coefficient D152?80, D254?00, and D352?80 cm2/min (Fig. 5d) are obtained

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from the numerical simulation of experimental data. These simulated results are good fitted with experimental data of chloride through layered soil. It is observed that the behavior of BTCs remain the same, when the order of layer soil is changed. It is also seen that the higher value of dispersion coefficient leads to early arrival of the BTC and the peak of BTC is reduced.

water and solute characteristics, the order of soil layering does not affect the effluent concentration distributions. The developed numerical model can be used for simulating the migration of contaminants through the landfill sites/ subsurface porous media.

Simulation of experimental BTCs of fluoride

This work was supported by the Department of Science and Technology New Delhi under research grant number DST-456-CED.

In this section, experimental BTCs of fluoride are simulated using numerical model. Fig. 6a–d represents the BTCs of fluoride through three-layered soil system, i.e. (natural soilzfine sandzmedium sand). The parameters dispersion coefficients D152?5, D251?25, and D351 cm2/ min, pore velocity V51?20 cm/min, and retardation factor R51, 1?1, 1?2 were used during simulation of experimental BTCs of fluoride through layered soil system (Fig. 6a). It is known that fluoride is a reactive chemical; hence while transporting through the soil media, some amount of fluoride is adsorbed through soil. Therefore, different values of retardation factor were used to simulate the experimental BTCs. It is seen that higher value of retardation factor leads to reduce the peak of BTC and retards the solute plume. It was seen that excellent agreement was obtained between observed experimental data and numerical simulated results with the value of retardation factor R51?1. Similarly, Fig. 6b–d represents the BTCs of fluoride through layered soil having different combinations of soil media in the column experiment. Different simulations were conducted to see the effect of layered system and sorption characteristics on the shape of experimental BTCs. The estimated value of retardation factor through simulation is very small; it indicates that sorption between liquid and solid has not reached in the equilibrium condition because of small transport time during experiment. The results of experimental BTCs indicate that the distribution of effluent concentration was not affected because of layered soil.

Conclusion Experimental and numerical results of BTCs have been presented for conservative and non-conservative solute transport in the multi-layered soil. Numerical implicit finite-difference method was used to get the solution of advective–dispersive transport equation for solute transport through multi-layered soil. The experimental BTCs of chloride and fluoride chemical through three-layered soil column have been simulated well by using the numerical model. Higher values of retardation factor and first-order degradation coefficient lead to reduce the magnitude of solute concentration. However, with a change in the value of transport parameters in the layered soil, the behavior of BTCs remains the same. The results show that for a watersaturated multi-layered soil column regardless of soil

Acknowledgment

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