### 1. Introduction

^{238}, U

^{235}and U

^{234}in the environment. After World War II, uranium was mined extensively for production of nuclear weapons and later for nuclear power plants to produce energy [1]. In India, 2.7% of the total electrical energy is produced from nuclear power plants [2]. Uranium element is extracted from uranium ore and the uranium ore residues are deposited in ponds. These ponds are referred as uranium tailing ponds, which contains the radioactive decay products of uranium and heavy metals [3, 4]. The major radiation risk for living organism from uranium tailings are exposure to gamma radiation, windblown radioactive dust dispersion and radon gas and its progenies [2]. The major environmental impacts of uranium tailings are failure of tailing dams, exposure to radiation, surface and groundwater contamination due to leakage of radioactive and other toxic elements [3–5]. There are many studies executed earlier to treat various contaminants from water at various levels. Mercury sorption experiment has been performed by silica/carbon nanotubes and silica/activated carbon [6]. Various types of water treatment and recycling techniques have been discussed in terms of their basic principles, applications, costs, maintenance and suitability [7]. Saleh et al. [8] carried out a study on preparation and investigation of a multifunctional material that can be used in wastewater treatment for removal of arsenic. Further, Saleh [9] used Nanocomposite of carbon nanotubes/silica nanoparticles for adsorption of Pb(II). The activated carbon developed from waste rubber tires is identified as an efficient material for removal of Chromium from wastewater [10]. The experimental results demonstrate that the combining of silica and nanotubes is a promising alternative material, which can be used to remove the mercury from wastewaters [11]. Later, Zare et al. [12] conducted kinetic and thermodynamic studies for the efficient removal of radioactive uranium from solvent phase using nanoparticles, which exhibited excellent thermal stability and large surface area. Tawfik et al. [13] used poly-ethyleneimine modified activated carbon/Fe as an effective magnetic adsorbent to remove uranium ions from aqueous solution as a function of batch adsorption parameters; and it was concluded that the PAF magnetic sorbent could be considered as a promising and effective adsorbent for the purification of wastewaters from uranium ions. However, understanding the processes involved on the migration of radionuclide from uranium tailing pond to sub-surface is a necessary prerequisite for forecasting the long-term performance and prediction of groundwater quality.

^{90}in the unsaturated Chinese loess under artificial rain conditions. Merk [24] studied the radionuclide transport from the concrete rubble when the radionuclide dissolves in the infiltrated water using HYDRUS-1D. Sanchez and Thorne [25] presented a mathematical model to study the behavior of U

^{238}series radionuclide entering soils in solution and their uptake by plants along with the decay chain of uranium in soil-plant system under different hydrological regimes. Nair et al. [26] developed a multi-compartmental source term model to assess the radionuclide leaching in a saturated or unsaturated porous medium such as a uranium tailing ponds.

^{238}U decay series after the uranium extraction from ore [22]. The

^{238}U decay chain contains four long-lived radionuclide (

^{238}U,

^{234}U,

^{230}Th,

^{226}Ra); five short-lived nuclides (

^{234}Th,

^{222}Rn,

^{210}Pb,

^{210}Bi,

^{210}Po); and five very short-lived nuclides (

^{234m}Pa,

^{218}Po,

^{214}Pb,

^{214}Bi,

^{214}Po). On the other hand,

^{222}Rn can escape from the ore and other short-lived progenies may decay to innocuous levels during the ore extraction processes. Thus, primarily uranium tailing ponds consists of long-lived radionuclide of

^{238}U,

^{234}U,

^{230}Th,

^{226}Ra. Subsequently, ingrowths of progenies will happen in the tailing ponds as well as in the percolated water.

^{238}U nuclide transport in unsaturated porous medium has not been analyzed extensively. Since, the uranium tailing ponds are located in the soil surface a suitable numerical model has to be developed for vertical transport of multi-species radionuclide incorporating the nonlinear soil hydraulic parameters under unsaturated condition. Hence, the motivation of the present work is to develop a one-dimensional decay chain transport model to predict the concentration of radionuclide from uranium tailing pond due to vertical leaching under unsaturated condition. Further, the developed model is extended to evaluate the transport of radionuclide in different soils which are generally available beneath the uranium tailing pond.

### 2. Physical System and Governing Equations

##### (1)

$$C(h)\frac{\partial h}{\partial t}=\frac{\partial}{\partial z}K\left(\frac{\partial h}{\partial z}\right)-\frac{\partial K}{\partial z}$$*θ*

*is the volumetric water content (cm*

_{w}^{3}/cm

^{3});

*h*is the pressure head (cm);

*K*is the unsaturated hydraulic conductivity (cm/s);

*t*is the time (s);

*z*is the vertical coordinate (cm) positive downward.

*θ*

*is generally smaller than the porosity. The water pathway modeling in unsaturated porous system is considerably complicated as compared with saturated porous system. The water content (*

_{w}*θ*

*), pressure head (h) and hydraulic conductivity (K) are highly correlated in the unsaturated case. The hydraulic conductivity in unsaturated porous medium is not only depends on the matrix material but also on the local pressure head [24]. Widely acknowledged empirical relationships were arrived by van Genuchten [41] and described in Eq. (2) and (3).*

_{w}##### (2)

$$K(h)={K}_{s}{\left[\frac{{\theta}_{w}-{\theta}_{r}}{{\theta}_{s}-{\theta}_{r}}\right]}^{1/2}\hspace{0.17em}{\left[1-{\left(1-{\left[\frac{{\theta}_{w}-{\theta}_{r}}{{\theta}_{s}-{\theta}_{r}}\right]}^{1/\eta}\right)}^{\eta}\right]}^{2}$$##### (3)

$${\theta}_{w}={\theta}_{r}+({\theta}_{s}-{\theta}_{r})\hspace{0.17em}{[1+{(\alpha |h|)}^{\beta}]}^{-\eta}$$*η*is an empirical constant affecting the shape of the retention curve,

*θ*

*is the saturated water content,*

_{s}*θ*

*is the and residual water content,*

_{r}*α*and

*β*are both empirical constants.

##### (4)

$${R}_{1}\frac{\partial {N}_{1}}{\partial t}=\frac{\partial}{\partial z}\left(D\frac{\partial {N}_{1}}{\partial z}\right)-v\frac{\partial {N}_{1}}{\partial z}-{R}_{1}{\lambda}_{1}{N}_{1}$$*N*

*is the concentration of the parent radionuclide in the aqueous phase (atoms L*

_{1}^{−3}or mol);

*D*is the hydrodynamic dispersion coefficient (L

^{2}T

^{−1}) (

*D = α*

_{L}*×v*);

*α*

*is the longitudinal dispersivity (L) can be produced by different pore sizes along the flow paths and/or by tortuosity;*

_{L}*v*is the pore water velocity (L/T) can be obtained by dividing the Darcy velocity by the effective porosity (which is expressed as

*v = q/θ*

*);*

_{w}*q*is obtained from Darcy’s law $q=-K\left[\frac{\partial (h-z)}{\partial z}\right]$;

*λ*

_{1}is the radioactive decay constant (T

^{−1}).

*i*

^{th}member of the decay chain can be written [22] as given in Eq. (5):

##### (5)

$${R}_{i}\frac{\partial {N}_{i}}{\partial t}=\frac{\partial}{\partial z}\left(D\frac{\partial {N}_{i}}{\partial z}\right)-v\frac{\partial {N}_{i}}{\partial z}-{R}_{i}{\lambda}_{i}{N}_{i}+{R}_{i-1}{\lambda}_{i-1}{N}_{i-1}$$*i*> 1 to

*M*;

*M*is the number of total nuclides involved in the decay chain. The ingrowth of the progenies from the previous parent radionuclide is included in the last term of Eq. (5). The sorption of radionuclides is described by linear and reversible. Hence, the retardation factor (

*R*

*) of the radionuclide ‘*

_{i}*i*’, which can be expressed in Eq. (6):

*k*

*is the distribution coefficient of radionuclide ‘*

_{di}*i*’ (L

^{3}M

^{−1});

*ρ*

*is the bulk density of the porous material (M L*

_{b}^{−3}). Fig. 2 illustrates the schematic representation of solving water flow and transport of radionuclides in an unsaturated porous medium.

### 2.1. Initial and Boundary Conditions

^{238}U and

^{234}U in the tailing pond is 0.129 Bq/L [2] considered as top boundary and all other radionuclides concentration in the tailing pond is assumed as zero. The concentration gradient for all radionuclide is assumed to be at zero for the bottom boundary condition. The graphical representation of boundary conditions for one-dimensional domain is shown in Fig. 3.

### 2.2. Numerical Scheme

##### (7)

$$\frac{{h}_{n}^{j+1}-{h}_{n}^{j}}{\mathrm{\Delta}t}=\frac{{k}_{n-(1/2)}^{j}\left(\frac{\mathrm{\Delta}{h}_{n-(1/2)}^{j+1}}{\mathrm{\Delta}z}+1\right)-{k}_{n+(1/2)}^{j}\left(\frac{\mathrm{\Delta}{h}_{n+(1/2)}^{j+1}}{\mathrm{\Delta}z}+1\right)}{{c}_{n}^{j}\mathrm{\Delta}z}$$*n*’ is the node number and superscript ‘

*j*’ is the time level.

### 2.3. Verification of the Model

### 3. Results and Discussion

^{238}U after 1, 10 and 50 d in the unsaturated subsurface system in the presence and absence of sorption process. It is observed that the volumetric water content profile abruptly reduced from 0.207 (cm

^{3}/cm

^{3}) to nearly 0.1 (cm

^{3}/cm

^{3}) within the shallow depth (up to 50 cm) in one day. However, the water content profile remains constant up to 350 cm and 1,450 cm for 10 d and 50 d, respectively, i.e., the unsaturated system up to these depths continuously receives water and further reduces to the low water content (0.1 cm

^{3}/cm

^{3}). Further, it is observed from Fig. 5 that the movement of

^{238}U seems similar to the profile of water content after one day in the absence of sorption process. The concentration of

^{238}U starts at 0.129 Bq/L from the soil surface (uranium tailing pond) and is reduced to zero at 40 cm depth after 1 d. Conversely, significant delay is observed in

^{238}U concentration profile (250 cm depth after 10 d and 900 cm depth after 50 d) as compared with the corresponding water content profile (350 cm depth after 10 d and 1,450 cm depth after 50 d). Additionally, the results of simulation indicate that there is strong delay in movement of

^{238}U in the presence of sorption. This is because of the distribution capacity of

^{238}U on soil particles (5.00 × 10

^{−4}L/mg) which hold huge amount of

^{238}U concentration as solid phase, which retard the movement

^{238}U in the aqueous phase. Due to the sorption process the concentration of

^{238}U becomes zero form 0.129 Bq/L from its source at 1.5, 2.5 and 5 cm depth after 1, 10 and 50 d, respectively. A closer observation between the presence and absence of sorption process implies that there is approximately 99% reduction in depth of penetration on

^{238}U concentration with the sorption process. It can be concluded from Fig. 5 that the water content variation in the unsaturated soil is directly affecting the movement of

^{238}U concentration. The presence of sorption leads to retard the movement of

^{238}U concentration, which actually aids to minimize the

^{238}U concentration in the deeper zone.

^{238}U transport in unsaturated soil in the presence and absence of sorption process for 10 d. The water content starts at 0.17 m

^{3}/m

^{3}from the soil surface and gradually reduced to 0.1 m

^{3}/m

^{3}at the depth of approximately 100 cm for the infiltration rate of 1 m/y with the saturated hydraulic conductivity of 2,907 m/y. Moreover, it can be observed from Fig. 6 that the water contents at the soil surface are 0.17, 0.207 and 0.22 m

^{3}/m

^{3}when the infiltration rates are 1, 10 and 20 m/y, respectively. The higher infiltration rate eventually attempts the water content to move deeper in the unsaturated porous media. For example, as the infiltration velocity increases (10 m/y and 20 m/y), a relatively large amount of water content is retained in the soil surface (0.207 m

^{3}/m

^{3}), and subsequently the depth of movement of water content is also increased (maximum water content is observed up to the depth of 250 cm and 500 cm for the infiltration rate of 10 m/y and 20 m/y, respectively). Further, the results show that the concentration of

^{238}U is reduced from 0.129 Bq/L at the soil surface to zero at the depth of 75 cm, 250 cm and 400 cm for the infiltration rate of 1, 10 and 20 m/y in the absence of sorption process. This shows the typical water content variation in the unsaturated soil is influencing the transport of

^{238}U and the variation in infiltration is also impacting the depth of penetration. The similar trent is also observed for

^{238}U transport in the presence of sorption process with considerable delay. This delay can be explained by the retradation induced by the solid phase of

^{238}U during the sorption phenomina. It can be concluded from Fig. 6 that, the behavior of variation in the water content distributions during various infiltration rates is significantly affecting the movement of

^{238}U in the unsaturated sub-surface system.

^{238}U and its progenies in the absence of sorption process in the unsaturated sandy soil with the assumed infiltration rate of 10 m/y during 1, 5 and 10 y. It is observed from Fig. 7 that there is a maximum concentration (0.129 Bq/L) observed for

^{238}U and

^{234}U at the soil surface (uranium tailing pond) and it is further reduced to zero concentration as the depth increases. Conversely, all other progenies initially start from very low concentration (nearly 0 Bq/L) at the soil surface and gradually increase to their corresponding peak concentration with depth and finally become zero concentration followed by its asymptoticity. The order of peak concentrations is observed such as

^{238}U =

^{234}U >

^{230}Th >

^{226}Ra >

^{234}Th >

^{210}Pb >

^{210}Bi >

^{222}Rn >

^{210}Po. As soon as the concentration of

^{238}U is available, the decay starts, gets converted into

^{234}Th, and subsequently into

^{234}U concentration. As

^{234}U is abundantly available from the source at the soil surface; its concentration profile is similar to

^{238}U. Further, the decay of

^{234}U produces the remaining progenies in the decay chain reaction. The lowest

^{210}Po concentration is due to the last product in the decay chain and relatively its own high decay rate (1.83 y

^{−1}). It is keenly observed from Fig. 7 that, the second lowest peak concentration of

^{222}Rn due to the highest decay rate (6.6 × 10

^{1}y

^{−1}) among all the uranium progenies in the uranium decay chain reaction. All the results present in Fig. 5 are independent of sorption process and the variations in the concentrations are observed only based on the respective decay rate. It is further observed that all the

^{238}U and its progenies are available up to the depth of 800 m after 10 y and dangerous for the deeper zone in the unsaturated sandy soil. Thus it can be concluded from Fig. 7 that the concentration of

^{238}U and

^{234}U are continuously arrived the deeper depth from the soil surface (uranium tailing pond) for longer time interval and an enhanced peak concentrations are observed at a various depths (50, 250 and 550 m) at various time interval (1, 5 and 10 y) for all other

^{238}U progenies except

^{234}Th concentration.

^{238}U and its progenies during various intervals in the presence of sorption process in unsaturated sandy soil has been illustrated in Fig. 8. Since the sorption process of all the

^{238}U and its progenies is considered in this simulation, a significant delay in movement and the reduction in peak are observed in all

^{238}U and its progenies concentration. It is observed that there are approximately one to two order of magnitude reductions in peaks for all species except

^{238}U and

^{234}U from Fig. 7 and 8 at 10 y. This peak reduction is due to the consideration of sorption process. Moreover, the maximum concentration of

^{238}U and

^{234}U in the soil surface is also abruptly reduced when depth increases, but which is moving long depth in the case of absence of sorption process. It is further observed that the peak concentration of

^{222}Rn is also reduced to one order even though the distribution coefficient is zero as compared to all other species. This reduction happens due to the distribution coefficients of the previous species which reduce its corresponding concentration in the aqueous phase of the decay chain and in turn, lead to the considerable reduction in peak

^{222}Rn concentration. Essentially, the sorption process hinders the movement of all the species in the aqueous phase due to its corresponding distribution coefficient which helps to attract the species from the aqueous phase to the solid phase. The order of peak concentrations in the sorption process is similar as the absence of sorption process such as

^{238}U =

^{234}U >

^{230}Th >

^{226}Ra >

^{234}Th >

^{210}Pb >

^{210}Bi >

^{222}Rn >

^{210}Po except the order of reduction in peak concentration for

^{238}U and its progenies. Further, it is observed from Fig. 8 that the concentration is virtually negligible after 1 y and 5 y as compared with 10 y. Moreover, the depth of penetration of

^{238}U and its progenies is reduced to less than 10 m and the peak is observed at nearly 2 m depth due to the presence of sorption process, whereas the

^{238}U and its progenies move up to 800 m and the peak is observed at nearly 550 m depth when the sorption process is not considered after 10 y. Since, the half-lives of the parent radionuclides are very long [22], it is great possibility that the concentration of

^{238}U and its progenies can move in deeper depth even though the sorption process is considered.

^{238}U and its progenies in the absence of sorption process in the unsaturated silty soil with the assumed infiltration rate of 3 m/y during 1, 5 and 10 y. The water content is varied from 0.438 m

^{3}/m

^{3}at the soil surface and gradually reduced to 0.099 m

^{3}/m

^{3}at the depth of approximately 12 m, 50 m and 100 m (not shown in the Fig. 9) for the infiltration rate of 3 m/y with the saturated hydraulic conductivity of 22 m/y after 1, 5 and 10 y, respectively. It can be noted that the concentration of

^{238}U and

^{234}U is following similar trend with maximum inflow concentration of 0.129 Bq/L at the soil surface and reducing to zero at 10, 45 and 90 m depth after 1, 5 and 10 y, respectively. As compared with the sandy soil (Fig. 7) the concentration movement with respect to the depth is significantly reduced in the silty soil, i.e., the concentration of

^{238}U and its progenies are become zero at the depth of 100, 450 and 800 m in the sandy soil whereas it is reduced to 10, 45 and 90 m in the silty soil (approximately 90% reduction in movement). Similarly, the peak concentrations are also observed in the shallow depths in the silty soil as compared with sandy soil (For example, the peak concentration of

^{230}Th is 50 m in the silty soil and 550 m in the sandy soil for 10 y). This reduction in movement in silty soil is primarily due to the decrease of two orders in hydraulic conductivity and other changes in soil hydraulic parameters such as water content, pressure head and van Genuchten parameters (Table 3) as compared with the sandy soil. However, the order of peak concentrations is relatively similar which is observed in the sandy soil such as

^{238}U =

^{234}U >

^{230}Th >

^{226}Ra >

^{234}Th >

^{210}Pb >

^{210}Bi >

^{222}Rn >

^{210}Po. Further, it is keenly observed that the maximum concentration of

^{238}U and

^{234}U are reducing with respect to depth in the silty soil, while the same (maximum) concentrations are observed for larger depths in sandy the soil (Fig. 7). For instance, the concentration of

^{238}U and

^{234}U are constant up to the depth of 250 and 550 m and slowly becoming zero in the sandy soil (Fig. 7), whereas the maximum concentration starts declining immediately just below the soil surface (uranium tailing pond as source) in the silty soil (Fig. 9) due to its corresponding soil hydraulic properties. Thus, it can be concluded from Fig. 9 that the

^{238}U and its progenies in the absence of sorption process in the unsaturated silty soil is significantly reduced its depth of movement predominantly due to the reduced unsaturated hydraulic conductivity and other soil hydraulic parameters such as water content, pressure head and van Genuchten parameters, which in turn, the enhance availability of

^{238}U and its progenies are in the shallow depths. However, the concentration of

^{238}U and its progenies are speared up to 90 m depth after 10 y, which shows that the groundwater aquifers may get affected if the water table is shallow.

^{238}U and its progenies in the presence of sorption process in the unsaturated silty soil. The

^{238}U and

^{234}U concentrations are released from the uranium tailing pond at the soil surface which have higher concentration (0.129 Bq/L) and become zero at 1 m after 1 y but very marginal downward movement is observed after 5 and 10 years. Similarly, other progenies of

^{238}U are also shown a low depth of transport in the unsaturated silty soil. This significant retardation in movement on

^{238}U and its progenies is predominantly happened by the sorption process of all the uranium species and the low hydraulic conductivity of soil. Approximately 90% reduction in the depth of penetration is observed in the sorption process when compared Fig. 10 with 9; (zero concentration is observed nearly at 1, 3 and 5 m in the presence of sorption process and 10, 45 and 90 m in the absence of sorption process after 1, 5 and 10 y); on the other hand almost 99% reduction in depth of penetration is observed in silty soil (Fig. 10) as compared with the sandy soil (Fig. 8) in the presence of sorption process (i.e., zero concentration is observed nearly at 1, 3 and 5 m in the silty soil and 100, 450 and 800 m in the in sandy soil with the sorption process after 1, 5 and 10 y). Moreover, it is observed from Fig. 9 and 10 that the peak concentration of all the uranium species except

^{238}U and

^{234}U are reduced nearly one order in the presence of sorption process as compared with the absence of sorption phenomena. It can be concluded from Fig. 10 that the concentration of

^{238}U and its progenies vanish at very shallow depths (approximately before 10 m) and offer a positive impact to stop the groundwater contamination.

### 4. Conclusions

^{238}U and its progenies in the vadose zone from uranium tiling pond situated on the soil surface. The one-dimensional coupled water flow and

^{238}U and its progenies decay chain reaction is developed using implicit finite difference scheme. In addition, this study is also extended to perform the movement of

^{238}U and its progenies concentration in different soils such as sand and silt. From the developed model, the following conclusions are arrived:

The vertical downward transport of

^{238}U and its progenies from uranium tailing pond at soil surface is highly dependent on the water content variation in the unsaturated soil and its other soil hydraulic properties such as unsaturated hydraulic conductivity, pressure head and van Genuchten parameters.The downward movement of

^{238}U and its progenies from the uranium tailing pond results in higher concentrations at the shallow depth irrespective of sorption process in the silty soil, whereas considerable increase in concentrations is observed at the deeper depth in the sandy soil. This is due to the high hydraulic conductivity accompanied by the increase in other soil hydraulic properties which yield a larger depth of movement in the sandy soil as compared with the silty soil.While, silt transmit a relatively lesser uranium concentration down the ground surface, the sand or alluvium transport a relatively larger fraction of uranium vertically downwards and hence, it is more likely that this particular geological unit has more probability of potentially contaminating the saturated groundwater system. On the contrary, with reference to root zone uptake, it is the silty formations that retain the uranium in a relatively larger amount and subsequently contaminate the root zone in the unsaturated zone. Further, sorption plays a vital role in deciding the resultant retardation, and in turn, the total migration pathway. Thus, a coupled effect of sorption and a given geological unit decide the resultant uranium transport in a given subsurface environment.