4 Assessment of effective transport parameters in a karst system under dynamic flow conditions by
4.4 Results
4.4 R
ESULTSThe TBCs obtained for the artificial tracer tests conducted in the subsurface channel are presented normalized with respect to the peak concentration in Figure 4‐3. TBCs normalized with respect to peak concentration (Cp) obtained from tracer tests conducted on surface features are provided in Figure 4‐4.
Various estimated/modeled parameters under different flow periods were correlated for a better understanding of the transport within the rapid flow system, in both the saturated, unsaturated media and the underground channel.
Figure 4‐3 Measured normalized TBCs (C/Cp) in the subsurface channel (over 5300 m) as a function of time after injection
Figure 4‐4 Measured TBCs from surface injections as observed in the main spring (J at the end of the subsurface channel) and at the beginning of the channel (D); J refers to TBCs at the spring outlet, and D is the beginning of the subsurface channel
4.4.1 Transport in the channel
4.4.1.1 Velocities and transit times
The tracer breakthrough curves (TBCs) retrieved from the 23 artificial tracer experiments undertaken in the underground channel displaying slight to very slight tailing (Figure 4‐4). Mean velocities estimated for discharge rates varying between 1.0 and 18.5 m3/s range respectively between 285 and 1910 m/hour (0.08 and 0.53 m/s). The velocity in the channel correlates (R=0.997) with the discharge rate according to a fourth degree polynomial relationship. The conduit network and its geometry may vary under varying flow conditions (Smart, 1988). Therefore, this relationship is not linear (Figure 4‐5) due to the change in the cross‐sectional area and the head difference which creates quadratic effects during various flow periods. The wetted phreatic diameter (φ) averaged over the entire distance (5300 m) varies proportionally with varying discharges, with a minimal apparent diameter during low flow periods of 4 m reaching a maximum of 7 m during high flow period. As a result, the slope of velocity as a function of discharge is less steep when the wetted section is widened (Figure 4‐5). Times of first arrival (tf) and transit times of the peak concentration (tp) correlate (R>0.99) with the mean transit time (tm= 1.202 tf = 1.021 tp). The transit time – discharge relationship over the distance of the subsurface channel (5300 m) is a power function. The duration of the tracer breakthrough curve, which ranges between 0.6 and 4.3 hours is also a power function of the discharge.
Figure 4‐5 Relationships between velocities (vm), transit time (tm), discharge (Q), and phreatic diameter ( )
4.4.1.2 Longitudinal dispersion and dispersivity
Longitudinal dispersion (D) and mean velocity (vm) increase with the discharge rate according to a polynomial of
Figure 4‐6 Relationships between longitudinal dispersion (D) and longitudinal dispersivity (α) and discharge (Q)
4.4.1.3 Attenuation of peak concentration
The normalized concentration peak (Cn; peak concentration to recovered mass) decreases with increasing longitudinal dispersion showing the effect of dispersion on dilution with increasing discharge rates. Different slopes are observed during high and low flow periods (Figure 4‐7).
Figure 4‐7 Correlation between longitudinal dispersion and longitudinal dispersivity and attenuation of the artificial tracer peak concentration (Cp/Mrecovered)
4.4.1.4 Immobile regions
The portion of immobile region in the channel is not very prominent, as the partition coefficient ranges between 0.93 and 1 (Figure 4‐8) portrayed by a subtle tailing. Nevertheless, the partition coefficient (β) increases with increasing velocities and distances. Additionally, the higher the percentage of immobile region, the higher is the exchange of tracer between mobile and immobile region with time (ω).
Figure 4‐8 Correlation between partition coefficient (β) and discharge (Q) as well as with the mass transfer coefficient (ω)
4.4.1.5 Transport parameters over varying distances
Dispersivities over a transport distance of 680 m range between 2 m and 4 m and decreases with discharge rates, whereas dispersivities over 5300 m vary between 4 m and 9 m under different flow periods. The dispersivities appear to be increasing with distances; such correlation is observed also by Seiler et al., (1989).
The artificial tracer test monitored at various observation points within the channel shows that mean velocity decreases with distance, while estimated longitudinal dispersivity increases with distance. The TBC shows a dilution effect by additional inflow of water within the channel between the monitored locations.
4.4.2 Transport outside the channel (compartments of the karst systems)
The results discussed hereafter are those of the tests conducted in a sinkhole leading directly to the subsurface channel (Figure 4‐2, (4)), in a sinkhole (Figure 4‐2, (5)), in an artificially dug pit hole (Figure 4‐2, (6)) and a borehole (Figure 4‐2, (7)). The results therefore portray the transport in the following media:
1. Sinkhole leading directly to the subsurface channel (phreatic cave) 2. Fissured saturated matrix (borehole)
3. Unsaturated rock matrix overlying the subsurface channel
4. Mixed media including the unsaturated zone and the subsurface channel 4.4.2.1 Velocities and transit times
4.4.2.2 Longitudinal dispersion and dispersivity
The artificial tracer tests conducted on the catchment area reveal that estimated longitudinal dispersivities range between 8 and 27 m. The estimated longitudinal dispersivities generally decrease with increasing velocities, as a result of which they are highest than the one observed in the subsurface channel (Figure 4‐9, b).
The calculated apparent phreatic diameter varies between 7 and 14 m, 7‐11 meters reflecting the flow in the sinkhole directly linked to the main sub channel system and 11‐14 m reflecting the phreatic diameter in the unsaturated zone.
The mobile region estimated from TBCs in tracer tests conducted in sinkholes or directly on the surface varies between 0.80 and 0.93 (Figure 4‐9, c). The partition coefficient is lowest as portrayed by the prominent tailing of the TBC for tracer tests performed on pit holes. The partition coefficient increases (decrease of immobile region) with increasing Peclet number which varies between 72 and 1000 (Figure 4‐9, d). As observed in the subsurface channel, longitudinal dispersion plays a role in the attenuation of the tracer (peak concentration), especially in low flow periods (steeper slope; Figure 4‐10).
a b
c d
Figure 4‐9 Relationships between various transport parameters (mean velocity to partition coefficient;
a, longitudinal dispersivity; b, and phreatic diameter; c) from the tracer tests performed in the subsurface
Figure 4‐10 Importance of dispersion in the attenuation of the maximum observed peak in all the compartments of the investigated karst system under various flow dynamics