Abstract
Abstract. Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally consistent equation is also developed. The governing equation of transient saturated groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained by combining the fractional continuity and water flux equations. To illustrate the capability of the proposed governing equation of groundwater flow in a confined aquifer, a numerical application of the fractional governing equation to a confined aquifer groundwater flow problem was also performed.
Highlights
Previous laboratory and field studies (Levy and Berkowitz, 2003; Silliman and Simpson, 1987; Peaudecerf and Sauty, 1978; Sidle et al, 1998; Sudicky et al, 1983) demonstrated substantial deviations from Fickian behavior in transport in subsurface porous media
The abovementioned studies focused on the fractional differential equation modeling of solute transport in fractional time and space, and not on the modeling of the underlying subsurface flows that transport the solutes
As shown by Kim et al (2014), non-Fickian behavior in transport can be obtained if the underlying flow field has a long memory in time, which can be described by a time-fractional governing equation of the specific flow field (Ercan and Kavvas, 2014, 2016)
Summary
Previous laboratory and field studies (Levy and Berkowitz, 2003; Silliman and Simpson, 1987; Peaudecerf and Sauty, 1978; Sidle et al, 1998; Sudicky et al, 1983) demonstrated substantial deviations from Fickian behavior in transport in subsurface porous media. 2 Derivation of the continuity equation for transient groundwater flow in a multi-fractional confined aquifer in fractional time
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
