A new model of groundwater flow within an unconfined aquifer: Application of Caputo-Fabrizio fractional derivative

Abstract Randublatung groundwater basin is one of the groundwaters basins with massive utilization of groundwater pumping. However, the knowledge of the comprehensive hydrogeological system in this groundwater basin is limited, so this research aims to determine a comprehensive hydrogeological conceptual model of the Randublatung groundwater basin. The methodology was conducted by collecting secondary and primary data of deep and shallow wells to evaluate boundaries of pattern and direction of groundwater flow and develop the aquifer system’s geometry. The result shows that the groundwater flow boundaries are Grogol River in the west, Wado River in the East, Bengawan Solo river in the South as a river boundary, and Rembang Mountains in the North as a constant head boundary. Therefore, groundwater flows from the hills area to the Bengawan Solo River and the north as the river’s flow. Based on the log bor evaluation, the aquifer system of the study area consist of an unconfined aquifer with a maximum thickness of 20 m and three layers of confined aquifers with thickness vary between 8 to 60 m. the hydraulic conductivity of the aquifers depends on the aquifer’s lithology range from sand, gravel, limestone, and sandstone. This hydrogeological conceptual model provides essential information for numerical groundwater models in the middle of the Randublatung groundwater basin.

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Variation of Groundwater Flow Caused by Any Spatiotemporally Varied Recharge

Water ◽

10.3390/w12010287 ◽

2020 ◽

Vol 12 (1) ◽

pp. 287

Author(s):

Ming-Chang Wu ◽

Ping-Cheng Hsieh

Keyword(s):

Analytical Solution ◽

Groundwater Flow ◽

Unconfined Aquifer ◽

Initial Water ◽

The Past ◽

Sloping Aquifer ◽

Taichung City ◽

Spatially Distributed ◽

Recharge Rates ◽

Rainfall Recharge

The objective of this study was to develop a complete analytical solution to determining the effect of any varying rainfall recharge rates on groundwater flow in an unconfined sloping aquifer. The domain of the unconfined aquifer was assumed to be semi-infinite with an impervious bottom base, and the initial water level was parallel to the impervious bottom of a mild slope. In the past, similar problems have been discussed mostly by considering a uniform or temporally varying recharge rate, but the current study explored the variation of groundwater flow under temporally and spatially distributed recharge rates. The presented analytical solution was verified by comparing its results with those of previous research, and the practicability of the analytical solution was validated using the 2012 and 2013 data of a groundwater station in Dali District of Taichung City, Taiwan.

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Modeling Groundwater Flow in an Unconfined Aquifer in an Alluvial Fan

Groundwater Updates ◽

10.1007/978-4-431-68442-8_46 ◽

2000 ◽

pp. 277-282

Author(s):

Ali M. Elhassan ◽

Akira Goto ◽

Masakazu Mizutani

Keyword(s):

Groundwater Flow ◽

Unconfined Aquifer ◽

Alluvial Fan

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Approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer

Hydrology and Earth System Sciences ◽

10.5194/hess-20-55-2016 ◽

2016 ◽

Vol 20 (1) ◽

pp. 55-71 ◽

Cited By ~ 8

Author(s):

C.-S. Huang ◽

J.-J. Chen ◽

H.-D. Yeh

Keyword(s):

Groundwater Flow ◽

Integral Transform ◽

Three Dimensional ◽

Vertical Component ◽

Hydraulic Head ◽

Unconfined Aquifer ◽

Specific Yield ◽

Specific Storage ◽

Sink Term ◽

Radial Collector Well

Abstract. This study develops a three-dimensional (3-D) mathematical model for describing transient hydraulic head distributions due to pumping at a radial collector well (RCW) in a rectangular confined or unconfined aquifer bounded by two parallel streams and no-flow boundaries. The streams with low-permeability streambeds fully penetrate the aquifer. The governing equation with a point-sink term is employed. A first-order free surface equation delineating the water table decline induced by the well is considered. Robin boundary conditions are adopted to describe fluxes across the streambeds. The head solution for the point sink is derived by applying the methods of finite integral transform and Laplace transform. The head solution for a RCW is obtained by integrating the point-sink solution along the laterals of the RCW and then dividing the integration result by the sum of lateral lengths. On the basis of Darcy's law and head distributions along the streams, the solution for the stream depletion rate (SDR) can also be developed. With the aid of the head and SDR solutions, the sensitivity analysis can then be performed to explore the response of the hydraulic head to the change in a specific parameter such as the horizontal and vertical hydraulic conductivities, streambed permeability, specific storage, specific yield, lateral length, and well depth. Spatial head distributions subject to the anisotropy of aquifer hydraulic conductivities are analyzed. A quantitative criterion is provided to identify whether groundwater flow at a specific region is 3-D or 2-D without the vertical component. In addition, another criterion is also given to allow for the neglect of vertical flow effect on SDR. Conventional 2-D flow models can be used to provide accurate head and SDR predictions if satisfying these two criteria.

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Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time

Earth System Dynamics ◽

10.5194/esd-11-1-2020 ◽

2020 ◽

Vol 11 (1) ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

M. Levent Kavvas ◽

Tongbi Tu ◽

Ali Ercan ◽

James Polsinelli

Keyword(s):

Groundwater Flow ◽

Governing Equation ◽

Water Flux ◽

Unconfined Aquifer ◽

Saturated Porous Media ◽

Unconfined Aquifers ◽

Heavy Tailed ◽

Consistent Equation ◽

Fractional Dimensions ◽

Fractional Space

Abstract. In this study, a dimensionally consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For the equation of groundwater motion within a multi-fractional multidimensional unconfined aquifer, a previously developed dimensionally consistent equation for water flux in unsaturated/saturated porous media is combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. Combining the fractional continuity and groundwater motion equations, the fractional governing equation of transient unconfined aquifer flow is then obtained. Finally, two numerical applications to unconfined aquifer groundwater flow are presented to show the skills of the proposed fractional governing equation. As shown in one of the numerical applications, the newly developed governing equation can produce heavy-tailed recession behavior in unconfined aquifer discharges.

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