New analytical model for constant-head pumping: Considering rate-dependent factor at well screen

Advanced Analytical Model for Interpreting Oscillatory Pumping Tests With Wellbore Skin and Rate‐Dependent Skin Effects

“…To include the rate‐dependent skin effects, an additional condition is required (Lin & Yeh, 2020a): $$$h(r,t)-r\left({S}_{f}+D\vert Q(t)\vert \right)\frac{\partial h(r,t)}{\partial r}=H(t),\ r={r}_{w}$$$ in which S f is the skin factor [–] accounting for the formation damage at the interface between the wellbore surface and the aquifer, and DQ ( t ) is the rate‐dependent skin [–] representing the head loss caused by the high velocity at the screen with the rate‐dependent factor D [L −3 T]. In addition, the far‐field aquifer conditions are assumed to be unaffected by the OPT: $$$h(r,t)=0,\ r\to \infty $$$ …”

“…The operating pumping rate Q(t) can be defined as To include the rate-dependent skin effects, an additional condition is required (Lin & Yeh, 2020a):…”

“…This approach implies that flow in the entire aquifer system is non‐Darcian, which may not be reasonable even during pumping since flow further from the well is typically Darcian. Accordingly, Lin and Yeh (2020a) proposed an analytical framework accounting for non‐Darcian flow through the well screen boundary condition and found that non‐Darcian flow due to pumping at the well screen results in head loss, known as the rate‐dependent skin, that is proportional to the pumping rate and can affect aquifer parameter estimation.…”