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dc.contributor.authorTrivedi, Niranjan Markandray-
dc.date.accessioned2014-09-24T10:48:44Z-
dc.date.available2014-09-24T10:48:44Z-
dc.date.issued2010-
dc.identifierPh.Den_US
dc.identifier.urihttp://hdl.handle.net/123456789/1682-
dc.guideKashyap, Deepak-
dc.description.abstractAxis-symmetric radial flow towards a pumping well in an unconfined aquifer is usually modeled by the saturated flow approach which deems the flow domain to be bounded on the top by a falling water table whose position at advancing times is unknown a priori. Further the boundary condition at the falling water table is required to simultaneously account for i) accretion over it comprising the delayed gravity drainage from the overlying unsaturated zone, and ii) pressure prevailing over it being atmospheric. Consequently, the flow is modeled under a variety of simplifications like: Dupuit Forchheimers' assumptions, time invariant flow domain, negligible water table slope, instantaneous release from storage (Neuman, 1974) and exponentially varying gravity drainage (Boulton, 1963 and Moench et al., 2001), etc. In the present study, a model is developed based on variably saturated flow approach which avoids the simplifications/assumptions mentioned above. The approach comprises modeling of flow in the entire formation thickness extending from the ground surface to the lower impermeable layer of the unconfined aquifer. Thus, the unsaturated flow occurring above the water table and saturated flow below it are simultaneously modeled. This excludes the above mentioned uncertainties related to domain variation and the boundary condition over the falling water table. In fact in the adopted modeling approach, positions of the falling watertable at advancing times and the accretions over it are out puts from modeling i.e., auxiliary state variables. The model also accounts for the well bore storage. As such in the present study this model is invoked to evaluate/study other models (Neuman, 1974 and Moench et al., 2001) enumerated above. The model developed in this study is based on a numerical solution of the nonlinear partial differential equation governing variably saturated axis-symmetric twodimensional (r-z plane) unconfined flow (VARUN) in a porous medium. Well bore storage effect is included while assigning the boundary condition at the well face. Commencing from an assigned initial piezometric head distribution, the model computes the head distribution at advancing times as the pumping from the well continues. The governing differential equation is solved numerically by the finite difference method invoking the constitutive functional relationships i.e., h{0) and K(9). The non-linear terms of the governing equation are linearized using a Picard iteration scheme and resulting algebraic equations are solved by alternative direction implicit explicit scheme. Further, the Picard iterations are designed to account for the well bore storage in the boundary condition at the well face. The computed, piezometric head distributions are further processed to arrive at the following auxiliary state variables at the advancing times: i) The moisture content distributions ii) Position of the water table iii) Vertical accretions over the falling water table iv) Volume of the drawdown cone and iv) Mass balance errors. The reported data from the unconfined aquifer tests of Cape Cod (Moench et al., 2001) and the Borden (Nwankwor et al., 1984, 1992 and Bevan et al., 2005) are used for the verification. In general the model computed drawdowns and moisture contents match fairly well with the reported data. The assumptions inherent in saturated flow modeling approach are evaluated by conducting numerical experiments on the model developed herein under various geometric/hydraulic conditions. The assumptions (particularly the stipulation of instantaneous gravity drainage, negligible slope ofthe water table and time-invariant flow domain) ofthe Neuman model (1974) are evaluated. The drawdowns obtained from VARUN and Neuman model [computed using computer code WTAQ (Barlow and Moench, 1999)] are compared under various geometric/hydraulic conditions. It is found that at intermediate times Neuman model underestimates the drawdowns apparently due to the delayed gravity drainage effect. At the latter times, the Neuman model overestimates the drawdowns possibly due to assumptions like time-invariant flow domain and no horizontal flow over the falling water table. These deviations are found to be more pronounced in the vicinity of the water table and under larger anisotropy. Conditions under which the Neuman model may be well-applicable are identified. A general delayed drainage concept (Moench, 2004) incorporates multiple delayed drainage parameters to quantify delayed vertical accretion over a falling water table. Time series of the accretion rates over the falling water table obtained under different geometric/hydraulic conditions are obtained from VARUN. These time series are subsequently invoked to arrive at the optimal model structures (i.e., optimal number of ii the indices) and the corresponding a 's by minimizing the squares of the residues and applying F statistic. Where as in general the 2-parameter Moench model (i.e., with two delayed drainage parameter) is found to be optimal, 1-parameter Moench model is found to be good enough under certain geometric/hydraulic conditions. A sensitivity analysis in respect of the estimated delayed drainage parameters indicate that the parameters are generally intensely sensitive to the medium (indexed in the analysis by the constitutive parameters and the vertical anisotropy), and not as sensitive to other variables like radial distance, well penetration and pumping rate. The conditions under which the above derived pattern of sensitivity does not hold have also been identified. The accretions corresponding to the optimized structures/parameters are subsequently imposed over the 1/2-Moench parameter models to compute the drawdown series. These drawdowns are compared with the corresponding VARUN produced drawdowns. The drawdown series generally match closely except for a few experiments characterized by high well penetration and low pumping discharge. inen_US
dc.language.isoenen_US
dc.subjectCIVIL ENGINEERINGen_US
dc.subjectFLOW TOWARDS MODELLINGen_US
dc.subjectFALLING WATERen_US
dc.subjectPUMPING WELLen_US
dc.titleMODELING OF UNCONFINED FLOW TOWARDS A PUMPING WELLen_US
dc.typeDoctoral Thesisen_US
dc.accession.numberG20653en_US
Appears in Collections:DOCTORAL THESES (Civil Engg)

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