Groundwater Recharge and Storage Processes in Karst Aquifers

 

MOHRLOK, U.1 & M. SAUTER 2

 

¹Institute for Hydromechanics, University of Karlsruhe,

Kaiserstr. 12, D-76128 Karlsruhe, Germany

E-Mail: ulf.mohrlok@bau-verm.uni-karlsruhe.de

²Applied Geology, Geological Institute, University of Tuebingen, Germany

E-Mail: martin.sauter@uni-tuebingen.de

 

 

ABSTRACT

The hydraulic properties of karst aquifers can be approximated assuming (a) a lower permeability fissured system with a high storage capacity which is drained by (b) a high permeability but low storativity conduit network. This simplified dualistic view of a karst system can be supported through observations of well and spring hydrograph behaviour, which frequently exhibit two major response frequencies to recharge input: a fast event response and a slow seasonal variation. This behaviour is directly linked with the water storage processes after recharge events and affected by the exchange flux between the fissured system and the draining conduit network. Field observations show that the maximum groundwater level is read several weeks after maximum spring discharge. This feature implies the presence of an intermediate storage which can be either located in the epikarst or the fissured system of the aquifer itself. The epikarst storage model assumes that the bulk of the recharge water is slowly released from the epikarst, while the aquifer storage model asumes that the bulk of recharge is conveyed via vertical shafts to the phreatic zone, where due to the difference in hydraulic gradient water flows from the conduit into the fissured system. In order to test the applicability of either model, the heat transport processes has been investigated. These investigations lead to a better understanding of the recharge and the linked storage processes in karst aquifers.

 

1 INTRODUCTION

Karstaquifers represent an important groundwater resource. However, they are highly vulnerable with respect to contamination due to fast transport through the karst conduit system and due to the limited attenuation of contaminants in karst terraines. In the context of contaminant risk assessment it is important to know in which compartment the bulk of the water is stored for extended periods of time, i.e. karst groundwaters are more at risk if recharge is stored close to the surface, e.g. in the epikarst. As a complementary investigation to the comparison of different groundwater flow modelling approaches with respect to different recharge mechanisms (Mohrlok & Sauter, 1997), this paper presents a new approach for the assessment of the recharge mechanism. A heat balance technique is used to trace the passage of the water from ground surface to the spring.

 

2 GENERAL CONCEPTS OF FLOW AND RECHARGE MECHANISMS

The karst groundwater flow system is usually conceptualised as consisting of two interacting flow systems, i.e. a) a highly conductive conduit system with low storativity and b) a much less conductive high storage fissured system (Kiraly, 1984; Sauter, 1991). The flow systems are believed to be hydraulically coupled. This type of dualistic view emerged from field observations of well and spring hydrograph responses which exhibit frequently a response pattern to recharge events as well as the time series of physico-chemical parameters of spring water quality of the Gallusquelle catchment, a typical karst spring of the Swabian Alb, SW-Germany, (Figure 1, Sauter, 1992). A sharp increase in spring flow, with a peak discharge of 1 - 2 days after the highest inten­sity in rainfall, a rapid flow component, is fol­lowed by a less rapid drop in discharge, a slow flow component. The peak discharge consists mainly of pre-event water, indicated by the lack of change in electrical conductivity and temperature, which im­plies that actual event water reaches the spring ap­proximately 0.5 to 2 days later. The ma­ximum groundwater level in the aquifer were read bet­ween 1 and 4 weeks after the event. This observation is interpreted as an intermediate storage effect. There are two possible explanations for this behaviour: a) the bulk of the recharge water is stored in the epikarst (epikarst storage, Figure 2a) or b) in the fissured system of the aquifer (aquifer storage, Figure 2b).

 

The epikarst storage model assumes that a small percentage of the infiltrating water (ca 10%) directly flows via the vertical shaft system into the conduit system of the aquifer. This flow component rapidly emerges at the spring and can be recognised by e.g. low electrical conductivity of the spring water, i.e. a low concentration in dissolved solids, a result of the short contact time between water and aquifer material. The remaining 90% of the effective infiltration slowly drains via the less permeable unsaturated zone to the fissured system of the aquifer producing the delayed peak in the groundwater hydrographs. A similar response of spring flow and groundwater hydrographs can be explained by the aquifer storage model. This model assumes that almost the complete effective infiltration is conveyed via vertical shafts to the phreatic zone. A small fraction of the total recharge water, the fast component, directly flows to the spring (see above) while the bulk of the recharge water flows from the conduit system into the fissured system due to the high hydraulic gradient. Because of the low hydraulic conductivity of the fissured system, the flow of this recharge component into the fissured system is delayed, thereby causing the lag between maximum discharge and maximum water levels in the groundwater hydrographs.

 

There is evidence that recharge is stored for some time within the epikarst, supporting the epikarst storage model. Time series of spring discharge and water temperature exhibit a strong correlation (Liedl et al., 1997). A very important feature of the temperature record is that recharge events always lead to a decrease in spring water temperature relative to background temperature, regardless whether recharge occurred during winter or summer. This observation can be explained by a conceptual model, which assumes that the residence time of water within the epikarst horizon is long enough for the recharge water to adapt to the rock temperature which is approximately 6 °C, the mean annual surface temperature. Figure 2c shows the vertical temperature profile through epikarst, vadose zone and phreatic zone. The water then flows through vertical shafts very rapidly so that no equilibration between water and rock temperature takes place. Therefore recharge water always reaches the aquifer with a temperature of less than 9°C which is the approximate background temperature of the aquifer. Renner & Sauter (1997) used this conceptual model to calculate input temperatures for a heat transport model in the karst aquifer. This model accounts for heat convection within the conduit system and for heat conduction processes between conduit water and rock matrix. By assuming an equivalent fracture (Figure 3), i.e. a fracture that represents the volume and the rock-water contact area of the conduit system, the model could successfully predict the temperature change after the June 1988 storm event (Figure 4). According to the model assumptions the storage processes could not be distinguished by that model because heat transfer linked to the exchange flux between the conduit and the fissured system was neglected.

 

3 HEAT BALANCE

 

3.1 CONCEPT

The heat balance approach employed below also takes into account the convective heat exchange from the conduit into the fissured system as well, i.e. all the important heat transport mechanisms. This strategy also allows the comparison between the two storage models analysing data of a single event.

 

Heat transfer is determined by the conductive heat flux into the rock matrix

 

(1)

 

with as the heat conductivity, A the interfacial area and the temperature gradient into rock matrix and the convective heat flux determined by the water flow through the conduit system,

 

(2)

 

with Q as the water flux, c the heat capacity of the water, is the water density and as the imposed temperature difference transported by the water. The respective quantity of heat can be obtained by integrating over the event duration t₀ or by approximation of the respective averaged heat flux

 

(3)

 

The event duration t₀ is defined as the time from onset of the recharge event until pre-event conditions after the storm event.

 

The heat balance can be formulated as

 

, (4)

 

where W_out is the integral heat quantity at spring outlet, W_in is the integral heat input from recharge and W_loss is the quantity of heat consisting of the heat conduction into the rock matrix and the heat convection from the conduits to the fissured system for the overall aquifer. Using averaged heat quantities for the duration of a recharge event this balance can be transformed to

 

(5)

 

Replacing the heat fluxes by their definitions (eq. 1 and 2) and eliminating the event duration t₀ yields

 

(6)

 

All quantities such as the spring discharge Q_out, the recharge Q_in, the exchange flux Q_ex , temperature difference at the spring , the temperature difference of the recharge water , the temperature difference of the exchange flux and the temperature gradient into the rock matrix are averages over the event duration t₀. Furthermore, is a spatial average for the whole aquifer.

 

The water heat capacity c, the water density and the rock heat conductivity are known parameters. The averaged spring discharge Q_out, and the averaged spring temperature difference can be derived from measurements. The recharge to the conduit network Q_in can be estimated from meteorological data for the different storage models. The input temperature difference is assumed to be the difference in the mean epikarst and groundwater temperature. If it is assumed that the bulk of exchange flux occurs near the input region it can be concluded that there is no significant temperature decrease between conduit water and exchange flux, i.e. = . Taking the interfacial area from the results of Renner & Sauter (1997), then the only unknown quantities are the temperature gradient and the exchange flux Q_ex.

 

Applying a similar heat balance to the heat transfer approach of Renner & Sauter (1997) eq. 6 simplifies to

 

(7)

 

Renner & Sauter (1997) postulate that the influx to the conduits equals the spring discharge Q_in = Q_out. The input temperature difference was a calibration target. Using their results the only unknown quantity is the temperature gradient .

 

Since a further assumption is applied for the temperature gradients and in the two approaches, the combination of eq. 6 and 7 leads to the estimation of the exchange flux Q_ex for different storage process distinguished by different values for the conduit inflow Q_in

 

(8)

 

Two extreme assumptions concerning the temperature gradients can be made. For the case of heat transfer by heat conduction alone, heat conduction into the rock matrix can be neglected and the temperature gradient vanishes, i.e. = 0. That means there are no temperature changes in the rock matrix. The other extreme is that the exchange flux does not affect the heat conduction and both temperature gradients are equal = .

 

3.2 APPLICATION TO EVENT OF JUNE 1988

This heat balance concept was applied to the recharge event of June 1988 to estimate the exchange flux and to evaluate the appropriate conceptual model for the recharge and the linked storage process. The averaged quantities were estimated from the recharge, discharge and spring temperature time series (Figure 1) and summarised in the following listing:

 

-         recharge (epikarst storage) Q_in = 0,022 m³/s

-         recharge (aquifer storage) Q_in = 0,276 m³/s

-         spring discharge Q_out = 0,252 m³/s

-         input temperature difference (epikarst storage) = 3°C

-         input temperature difference (aquifer storage) = 3°C

-         input temperature difference (calib., Renner & Sauter, 1997) = 1.7°C

-         spring temperature difference = 0.07°C

 

Using these values, the two extreme assumptions for the temperature gradients yield the following exchange fluxes (eq. 8) in the case of epikarst storage:

 

Q_ex = 0,016 m³/s = 73 % Q_in for = 0

Q_ex = - 0,121 m³/s for =

 

In the case of aquifer storage the estimations for this flux are

 

Q_ex = 0,270 m³/s = 98 % Q_in for = 0

Q_ex = 0,133 m³/s = 48 % Q_in for =

 

Two major results were obtained. First, considering the conceptual model of epikarst storage either in contradiction to the assumption a large amount of the recharged groundwater to the conduit network flows into the fissured system or there need to be a groundwater flow from the fissured system to the conduit network, implied by the negative sign, carrying approximately half of the input temperature difference. Also this is not convincing to the fact that the groundwater flows slowly within the fissured system and that there is enough time for temperature adaptation.

 

Second, the quantity of recharged groundwater that is stored in the fissured system could be estimated from the heat transfer using the aquifer storage concept. Applying this concept the loss of heat to the rock matrix could not only be transferred by heat conduction alone. The role of heat conduction in that case could be evaluated by comparison with the rise of the groundwater table close to the conduit network.

 

4 CONCLUSION

A main detail in the overall understanding of the transport processes in karst aquifers are the recharge and the linked storage processes. Recent works in the Gallusquelle catchment area include field investigations, groundwater flow modelling with respect to the dual permeability dual porosity approach and heat transport modelling. In the presented paper additionally a simple heat balance concept was introduced to evaluate two conceptual models for the storage of recharged groundwater either in the epikarst or in the aquifer itself. The application of this heat balance to the recharge event in June 1988 shows that the role of the epikarst is not the complete storage of recharge water because there is some evidence to significant groundwater exchange between the conduits and the fissured system. Further detailed studies of the heat transfer processes are necessary and have to be combined with a detailed interpretation of groundwater level changes.

 

REFERENCES

Kiraly, L., 1975. La régularisation de l`Areuse (Jura Suisse), simulée par modèle mathematique. In: A. Burger & L. Dubertret, (eds.) Hydrogeology of Karstic Terraines, Int. Cont. To Hydrogeology, Heise, Hannover, 94-99.

Liedl, R., Renner, S. & Sauter, M., 1997. Obtaining information on fracture geometry from heat flow data. Proc. 12th International Congress of Speleology, Switzerland. Vol. 2, 6th Conference on Limestone Hydrology and Fissured Media. 153-156.

Mohrlok, U. & Sauter, M., 1997. Modelling groundwater flow in a karst terrane using discrete and double-continuum approaches: importance of spatial and temporal distribution of recharge. Proc. 12th International Congress of Speleology, Switzerland. Vol. 2, 6th Conference on Limestone Hydrology and Fissured Media. 167-170.

Renner, S. & Sauter, M., 1997. Heat as a natural tracer: Characterisation of a conduit network in a karst aquifer using temperature measurement of the spring water. In: Günay, G. & Johnson, A.I. (eds.), Proc. 5th International Symposium and Field Seminar on Karst waters & environmental impacts, Antalya, Turkey. 423-431.

Sauter, M., 1991. Assessment of hydraulic conductivity in a karst aquifer at local and at regional scale. Proc. Third Con­ference­ on Hydrogeology, Ecology, Monitoring and Management of Ground Water in Karst Terranes, Dec. 1991, Nash­ville.

Sauter, M., 1992. Quantification and forecasting of regional groundwater flow and transport in a karst aquifer (Gallusquelle, Malm, SW Germany). Tübinger Geowissenschaftliche Arbeiten, C13, 150p.

 

 

Figure 1: Time series of hydraulic and physico-chemical parameters of spring water of a typical recharge event in the Gallusquelle karst aquifer catchment (Sauter, 1992)

 

 

Figure 2: Schematic representation of the conceptualisation of the epikarst and the aquifer storage model. Figure 2c represents the temperature profile through epikarst, vadose and phreatic zone, providing some support for the epikarst model (see text).

 

 

Figure 3: Conceptual model of the equivalent fracture model, used for simulating heat transport in a karst conduit system (Renner & Sauter, 1997)

 

 

Figure 4: Comparison between observed and simulated temperature difference, as compared to pre-event background temperature for the recharge event of June 1988.