but they did note the possibility of accounting for it in principle by incorporating their uncoupled drainage function in the solution of @moench1997, which considers a partially penetrating well of finite radius.

[@tartakovskyneuman2007] similarly combined the confined aquifer flow equation , but with the original axis-symmetric form of considered by @kroszynskidagan1975. Also like @kroszynskidagan1975, their unsaturated zone was characterized by a single exponent $\kappa_a=\kappa_k$ and reference pressure head $\psi_a=\psi_k$. Unlike @kroszynskidagan1975 and @mathiasbutler2006, [@tartakovskyneuman2007] assumed an infinitely thick unsaturated zone.

[@tartakovskyneuman2007] demonstrated flow in the unsaturated zone is not strictly vertical. Numerical simulations by @moench2008 showed groundwater movement in the capillary fringe is more horizontal than vertical. [@mathiasbutler2006] and @moench2008 showed that using the same exponents and reference pressure heads for effective saturation and relative permeability decreases model flexibility and underestimates $S_y$. @moench2008 predicted an extended form of @tartakovskyneuman2007 with two separate exponents, a finite unsaturated zone, and wellbore storage would likely produce more physically realistic estimates of $S_y$.

[@mishraneuman2010] developed a new generalization of the solution of [@tartakovskyneuman2007] that characterized relative hydraulic conductivity and water content using $\kappa_a \neq \kappa_k$, $\psi_a
\neq \psi_k$ and a finitely thick unsaturated zone. @mishraneuman2010 validated their solution against numerical simulations of drawdown in 