An analytical solution for non-Darcian flow in a confined aquifer using the power law function

By Z. Wen, Hongbin Zhan. Advances in Water Resources, 2008

72 citations recorded by the source corpus.

Abstract We have developed a new method to analyze the power law based non-Darcian flow toward a well in a confined aquifer with and without wellbore storage. This method is based on a combination of the linearization approximation of the non-Darcian flow equation and the Laplace transform. Analytical solutions of steady-state and late time drawdowns are obtained. Semi-analytical solutions of the drawdowns at any distance and time are computed by using the Stehfest numerical inverse Laplace transform. The results of this study agree perfectly with previous Theis solution for an infinitesimal well and with the Papadopulos and Cooper’s solution for a finite-diameter well under the special case of Darcian flow. The Boltzmann transform, which is commonly employed for solving non-Darcian flow problems before, is problematic for studying radial non-Darcian flow. Comparison of drawdowns obtained by our proposed method and the Boltzmann transform method suggests that the Boltzmann transform method differs from the linearization method at early and moderate times, and it yields similar results as the linearization method at late times. If the power index n and the quasi hydraulic conductivity k get larger, drawdowns at late times will become less, regardless of the wellbore storage. When n is larger, flow approaches steady state earlier. The drawdown at steady state is approximately proportional to r1−n, where r is the radial distance from the pumping well. The late time drawdown is a superposition of the steady-state solution and a negative time-dependent term that is proportional to t(1−n)/(3−n), where t is the time.

Subfields: Environmental Engineering, Mechanical Engineering, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/dbd459ab964ac5b252dbd3e6320e4a1206e56ef3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Environmental Engineering

1. Yuedong Yao
2. M. Sedghi-Asl
3. H. Rahimi
4. J. Ge
5. R. Salehi

In Mechanical Engineering

1. Yuedong Yao
2. M. Sedghi-Asl
3. H. Rahimi
4. J. Ge
5. R. Salehi

In Ocean Engineering

1. Yuedong Yao
2. J. Ge

Citations in the corpus

• Non-Darcy Flow of Water Through a Packed Column Test (2013, background): “The Izbash equation has been investigated in several other studies (see Yamada et al. 2005; Wen et al. 2006, 2008a).”
• Characteristics of non-Darcy flow in low-permeability reservoirs (2011, methodology): “By using the power function of the Izbash equation (Wen et al, 2008), a single power function was used in the equation of the whole flow regime.”