Numerical simulation of pumping tests in multilayer wells with non-Darcian flow in the wellbore

An important feature of pumping in a multilayer system is the dynamic interaction between the aquifers via non-Darcian vertical flow within the wellbore, An equivalent hydraulic conductivity (EHC) approach is used to include this transient interaction as a special leakage through the confining layer in the flow system. Different flow regimes (laminar and turbulent flows, and the transition range) are involved in a multilayer pumping test where the relation between the hydraulic gradient and flow velocity is complicated. The change of flow regimes is accommodated by varying the content of EHC as a function of the friction factor. For a particular well, the relation between friction factor and Reynolds number is unique and is obtained by interpolating Nikuradse's experimental results. A quasi-three-dimensional Galerkin finite-element method is used to integrate the vertical one-dimensional now in the wellbore and confining layers and the two-dimensional flow in the aquifers, This approach makes it possible to couple the aquifer and wellbore flows of different flow regimes and to salve them in a single numerical framework based on the same linear relation between gradient and velocity. A carefully designed pumping test in a multilayer aquifer system near Beihai City, Guangxi Autonomous Region, China, is used to demonstrate the performance of the approach.