IJW0701-0202 CASARES-SALAZAR.pdf

15
14 Int. J. Water, Vol. 7, Nos. 1/2, 2013 Copyright © 2013 Inderscience Enterprises Ltd. Field scale longitudinal dispersivities estimation in a karstic aquifer Rafael Casáres-Salazar*, Roger González-Herrera and Eduardo Graniel-Castro Facultad de Ingeniería, Universidad Autónoma de Yucatán (UADY), Avenida Industrias No Contaminantes x Anillo Periférico Norte, tablaje catastral No. 12685, Merida, Yucatan, Mexico Fax: (52 999)-930-05-59 E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] *Corresponding author Abstract: To simulate contaminant advective transport it is required to provide dispersivity values to the models, values that are unknown in many cases. In this paper a methodology is presented to estimate longitudinal dispersivities at field scale, based on the monitoring of groundwater quality at an unconfined aquifer that is below a waste disposal site with no liners for groundwater protection, and by applying a one-dimensional advective transport model. Chloride was used as a tracer, which is known to be present in dump site leachates. As part of the results, an equation was obtained that relates longitudinal dispersivity against the observation scale for the unconfined karstic aquifer of Yucatan, México. Some scenarios were employed for the longitudinal dispersivity estimation and for the solute transport simulation. In this way, a sensitivity analysis was performed to calculate the longitudinal dispersivities by varying the hydraulic conductivity and the hydraulic gradient. As a simulation exercise, a sensitivity analysis was also carried out to calculate the travel time that a particle would require to reach a certain distance depending on the longitudinal dispersivity value. Keywords: groundwater; advective transport; longitudinal dispersivity; observation scale; tracer; karstic aquifer; sensitivity analysis; hydraulic conductivity; hydraulic gradient. Reference to this paper should be made as follows: Casáres-Salazar, R., González-Herrera, R. and Graniel-Castro, E. (2013) ‘Field scale longitudinal dispersivities estimation in a karstic aquifer’, Int. J. Water, Vol. 7, Nos. 1/2, pp.14–28. Biographical notes: Rafael Casáres-Salazar holds a Hydrology Master degree (2006) by the Engineering School of the Autonomous University of Yucatan, Mexico. He has practised hydrogeology in many consultant projects in the Yucatan peninsula. His research interests are on the hydrodynamics and solute transport modelling in aquifers and surface waters, the definition of aquifer conceptual models and the estimation of its hydraulic properties as a contribution to sustainable development.

Transcript of IJW0701-0202 CASARES-SALAZAR.pdf

14 Int. J. Water, Vol. 7, Nos. 1/2, 2013

Copyright © 2013 Inderscience Enterprises Ltd.

Field scale longitudinal dispersivities estimation in a karstic aquifer

Rafael Casáres-Salazar*, Roger González-Herrera and Eduardo Graniel-Castro Facultad de Ingeniería, Universidad Autónoma de Yucatán (UADY), Avenida Industrias No Contaminantes x Anillo Periférico Norte, tablaje catastral No. 12685, Merida, Yucatan, Mexico Fax: (52 999)-930-05-59 E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] *Corresponding author

Abstract: To simulate contaminant advective transport it is required to provide dispersivity values to the models, values that are unknown in many cases. In this paper a methodology is presented to estimate longitudinal dispersivities at field scale, based on the monitoring of groundwater quality at an unconfined aquifer that is below a waste disposal site with no liners for groundwater protection, and by applying a one-dimensional advective transport model. Chloride was used as a tracer, which is known to be present in dump site leachates. As part of the results, an equation was obtained that relates longitudinal dispersivity against the observation scale for the unconfined karstic aquifer of Yucatan, México. Some scenarios were employed for the longitudinal dispersivity estimation and for the solute transport simulation. In this way, a sensitivity analysis was performed to calculate the longitudinal dispersivities by varying the hydraulic conductivity and the hydraulic gradient. As a simulation exercise, a sensitivity analysis was also carried out to calculate the travel time that a particle would require to reach a certain distance depending on the longitudinal dispersivity value.

Keywords: groundwater; advective transport; longitudinal dispersivity; observation scale; tracer; karstic aquifer; sensitivity analysis; hydraulic conductivity; hydraulic gradient.

Reference to this paper should be made as follows: Casáres-Salazar, R., González-Herrera, R. and Graniel-Castro, E. (2013) ‘Field scale longitudinal dispersivities estimation in a karstic aquifer’, Int. J. Water, Vol. 7, Nos. 1/2, pp.14–28.

Biographical notes: Rafael Casáres-Salazar holds a Hydrology Master degree (2006) by the Engineering School of the Autonomous University of Yucatan, Mexico. He has practised hydrogeology in many consultant projects in the Yucatan peninsula. His research interests are on the hydrodynamics and solute transport modelling in aquifers and surface waters, the definition of aquifer conceptual models and the estimation of its hydraulic properties as a contribution to sustainable development.

Field scale longitudinal dispersivities estimation in a karstic aquifer 15

Roger González-Herrera is an Associate Professor and Researcher at the Postgraduate and Research Unit of the Engineering School of the Autonomous University of Yucatan. He has published many research papers on the Yucatan karstic aquifer. His research interests include the hydrodynamics of coastal aquifers, transport and natural attenuation of contaminants in karstic systems.

Eduardo Graniel-Castro is an Associate Professor and Researcher of the Postgraduate and Research Unit of the Engineering School of the Autonomous University of Yucatan. He was coordinator of the hydrology branch of the engineering postgraduate programme during 2004–2008. He has published many papers about the contamination and related topics regarding the aquifer underneath the city of Merida, Yucatan, Mexico and other parts of the Yucatan peninsula.

1 Introduction

The transport of a non-reactive (conservative) dissolved contaminant in groundwater is controlled by the following mechanisms:

• Advection. It refers to solute transport induced by groundwater flow.

• Hydrodynamic dispersion. It refers to the tendency of a solute plume to propagate outside the path it is expected to take by the advective field.

• Molecular diffusion. It is the component of hydrodynamic dispersion that is influenced by ion or molecular movement and refers to solute transport from high to low concentration zones.

In this paper we discuss the hydrodynamic dispersion concept for a karstic aquifer, which causes contaminated groundwater to occupy a larger volume with respect to the volume that it would occupy if it were influenced by the advective field exclusively. This causes the maximum concentration of contaminants in the plume to diminish, taking place to a natural attenuation as the plume disperses as this process irreversible (Lehr, 1988). There are two components of dispersion:

• Longitudinal dispersion. Solute propagation in the preferential flow direction.

• Transverse dispersion. Solute propagation perpendicular to the preferential flow direction.

Longitudinal dispersion is the process by which part of the fluid and solutes travels faster than the average lineal velocity, and other part travels slower; therefore, solutes disperse along the flow direction and their concentrations diminish. Mechanical dispersion along the transverse direction is much less than dispersion in the longitudinal direction (Freeze and Cherry, 1979).

The hydrodynamic dispersion coefficient (D) is defined as the product of the longitudinal dispersivity (α) and the flow velocity of groundwater (V). It can be

16 R. Casáres-Salazar et al.

understood as a characteristic mixing length and as a measure of the contaminant dispersion (Bedient et al., 1999).

For practical purposes the value of the horizontal transversal dispersivity could be considered as one order of magnitude lower than longitudinal dispersivity, whereas the vertical transverse dispersivity could be considered as two orders of magnitude lower than longitudinal dispersivity (Gelhar et al., 1992).

The observation scale is defined as the distance between the observation point and the contaminant source. The observation scale can exert an influence on magnitude of the dispersivity, because as the trajectory increases, the groundwater finds its way through larger variations in the aquifer. Gelhar et al. (1992) carried out a wide research where they determined 59 values of longitudinal dispersivity in different geological media at field scale. To achieve this purpose they applied tracer tests and took into account contaminant events and environmental tracers, in porous media and in fractured rocks as well. They report that longitudinal dispersivity increases as the observation scale does, as indicated in Figure 1 and Figure 2. So, in Figure 1 it can be observed that there is little difference among the data reported for porous media and those from fractured rocks. Moreover, they report that at a considerably large distance the heterogeneities of the medium will no longer exert a significant influence on the increment of the longitudinal dispersivity, so it will reach a constant value.

Figure 1 Longitudinal dispersivity vs. observation scale, identified by kind of test and type of aquifer

Source: Gelhar et al. (1992)

Field scale longitudinal dispersivities estimation in a karstic aquifer 17

Figure 2 Longitudinal dispersivity vs. observation scale with data classified according to reliability

Source: Gelhar et al. (1992)

The determination of dispersivity values required to use for solute transport simulations is not an easy matter and it has been a controversial topic. Gelhar et al. (1992) report that at a certain scale of observation the longitudinal dispersivity values can vary by two or three orders of magnitude, being the most confident values in the lower portion of the range, as presented in Figure 2; for that reason, they recommend to take the dispersivity values at the lower half of the range, for a specific observation scale. They explain it by considering that if the values at the upper half of the range were used, it would simulate an excessive dilution and the environmental consequences of it may be wrongly estimated. Therefore, as the dispersivity increases the dispersion does too, and so dilution takes place.

This explains the concept of dispersivity and its importance in solute transport simulations: dispersivity is a measure of the solute dispersion in an aquifer since dilution increases as dispersivity does, the latter being dependent on the observation scale. Dispersion at field scale is due mainly to macroscopic heterogeneities rather than to the heterogeneity associated with the rock matrix pores. Generally, macroscopic dispersion of a solute in the aquifer tends to increase as the number or heterogeneities does (Zheng and Bennett, 1995).

On the other hand, conservative solutes are transported at the same velocity of groundwater flow, which is directly proportional to the hydraulic conductivity and

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inversely proportional to the porosity. That is to say, the time a solute takes to travel a given distance will depend primarily on the velocity of the groundwater flow, whereas the concentrations and extension of the contaminant plume will depend in first instance on the longitudinal and transverse dispersivities.

Heterogeneities in hydraulic conductivity and porosity of the aquifer exert an influence on the transport of solutes; so, it is imperative to define the variations of these parameters in the aquifer, both in the horizontal and vertical direction. Also, the heterogeneity in other properties or processes that affect the velocity can have similar effects. For example, temporal and spatial variations in the recharge and discharge of the aquifer can cause changes in the velocity field, which in turn generate effects in the solute migration; therefore, the transport models that consider the recharge and discharge uniformly in space and time are subject to this limitation and will fail to reproduce such effects (Zheng and Bennett, 1995).

Figure 3 Study zone: old waste disposal site of the city of Merida, located at the NW of the urban zone, at the state of Yucatan, Mexico

Dzitya town

Garbage

Engineering

N1

UW2

D2

D3

C1

P6

I5

UW5

UW3

P4

P7M1

UW6UW1

P1

P2

S6S5

S4S3S2S1

school

MeridaCity of

(NW)

MEXICO

STATE OF YUCATAN

hill

(UADY)

Field scale longitudinal dispersivities estimation in a karstic aquifer 19

2 Methods

The study area corresponds to the unconfined karstic aquifer underlying the old waste disposal site of the city of Merida, Yucatan, Mexico (Figure 3). This site, unlined and nowadays closed, acted during many years as a continuous source of contaminants to the shallow aquifer, which water table is located six metres below the ground level, approximately. A system of fractures has been developed allowing a rapid percolation of the rainfall through them and transporting the contaminants from wastes to the aquifer. The monitoring points shown in Figure 3 were used to determine the main direction of groundwater flow (N-30°-W) and to map the extension of the contaminant plume in the aquifer, at water table level (Figure 4). In particular, boreholes S1, S2, S3, S4, S5 and S6 (located in the main direction of groundwater flow) were used to estimate longitudinal dispersivities.

Figure 4 Contours of chloride isoconcentration, May 2000, for the determination of the groundwater flow direction and the mapping of the contaminant plume at water table (see online version for colours)

Chloride, May 2000

80 ppm

140 ppm

200 ppm

20 ppm

Since chloride ion is known to be present in the leachate of the old waste disposal site, it was used as a tracer in spite of being a conservative element in groundwater, insensitive to the effects of ion exchange, adsorption and biological activity, which makes it a good indicator of the movement of contaminants in the aquifer (Custodio and Llamas, 1976). For such reasons, groundwater samples were collected at boreholes S1, S2, S3, S4, S5 and S6 at different depths – ranging from 0 to 30 m below the water table – to determine the concentration of this element in the aquifer.

To estimate longitudinal dispersivities and to carry out the solute transport simulation a one-dimensional model was used. The model, solved by Bear in the year of 1961 for background concentration of zero, was developed for a constant and continuous source of

20 R. Casáres-Salazar et al.

contaminants in a homogeneous and isotropic medium. It is introduced in Bedient et al. (1999) as follows:

exp2 2 2

Co L Vt VL L VtC erfc erfcDDt Dt

⎛ ⎞− +⎡ ⎤ ⎡ ⎤⎡ ⎤= +⎜ ⎟⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦ ⎣ ⎦⎝ ⎠ (1)

where the hydrodynamic dispersion coefficient D is calculated as D = α V, being α the longitudinal dispersivity; V is the flow velocity; Co is the concentration of the contaminant at the source; C is the concentration of the contaminant calculated at a given distance L measured from the contaminant source and on its trajectory after a time t; and erfc is the complementary error function whose values can be found in specialised texts. The second term of the right member of equation (1) can be neglected in most of the practical situations. The assumptions of the model are the following:

• the tracer is ideal, with constant density and viscosity

• the fluid is incomprehensible

• the medium is homogeneous and isotropic

• transport is only considered in the saturated zone.

It is worth mentioning that the aquifer under study is karstic, heterogeneous and anisotropic while the model [equation (1)] was developed for a homogeneous and isotropic medium.

Although, at a macro scale, it can be satisfactorily modelled as an equivalent porous medium (González et al., 2002); so, the results should be taken with due caution. A similitude to this topic is the case of pumping test analysis, where the applicability of the formulas in fractured or karstic aquifers given the discrete nature of these formations is doubtful. In such cases, the interpretation problem is solved by simplifications, which are not always adapted to field observations; so, in karstic aquifers, hydraulic parameters are estimated only by strong simplifications, conceptualising the aquifer as an equivalent porous medium (COST Office, 2005).

3 Results and discussion

In order to know the change in the magnitude of longitudinal dispersivity against the variation of the hydraulic parameters involved in its estimation, particularly the hydraulic conductivity (K) and the hydraulic gradient (i) a sensitivity analysis were performed for borehole S1. Furthermore, this analysis distinguished between values of hydraulic conductivity and hydraulic gradient suitable for the estimation of the longitudinal dispersivities associated with different scales of observation.

For this sensitivity analysis six scenarios were analysed, in each of them values of K and i were allowed to vary, based on the determinations of several investigations carried out in the aquifer of Yucatan, and particularly in the study zone. Table 1 presents the values considered for each of the sensitivity analysis scenarios; as such it was obtained the groundwater flow velocity from equation (2), which arises from Darcy’s Law:

Field scale longitudinal dispersivities estimation in a karstic aquifer 21

KiVn

= (2)

where n is the medium porosity and is considered to be equal to 0.35 for the study zone (González et al., 2002). Table 1 Considered values for the sensitivity analysis scenarios, and determination of the

groundwater velocity

K = 319 m/d Graniel (2001) i = 0.0000796 Sánchez (1992) n = 0.35 González et al. (2002)

Scenario 1

V = 0.0725 m/d K = 319 m/d Graniel (2001) i = 0.000008 Marin et al. (2001) n = 0.35 González et al. (2002)

Scenario 2

V = 0.0073 m/d K = 44,928 m/d Reeve and Perry (1990) i = 0.0000796 Sánchez (1992) n = 0.35 González et al. (2002)

Scenario 3

V = 10.2179 m/d K = 44,928 m/d Reeve and Perry (1990) i = 0.000008 Marin et al. (2001) n = 0.35 González et al. (2002)

Scenario 4

V = 1.0269 m/d K = 23,000 m/d Sánchez (1999) i = 0.0000796 Sánchez (1992) n = 0.35 González et al. (2002)

Scenario 5

V = 5.2309 m/d K = 23,000 m/d Sánchez (1999) i = 0.000008 Marin et al. (2001) n = 0.35 González et al. (2002)

Scenario 6

V = 0.5257 m/d

As an example, the following procedure is presented to calculate longitudinal dispersivity for the scale of observation corresponding to borehole S1 under Scenario 1, by applying equation (1) and neglecting the second term on the right. The input data are as follows.

Borehole S1 is located at a distance L = 255 m from the source of contaminants. The maximum concentration of chloride ion observed in this borehole was 439.58 mg/l (at 25 m below water table); subtracting the background concentration in the aquifer (19 mg/l) results in a concentration of 420.58 mg/l; this value corresponds to variable C in the Bear’s one-dimensional model [equation (1)]. The concentration of chloride ion in the source is 4,690 mg/l (Kú, 1998). The time elapsed since the beginning of the implementation of the area method in the old waste disposal site – this corresponds to the date when the solid wastes began to accumulate, which is March 1993 – until the date

22 R. Casáres-Salazar et al.

when there were determined the concentrations of chloride ion – these concentrations were determined on November 2000 – is approximately 93 months, or 2,790 days. From Table 1, the velocity considered for Scenario 1 is 0.0725 m/d.

Scenario 1: L = 255 m, C = 420.58 mg/l, Co = 4,690 mg/l, t = 2,790 days, V = 0.0725 m/d.

221.85360.1793

1.8536being

then ( ) 0.1793and 0.9495

1.8536therefore 0.9495

thus 3.8 m

C L VterfcCo Vt

erfc

erfc

−⎛ ⎞= ⎜ ⎟

⎝ ⎠⎛ ⎞

= ⎜ ⎟⎝ ⎠

=

==

=

=

α

α

βα

ββ

αα

Following the same procedure stated for borehole S1, values of longitudinal dispersivity (α) corresponding to Scenario 2 to Scenario 6 were computed, summarising the results in Table 2, where it can be noted that longitudinal dispersivity is highly sensitive to K and i values used for its determination. Table 2 Results of the longitudinal dispersivity determinations for each of the scenarios,

applied to borehole S1

Scenario α (m) Observations

1 3.8 It is within the range reported by Gelhar et al. (1992) 2 748 Out of range 3 7,757 Out of range 4 661 Out of range 5 3,902 Out of range 6 281 Slightly out of range

Note: It is accepted exclusively the dispersivity corresponding to Scenario 1.

According to Figure 2, after Gelhar et al. (1992), for a scale of observation of approximately 255 m (distance from the source of contaminants to borehole S1), longitudinal dispersivity varies in a range of approximately 1 to 200 m, with a greater degree of confidence at lower values of this range. For that reason, from Table 2 it is concluded that Scenario 1 data are appropriate for the estimation of the longitudinal dispersivities at the rest of the boreholes (S2 to S5). These data are the following:

K = 319 m/d (Graniel, 2001)

i = 79.6 mm/km = 0.0000796 (Sánchez, 1992)

n = 0.35 (González et al., 2002)

Field scale longitudinal dispersivities estimation in a karstic aquifer 23

V = 0.0725 m/d (Calculated with Darcy’s Law).

It is inferred that the data for the rest of the scenarios are not appropriate for the aquifer of study, due to the following.

Regarding to the hydraulic conductivity, the high 44,928 m/d value reported by Reeve and Perry (1990) was estimated with a tidal analysis, so it must take into account the major karstic conduits of extremely high hydraulic conductivity. Similarly, the high 23,000 m/d value reported by Sánchez (1999) was obtained with a numeric model of an extended domain (N-NW of Yucatan), which also must consider the major karstic conduits for proper calibration. The relative low accepted value of 319 m/d reported by Graniel (2001) was obtained through tracer tests at a specific site in the city of Merida, this site having a hydrogeologic ambient similar to the study zone of the present investigation; so, this value appears not to consider the major karstic conduits – at least at a great extent – but the porous matrix medium at a more local scale.

Regarding to the hydraulic gradient, the 0.000008 (8 mm/km) value reported by Marin et al. (2001) was obtained with a numeric model of an extended domain (Northwestern Yucatan), which must consider the major karstic conduits for proper calibration. The accepted value of 0.0000796 (79.6 mm/km) reported by Sánchez (1992) was obtained for the same site of the present investigation.

And with regard to the porosity value employed (n = 0.35) reported by González et al. (2002), this is the only value determined for the Yucatan aquifer, having been employed in the cited reference to model the regional groundwater flow of northwest Yucatan.

Table 3 presents the maximum concentrations of chloride ion found at the observation boreholes S1 to S6, as well as the depths to which such concentrations were found. They are considered the maximum concentrations regardless of the depth where they where found in the aquifer, because the contaminants may divert vertically through the preferential conduits of the karstic system and also because the greater density of the leachate may cause it to sink in the aquifer. The table includes the column ‘maximum concentration minus background concentration’ (background concentration = 19 mg/l), which corresponds to C parameter in the one-dimensional model employed to estimate the dispersivities [equation (1)]. Table 3 Maximum concentrations of chloride ion found in the aquifer

Borehole Maximum concentration (mg/l)

Depth below water table (m)

Max. concentration minus background concentration. (mg/l)

S1 439.58 25 420.58 S2 372.76 15 353.76 S3 369.36 25 350.36 S4 278.07 35 259.07 S5 260.23 15 241.23 S6 251.84 25 232.84

With these data the longitudinal dispersivity values were obtained for the distances given by the location of the observation points with respect to the centre of the old dump site, which is the source of contaminants. The results are presented in Table 4.

24 R. Casáres-Salazar et al.

Table 4 Longitudinal dispersivity values estimated for various observation scales

Borehole Distance (L) in metres α, in metres

S1 255 3.8 S2 272 5.8 S3 294 10.0 S4 350 21.1 S5 439 50.7 S6 532 98.5

The longitudinal dispersivity values that were presented in Table 4 are within the range obtained by Gelhar et al. (1992), represented in Figure 2; so it is concluded that the application of such figure can be extended to the karstic aquifer of Yucatan.

Data from Table 4 were used to adjust equation (3) that relates L vs. α, the corresponding graphic being presented in Figure 5.

20.0009 0.3694 39.878L L= − +α (3)

with the domain 255 ≤ L ≤ 532, where α and L are in metres, and with a correlation coefficient R = 0.9998.

Figure 5 Graph of L vs. α, based on the estimated dispersivities at the old waste disposal site of the city of Merida, Yuc. (see online version for colours)

0102030405060708090

100110

0 100 200 300 400 500 600L (m)

α (m)

4 Solute transport simulation in the Yucatan karstic aquifer

In this section the transport of solutes in the unconfined karstic aquifer of Yucatan is simulated, with the old waste disposal site of the city of Merida acting as a source of contaminants. The groundwater flow direction is NW, which points towards the town of Dzitya, located at a distance of 1,500 m downgradient of the source of contaminants. The

Field scale longitudinal dispersivities estimation in a karstic aquifer 25

plume of contaminants descends between 20 and 25 metres below the water table, so that the simulated concentrations of the contaminant in the aquifer will be for those depths.

To overcome the uncertainty on the longitudinal dispersivity value required to carry out the solute transport simulation, it is suggested to consider at least three scenarios for a given observation scale: one using the higher dispersivity, other with an average dispersivity value, and another one with the lowest value, based on Figure 2, taken after Gelhar et al. (1992). Another way to get a suitable value for the longitudinal dispersivity consists of applying equation (3) proposed in this paper for karstic aquifers, only if the observation scale is within the domain of such equation. In this study, there were simulated the following scenarios, not being possible to apply equation (3) because the observation scale does not belong to its domain.

• Scenario a: α = 100 m. At borehole S6, located at a distance L = 532 m from the source of contaminants, the longitudinal dispersivity value is estimated to be 98.5 m; therefore, for L = 1500 m, α has to be greater than 98.5 m, taking it equal to 100 m for this scenario.

• Scenario b: α = 150 m, average value between Scenario a and Scenario c.

• Scenario c: α = 200 m, based on the upper limit of the dispersivities range in Figure 2 reported by Gelhar et al. (1992) for an observation scale of L = 1,500 m.

It is worth mentioning that it was not carried out a simulation for the minimum dispersivity value reported in Figure 2 (α = 6 m, for L = 1,500 m) since this value is unrealistic for the study area, according to Table 4 and Figure 5.

The values for the parameters used in the solute transport simulation are presented in Table 5. Table 5 Input parameters for the solute transport simulation

Parameter Reference

L = 1500 m Distance from the old dump site centre to Dzitya town Co = 4,690 mg/l Kú (1998) K = 319 m/d Graniel (2001) i = 0.0000796 Sánchez (1992) n = 0.35 González et al. (2002) V = 0.0725 m/d Calculated with Darcy’s Law

Table 6 presents the results of the solute transport simulations considering the three scenarios of different α value. The time in the table indicates how long a borehole, located at a distance of 1,500 m from the source of contaminants – equivalent to the distance between the old dump site and the town of Dzitya – will take to reach a chloride concentration of 250 mg/l. We chose this value for the chloride concentration since it is the maximum permissible limit that allows the Mexican official norm NOM-127-SSA1-1994 (DOF, 2000) for human consumption water quality. It is worth mentioning that this time starts to count since the beginning of the implementation of the area method in the old waste disposal site – March 1993 –, and the results will be subjected to the same conditions of contaminant emissions during all the time of simulation and under the assumptions of the model used.

26 R. Casáres-Salazar et al.

Table 6 Time for a contaminated borehole, located at 1,500 m from the source of contaminants, to reach a chloride concentration of 250 mg/l

Scenario α (m) Time to manifest 250 mg/l (years) Date to manifest 250 mg/l

a 100 32 March, 2025 b 150 27.67 November, 2020 c 200 25 March, 2018

Figure 6 presents the comparative curves of time vs. concentration for the three scenarios of the solute transport simulation.

Figure 6 Comparative curves of time vs. concentration for scenarios a, b and c of the solute transport simulation

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 10000 20000 30000 40000 50000 60000 70000 80000

Con

cent

ratio

n C

(mg/

l) +

back

grou

nd c

once

ntra

tion

Time (days)

Scenario a Scenario b Scenario c

From Table 6, it can be noted that as the longitudinal dispersivity increases, the time that will take to reach a concentration of 250 mg/l at a distance of 1500 m decreases. This confirms what is reported by Gelhar et al. (1992): the higher the dispersivity, the larger the dispersion and dilution of contaminants in the aquifer.

Considering the solute transport scenarios presented in Table 6, the time that the contaminant will take to reach Dzitya is estimated to be between 25 and 32 years, which will take place between March 2018 and March 2025, under the assumption of keeping the same conditions in the source of contaminants and the assumptions of the model applied. However, today it is known that the dump site has been closed, so that the leachate that may be releasing should be the remnant of the garbage that was accumulated over several years.

From the differences observed in Table 6 with respect to the values of α and the times that the solute will take to travel the given distance (L = 1,500 m), it can be concluded

Field scale longitudinal dispersivities estimation in a karstic aquifer 27

that the results of the simulation are sensitive to the α value. Therefore, due to the uncertainties associated with the α value, it is suggested to simulate at least three scenarios for the solute transport simulation, varying the values of α and maintaining the other parameters constant, considering that the modeller is sure about the accuracy of them.

Finally, it is noted that in the absence of the hydrodynamic dispersion, the plume of contaminants would arrive to the distance L = 1,500 m at a time t = L / V = 1,500 m / 0.0725 m/d = 20,689 days = 56.68 years, transported by the flow vectors at the groundwater velocity exclusively. Thus, with this case study it is shown how part of the fluid and solutes travels faster than the groundwater velocity, this being attributed to the longitudinal component of the dispersion, which refers to the spread of the solute in the preferential flow direction.

5 Conclusions

Investigations carried out in the Yucatan karstic aquifer confirm that longitudinal dispersivity increases with distance, or observation scale. In addition, the estimates of this parameter corroborate the graph of Gelhar et al. (1992) which relates L vs. α, obtained at porous and fractured aquifers, thus enabling it to apply to the karstic aquifer of Yucatan.

The longitudinal dispersivity is highly sensitive to the values of hydraulic conductivity and hydraulic gradient employed in its estimation.

Results of the solute transport simulation are sensitive to the value of α, so it is recommended to consider at least three scenarios for a given observation scale: one using the higher dispersivity, other with an average dispersivity value, and another one with the lowest value, based on Figure 2, after Gelhar et al. (1992). In the case of a karstic aquifer it can be further considered the use of equation (3) to determine α – only if the observation scale is within the domain of such equation – in the absence of dispersivity values estimated at the study site.

The results of the solute transport simulation confirm that the higher the dispersivity, the larger the dispersion and dilution of contaminants in the aquifer.

It is worth mentioning that the results of the simulation in the present investigation should be taken cautiously due to the simplifications taken for the aquifer under study, which is karstic, heterogeneous and anisotropic.

Acknowledgements

The research reported in this paper was supported through a grant from the National Council of Science and Technology of Mexico (Consejo Nacional de Ciencia y Tecnología) and the government of the State of Yucatan (Fondos Mixtos del Gobierno del Estado de Yucatan). Authors are grateful with reviewers comments that improved this paper.

28 R. Casáres-Salazar et al.

References Bedient, P.B., Rifai, H.S. and Newell, C.J. (1999) Groundwater Contamination. Transport and

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