Analytic solutions for interface flow in combined confined and semi-confined, coastal aquifers

Analytic solutions are presented for steady interface flow in aquifers consisting of a confined and a semi-confined section. The total discharge is constant in the confined section and is directed towards the semi-confined section, which is bounded on top by a leaky layer that separates the aquifer from the sea. All solutions are based on the Dupuit approximation. The interface position is fully determined by two dimensionless parameters. The first parameter is the product of the uniform gradient towards the sea and the dimensionless leakage factor divided by the dimensionless density difference. The second dimensionless parameter is the length of the semi-confined section divided by the leakage factor. Four types of flow are distinguished. For cases I and II the interface does not reach the end of the semi-confined section, while it does for cases III and IV. For cases I and III the interface extends into the confined section, while for cases II and IV it remains entirely in the semi-confined section. Analytic solutions are presented for the position of the interface for all four cases. Diagrams are presented to determine the type of flow and the position of the interface toe based on the two dimensionless parameters. The pre-development position of the interface along the Georgia coast is computed as an illustration of the practical application of the presented formulas. Another practical application is the estimation of how far a numerical model of seawater intrusion should be extended into the sea for accurate simulations.