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 i 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 flow 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 solve 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.