Comment on “Analytical solution incorporating nonlinear radial flow in confined aquifers” by Zekâi Şen

Abstract

A constant discharge Q was used in the simulation ran. For each time the radi• distance was varied in the definition of the dimensionless time factor u, which is related to the Boltzmann variable. We readily obse•e that a co,elation

New Results on Transient Well Tests Analysis Considering Nonlaminar Flow in the Reservoir

“…Instead, we can derive an equivalent expression to Eq. 9 for the case of partial penetration, assuming that the thickness inside the skin zone is h p and that 1/r e [0 ; i.e., s Ȁ t * ƪ hkń ǒ h p k s Ǔ * 1 ƫ ln ǒ r s ńr w Ǔ * 1.6351 10 *16 òkqBń ǒ mh Ǔ ƪǒ b s h 2 ńh 2 p Ǔǒ 1ńr w * 1ńr s Ǔ ) bńr s ƫ [ 0 , (12) . .…”

“…However, under nonlaminar flow conditions, Boltzmann transformation cannot be used in general to correlate pressure and/or velocity. 12 This work analyzes the problem of non-Darcy flow as one of variable permeability and at the same time as a perturbation of the corresponding laminar flow problem. In this way, using the solution pro-posed by Oliver, 13 a solution to the transient nonlaminar flow problem is obtained.…”

Recent advances in modeling of well hydraulics

“…The analytical solutions for transient non-Darcian flow developed based on the Forchheimer equation and Boltzmann transform was first presented by Sen [336,337] for an infinitesimal well and later by Sen [101] for large-diameter wells in confined aquifers. However, Camacho-V. and Vasquez-C. [338] questioned the validity of using Boltzmann transform in solving the non-Darcian flow problems and considered those solutions as approximate solutions rather than analytical solutions. Based on the volumetric approach, Birpinar and Sen [339] developed an analytical solution for radial Forchheimer flow toward a fully penetrating and infinitesimally small diameter well in leaky aquifers.…”

Forchheimer flow to a well-considering time-dependent critical radius

“…The third is that the solution of Sen (1988) does not agree with the new solution near the well at the early time. This is probably because of the Boltzmann transform method used by Sen (1988) to deal with the non-Darcian flow at the early time, which has been discussed in several previous studies (Camacho and Vasquez, 1992;Wen et al, 2008b). (Mathias et al, 2008), the two-region flow model (Sen, 1988), and the new model in early pumping stage.…”

“…For example, Sen (1990Sen ( , 2000 employed the Boltzmann transform method to analytically solve the problems related to the nonDarcian flow. This method was showed to be problematic, since both initial and boundary conditions cannot be simultaneously transformed into a form only containing the Boltzmann variable (Camacho and Vasquez, 1992;Wen et al, 2008a). Wen el al.…”