### Abstract

A new analytical solution of the flow equation has been developed to estimate the time to reach a near-equilibrium state in mixed aquifers, i.e., having unconfined and confined portions, following a large hydraulic perturbation. Near-equilibrium is defined as the time for an initial aquifer perturbation to dissipate by an average 95% across the aquifer. The new solution has been obtained by solving the flow system of a simplified conceptual model of a mixed aquifer using Laplace transforms. The conceptual model is based on two assumptions: (1) the groundwater flow can be reduced to a horizontal 1-D problem and (2) the transmissivity, a function of the saturated thickness, is assumed constant on the unconfined portion. This new solution depends on the storativity of the unconfined portion, the lengths of the unconfined and confined portions and the transmissivity, assumed to be constant and equal in both portions of the mixed aquifer. This solution was then tested and validated against a numerical flow model, where the variations of the saturated thickness and therefore variations of the transmissivity were either ignored, or properly modeled. The agreement between the results from the new solution and those from the numerical model is good, validating the use of this new solution to estimate the time to reach near-equilibrium in mixed aquifers. This solution for mixed aquifers, as well as the solutions for a fully confined or fully unconfined aquifer, has been used to estimate the time to reach near-equilibrium in 13 large aquifers in the world. For those different aquifers, the time to reach near-equilibrium ranges between 0.7 kyr to 2.4 × 10
^{7}
kyr. These results suggest that the present hydraulic heads in these aquifers are typically a mixture of responses induced from current and past hydrologic conditions and thus climate conditions. For some aquifers, the modern hydraulic heads may in fact depend upon hydrologic conditions resulting from several past climate cycles. Key Points New analytical solution to assess time to reach equilibrium in mixed aquifers Current hydraulic heads may be a complex mixture of past and present climate Some large aquifers may have never been in steady state since their formation

Original language | English |
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Pages (from-to) | 6893-6908 |

Number of pages | 16 |

Journal | Water Resources Research |

Volume | 49 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2013 |

### Keywords

- analytical solution
- mixed aquifers
- time constant
- transient state

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## Cite this

*Water Resources Research*,

*49*(10), 6893-6908. https://doi.org/10.1002/wrcr.20534