Modelling exchanges between karst conduits and fractured matrix

A karst aquifer can be conceptualized as two interacting hydraulic domains:

• Karst conduit network: highly permeable structures that facilitate rapid groundwater flow and drainage.
• Fractured rock matrix: a much larger storage domain, where groundwater flow is generally slower and can be represented using an equivalent Darcy-type approach.

The hydraulic exchanges between these two domains are driven by differences in hydraulic head. Their relative contributions control the aquifer response to pumping and the evolution of groundwater levels within the system. This response also depends on the location of the pumping well into the heterogeneous aquifer (PWa or PWb on the figure here below).

Quantifying exchanges between conduits and fractured matrix: the Cent-Fonts karst system

A long-duration pumping test was conducted in the main karst conduit of the Cent-Fonts system (PWa on figure here below). Pumping was maintained at a constant rate of 400 L/s for approximately one month, resulting in the complete cessation of spring discharge. A double-continuum model was developed to simulate the hydraulic response of the conduit network and the surrounding fractured matrix.

The model reproduced the observed drawdown in the conduit with a relative root mean square error of 2.3%.

The modelling results showed that:

• The fractured matrix plays a major role in controlling the hydraulic response to pumping.
• The karst conduit network behaves as a drainage system, receiving groundwater from the surrounding fractured matrix.
• The capacitive effect of the conduits, associated with the drainage of water-filled conduit sections, also contributes to the observed response.
• Matrix-to-conduit exchanges become particularly important at longer pumping times.

This approach provides a way to quantify exchanges between the two hydraulic domains and improve the interpretation of long-duration pumping tests.

Diagnostic plots applied to pumping tests in karst systems

The interpretation of pumping tests in karst aquifers is challenging because the measured hydraulic response results from the successive contributions of different hydraulic compartments.

The diagnostic plot method, based on the logarithmic derivative of drawdown, makes it possible to identify successive flow regimes and relate them to the hydraulic structures involved.

Depending on the aquifer configuration, the diagnostic plots can reveal:

• Conduit storage: an initial response controlled by water stored in the karst conduit.
• Bilinear flow: simultaneous flow within the conduit and the surrounding fractured matrix.
• Linear flow: groundwater transfer from the fractured matrix towards a major drainage structure.
• Pseudo-radial flow: a response associated with the contribution of the surrounding matrix at longer pumping times.
• Additional karst structures: the delayed contribution of another conduit or major karst cavity.

The method provides a framework for interpreting the hydraulic response of complex karst systems beyond conventional homogeneous aquifer models.

Identifying hydraulic connections between karst compartments

The diagnostic plot approach was applied to pumping tests in the Robol well (PWb location), in the Bas-Agly karst system (Corbières, France). The well intersects a small karst conduit at approximately 420 m depth.

The analysis revealed successive hydraulic regimes:

1. An initial bilinear flow regime involving the small conduit and the surrounding fractured matrix.
2. A subsequent contribution from the fractured matrix.
3. The delayed hydraulic contribution of a major karst cavity or conduit.

The interpretation was further supported by electrical conductivity measurements. During the test, the conductivity increased sharply, reaching approximately 960 µS/cm, indicating the contribution of more mineralized groundwater from the matrix. It subsequently decreased towards the conductivity of the conduit water (≤750 µS/cm), coinciding with the contribution of another karst volume.

These observations illustrate how hydraulic derivatives and water-quality monitoring can be combined to identify exchanges and hydraulic connections between different karst compartments.

What pumping tests reveal about karst aquifers

These studies demonstrate that pumping tests can provide much more than estimates of conventional aquifer parameters. When interpreted using appropriate conceptual and analytical approaches, they can help to:

• Identify the hydraulic compartments contributing to groundwater flow.
• Distinguish conduit-controlled and matrix-controlled flow regimes.
• Characterize hydraulic exchanges between conduits and fractured rock.
• Detect connections between distinct karst structures.
• Improve the conceptual understanding of aquifer functioning.

Combining numerical modelling, diagnostic plots and complementary field measurements offers a more comprehensive understanding of groundwater dynamics in karst aquifers.

Related publications

Version française - pompages d'essai en aquifère karstique