The distributed-order fractional diffusion-wave equation of groundwater flow: theory and application to pumping and slug tests

Su, Ninghu, Nelson, Paul N., and Connor, Sarah (2015) The distributed-order fractional diffusion-wave equation of groundwater flow: theory and application to pumping and slug tests. Journal of Hydrology, 529 (Part 3). pp. 1262-1273.

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Abstract

We present a distributed-order fractional diffusion-wave equation (dofDWE) to describe radial groundwater flow to or from a well, and three sets of solutions of the dofDWE for flow from a well for aquifer tests: one for pumping tests, and two for slug tests. The dofDWE is featured by two temporal orders of fractional derivatives, b1 and b2, which characterise small and large pores, respectively. By fitting the approximate solutions of the dofDWE to data from slug tests in the field, we determined the effective saturated hydraulic conductivity, Ke, transmissivity, Tf, and the order of fractional derivatives, b2 in one test and b2 and b1 in the second test. We found that the patterns of groundwater flow from a well during the slug tests at this site belong to the class of sub-diffusion with b2 < 1 and b1 < 1 using both the short-time and large-time solutions. We introduce the concept of the critical time to link Ke as a function of b2 and b1. The importance of the orders of fractional derivatives is obvious in the approximate solutions: for short time slug tests only the parameter b2 for flow in large pores is present while for long time slug tests the parameters b2 and b1 are present indicating both large and small pores are functioning.

Item ID: 42303
Item Type: Article (Research - C1)
ISSN: 0022-1694
Funders: James Cook University, Department of Natural Resources and Mines (NRM), Australian Research Council (ARC), International Science & Technology Coorperation Project of China (ISTCPC), National Natural Science Foundation of China (NNSF)
Projects and Grants: ARC Linkage Project LP0669439, ISTRPC 2012DFB30030, NNSFC 41401539, NNSFC 11171281
Date Deposited: 03 Feb 2016 01:48
FoR Codes: 04 EARTH SCIENCES > 0406 Physical Geography and Environmental Geoscience > 040603 Hydrogeology @ 60%
01 MATHEMATICAL SCIENCES > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis @ 40%
SEO Codes: 96 ENVIRONMENT > 9611 Physical and Chemical Conditions of Water > 961103 Physical and Chemical Conditions of Water in Fresh, Ground and Surface Water Environments (excl. Urban and @ 50%
96 ENVIRONMENT > 9609 Land and Water Management > 960913 Water Allocation and Quantification @ 50%
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