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This paper presented the first part of the studies about the development of a tool for groundwater contamination prediction, conducted by the Laboratory of Sciences and Technology of Water (UAC/Benin). The investigation made consisted in estimating the combined effect of retardation factor and biodegradation on migration processes of leachate, in the underlying soils of household waste dumpsites, without active safety barrier. Leachate infiltration tests for different initial conditions were made on soil columns and the breakthrough curves were traced for electrical conductivity, the 5 day biochemical oxygen demand (BOD
_{5}) and total kjeldahl nitrogen TKN. A mathematical migration model was developed and solved numerically by finite difference method and implemented with Matlab R2013a. Thus, the calibration of the model was made with electric conductivity data by determining the dispersion coefficient of the studied soils (
*D* = 0.96 cm
^{2}/min). Simulations for model verification showed that the established model can perfectly predict the migration of biodegradable organic pollution (BOD
_{5}) but did not give conclusive results for the monitoring of nitrogenous organic matter (TKN). The influence of the retardation factor on the migration of biodegradable organic pollutants in soils was linear, while the biodegradation rate of the organic material on migration showed an exponential pattern.

The migration of solutes in a porous medium is usually controlled by three mechanisms: Convection, molecular diffusion and mechanical dispersion [

Major phenomena or reactions encountered during migration of leachates in soil, include: Solubilisation at acidic pH and the precipitation at a basic pH [

In this paper, a risk assessment tool was developed based on a model coupling the convection-dispersion to the biodegradation of organic pollutants during leachate migration processes in soils for the prediction of groundwater contamination in the context of developing countries.

Generally, the change in concentration of a passive pollutant A between two points of a soil column is considered as a one-dimensional transport problem, which is simultaneously subjected to the phenomena of convection and dispersion [

∂ c A ∂ t = D z ∂ 2 c A ∂ z 2 − q z ∂ c A ∂ z + S ( c A ) (2.1)

where: c A is the concentration of the pollutant A ( M ⋅ L − 3 ) , D z is the overall coefficient of diffusion-dispersion ( L 2 ⋅ T − 1 ) , is the Darcy velocity, ( L ⋅ T − 1 ) , z and t are the spatial (L) and time (T) variables, and S ( c A ) describes the set of reactions and contributions that take place in the porous medium ( M ⋅ L − 3 ) also called source.

Notice that: c A = c A p + c A s ; with:

∂ c A p ∂ t = ε ∂ c A ∂ t , change in concentration of A in the soil void; (2.2)

∂ c A s ∂ t = ( 1 − ε ) ∗ ρ s ∗ K d ∂ c A ∂ t , change in concentration of A at soil grain surface.(2.3)

where ε is the porosity of the soil expressed in %, ρ s is the density of the solid matrix ( M ⋅ L − 3 ) , and K d is the exchange capacity between the fluid and the solid matrix.

Assuming that the major reaction taking place in the porous medium is a first- order biodegradation reaction of organic matter by oxidation of organic compounds. The source term of (2.1) is written as follows: S ( c A ) = ∂ c A ∂ t = − λ D ⋅ c A

[

∂ c A ∂ t = D z ε R ∂ 2 c A ∂ z 2 − v z ε R ∂ c A ∂ z − λ D ε R ⋅ c A ; with R = 1 + ( 1 − ε ) ε ∗ ρ s ∗ K d (2.4)

where R is the retardation coefficient reflecting the slowing of studied pollutant; it depends on the affinity that has the pollutant to the solid matrix.

The Darcy velocity in Equation (2.4) assumes that the pollutant transport takes place in an empty column. However, the column is filled with a soil of porosity. Therefore, the Darcy velocity is replaced with the interstitial velocity: u z = q z / ε , and then the effective dispersion coefficient appears and is expressed as: D = D z / ε .

For solute transfer in soil, the diffusivity is usually smaller than the dispersion [

the axial dispersion [

of a dissolved biodegradable organic substance in the granular porous medium is expressed by:

∂ c A ∂ t = D R ∂ 2 c A ∂ z 2 − u z R ∂ c A ∂ z − λ ⋅ c A (2.5)

Equation (2.5) expresses the coupling “biodegradation - convection dispersion”, taking place during the migration of soluble contaminants in soil. The finite difference method or the finite volume solves this equation.

Model calibration and verification often require some selected initial values and certain key parameter values. In this study, experimental tests of injections of leachate on soil column were performed according to the protocol for measuring the axial dispersion [

The columns of sampled soils were monolithic type. Identification of soil sampling location was made according to ISO 15175:2004 standard, applied to all dumpsites of the municipality of Abomey-Calavi in Benin. The studied soil is a loamy soil. The geotechnical characteristics of the soil of the samples are shown in

The characteristics of the leachate used for infiltration tests are presented in _{5} and TKN were measured. These data were used to trace the breakthrough curves of these parameters. The biodegradation rate of dissolved organic carbon was determined according to the method presented in [^{−1}.

The discretization of Equation (2.5) was made here by the finite difference method on uniform mesh. Consider that along a vertical soil column with sufficiently large length L, a liquid with initial concentration C 0 flows with interstitial velocity u z . At a moment t 0 , a pollutant of concentration C is injected at the upper end of the column and migrates in the axial direction towards the lower end. It is convenient to define the appropriate boundary conditions (Dirichlet conditions here):

Porosity | Macro-pores | Permeability. k (m/s) | Hydraulic Grad. I | Darcy Velocity (m/s) | Interstitial Velocity (m/s) |
---|---|---|---|---|---|

27.5% | 21% | 2.36E−06 | 8.8 | 2.08E−06 | 7.55E−06 |

ASTM D4404-10 | ISO 17312:2005 |

Parameters | Unit | Max | Min | Mean | SD | Precision | Methods standard |
---|---|---|---|---|---|---|---|

pH | 4.09 | 3.84 | 3.93 | 0.14 | ±0.001 | ISO 10523:2008 | |

Elec. Cond. | (µS/cm) | 3812 | 3361 | 3554 | 232 | ±1 | ISO 7888:1985 |

COD | (mg O^{2}/l) | 14,086 | 12,017 | 13,218 | 1074 | ±1 | ASTM D1252 |

BOD_{5} | (mg O^{2}/l) | 6301 | 5326 | 5822 | 488 | ±1 | NFT 90-103 |

TKN | (mg/l) | 21 | 16 | 18 | 3 | ±1 | ASTM D3590 ? 11 |

C ( 0 , t ) = C ; C ( ∞ , t ) = C 0 ; C ( z , 0 ) = C 0 . (3.2)

The differentiation schemes used are:

{ ( ∂ C ∂ t ) i j = C i j + 1 − C i j Δ t ( ∂ 2 C ∂ z 2 ) i j = C i + 1 j − 2 C i j + C i − 1 j Δ z 2 ( ∂ C ∂ z ) i j = C i + 1 j − C i − 1 j 2 Δ z (3.3)

where: L is divided into N intervals with ends or nodes z i , i ranges from 1 to N + 1; C i j is the concentration at the node z i = i Δ z at t = j Δ t . Thus Equation (2.5) is equivalent to the set of:

C i j + 1 = ( α + β ) C i − 1 j + ( 1 − 2 α − γ ) C i j + ( α − β ) C i + 1 j with { α = D Δ t R Δ z 2 β = u z Δ t 2 R Δ z γ = λ Δ t (3.4)

i ranges from 1 to N − 1.

The system (3.4) has been implemented by the successive over-relaxation method. The calculations were performed with Matlab R2013a. The initial values were: length of the column (𝐿), time of simulation (𝑇), space step (∆z), time step (∆𝑡), flow velocity ( u z ), retardation factor (𝑅), initial concentration (C) and a starting value for axial dispersion coefficient (D).

The retardation factor R of the pollutant over a water molecule is defined by the quotient of the residence time of the pollutant ( t s ) over the residence time of the water molecule [

R = t s L θ ⋅ v z

where: L is the length of the column; θ is water content in the column and v z the Darcy velocity in column input [

^{2}/min [

To quantify the model’s prediction, the Relative Root-mean-square Error (RRE) was used to compare simulated versus observed values, with the best fitting simulation returning the lowest RRE.

The dispersion coefficient obtained after model calibration was used as input for the verification of the model (

The measured data were separated into two subsets: one subset for model calibration and another subset for model validation. 48 infiltration tests were carried out on soil columns A of 30 cm length. The subset for the model calibration encompassed the electrical conductivity (EC) data of the columns A. The simulated parameters for model verification include BOD_{5} and TKN, registered at the outlet of columns A.

The influence of the hydraulic gradient on the leachate infiltration rate was

shown in

Note that for a hydraulic gradient of 8.8, the actual infiltration rate measured when characterizing the soil ( 7.55 × 10 − 4 cm / s ) was close to the one obtained experimentally ( 8.07 × 10 − 4 cm / s ). Thus, the rate of flow of leachate in soils for subsequent simulations was taken as 8 × 10 − 4 cm / s .

The time of simulation was computed to simulate one-month leachate migration during the rainy season. A time step of 1 second (s) was used throughout the simulations. The simulated Breakthrough curves and the experimentally-derived breakthrough curve for model calibration are shown in

Simulations | Sim1 D = 0.048 | Sim2 D = 0.48 | Sim3 D = 0.96 | Sim4 D = 1.2 | Sim5 D = 1.28 |
---|---|---|---|---|---|

RRE (in %) | 40.96 | 17.78 | 11.22 | 11.45 | 11.67 |

A comparison of model results to measured data, illustrated by RRE (

For the model verification, a longer time step was selected. This time was calculated to correspond to a simulation of the amount of leachate produced during the long rainy season (from March to June) in southern Benin. The verification process involves running the model with the calibrated dispersion coefficient D = 0.96 cm 2 / min and comparing the results to the independent data set for model verification.

In the numerical simulation of BOD_{5} migration, the biodegradation rate of the studied leachate was considered, which is 0.000037 d^{−1}. This value was taken equal to zero upon insertion of input parameters for the model calibration with the electrical conductivity.

As in the case of electrical conductivity data for model calibration, a bearing was clearly observed on the measured BOD_{5} data for model verification between 660 and 990 min. The end result for BOD_{5} simulation (4197 mg O_{2}/l) was less than measured outcome (4914 mg O_{2}/l), with a simulation result correction of 21% again approximating the experimental result. The calibrated dispersion coefficient (D) adequately modelled the diffusion of organic pollution for the studied soil. The verification of the migration model for the transport of organic matter in soil (BOD_{5}) gave satisfactory results.

columns. As can be seen, the calibrated dispersion coefficient did not reflect the experimental evolution of the nitrogenous organic matter, and ammonia/ ammonium in the soil. The verification of the migration of TKN in soil columns A was not conclusive.

The analysis of the breakthrough curve of measured TKN showed a reduction of 99.65% of the nitrogenous organic matter at the end of the experimentation, which was above the recorded reductions for electrical conductivity (10.69%) and BOD_{5} (15.69%). Usually, TKN is mostly made up of biodegradable organic compounds and therefore, a similar behavior to BOD would be expected. The failure of the validation of the TKN migration model could come from the difference recorded in the reductions of TKN and BOD. A low ratio of organic nitrogen to NH_{3}/ NH 4 + could explain this difference in the reductions. Therefore it can be inferred that the retardation phenomena and biodegradation of organic matter reactions are not sufficient to model the migration of TKN in soil. The model should look at the different components of TKN separately. In another hand, since the retardation coefficient R was calculated based on EC measurements, it might be that the model works for large humic macromolecule (forming part of BOD, for instance), rather than for much smaller molecules as ammonia (in TKN).

At this stage of the study, the designed model properly evaluate the effect of retardation factor on the migration of macromolecules contained in leachate. For much smaller molecules as ammonia, a recalibration of the retardation factor seem to be necessary. A proper model of migration of biodegradable organic matter in the underlying soils would then require a coupling of two retardation factors: one for the macromolecules contained in the leachate and another one for the smaller monovalent ion (such as Na^{+} in EC) or ammonia,

Retardation coefficient (R) represents the delay accused by a pollutant molecule with respect to the water molecule introduced at the same time at the inlet of a soil column. The value for the retardation factor coefficient taken for model calibration and verification in this study was 2.5. _{5} migration for different values of retardation factor.

The analysis of the curves in _{5} in soil columns was slowed by the increased retardation factor. The simulation of the dispersion of organic matter with R = 2.5 was the one that best approximates the measured results. Therefore the method used to measure the retardation coefficient is effective. For a non-delayed migration of pollutants, expressed by a retardation factor equal to 1, the simulated results are far removed from experimental result. The retardation factor is an essential parameter in modelling the migration of biodegradable organic matter in soils of waste dumpsites.

The influence of the retardation factor in the migration of biodegradable organic pollutants in soils was linear, and expressed in the present experimental study by the following equation: (

y = − 0.13 x + 1.05 (4.1)

The biodegradation rate expresses the speed of consumption of organic pollution by aerobic and anaerobic bacteria. Numerical simulations (_{5} model calibration. This can be explained by the fact that the organic matter biodegradation kinetics is an exponential function, thus, at the resolution of the experimentation, it is difficult to observe the effects of the biodegradion for short times of 1 and 2 days. An increase of around 10^{−}^{4} of biodegradation rate causes a halving of organic pollution at the outlet of the soil columns. It could be

the interesting to test longer times/longer columns in order to properly evaluate the biodegradation effect. For a practical point of view, it would be then beneficial to proceed to a bacteria activation of the soil before the deposit of household waste.

The influence of the rate of biodegradation on migration of biodegradable organic pollutants in our experimental investigation (

y = − 0.76 ⋅ e − 1688 x (4.2)

The phenomenon of natural biodegradation of organic matter was combined with the principle of convection-dispersion to model migration of leachates in soil. The resolution of this model by the finite difference method showed that the migration in soil of macromolecules contained in leachate can be predicted based on retardation factor determine by infiltration test on soil columns. For much smaller molecules as ammonia, a recalibration of the retardation factor is necessary. Therefore a model that aims to predict the migration in soil of both macro and micromolecule of leachate seem to require a coupling of two type of retardation factor: one for macromolecule such as BOD and one for micro molecule such as ammonia. The model at this stage failed to predict the biodegradation during of organic matter during the migration of leachate in the soil. Longer test times and longer test columns are required in order to properly evaluate the biodegradation effect of leachate during it migration in soils. Increasing the bacterial activity of the underlying soils of garbage dumpsites could be a solution for natural reduction of pollutants migrating to groundwater.

The authors gratefully acknowledge the International Foundation for Science (IFS), Stockholm, for supporting the present work under the IFS Grant W/5840-1.

The author(s) declare(s) that there is no conflict of interest regarding the publication of this paper.

Djihouessi, M.B., Onifade, S., Aina, M.P., Labité, H.E. and de Paule Codo, F. (2018) Migration of Biodegradable Organic Matter in Underlying Soils of Household Waste Dumpsites: A Case Study in Abomey-Calavi, Benin. Journal of Crystallization Process and Technology, 8, 18-32. https://doi.org/10.4236/jcpt.2018.81002