An Integral Transform Approach For A Mixed Boundary Problem Involving A Multilevel Slug Test In Confined Aquifer

The multilevel slug test is a kind of single-well hydraulic tests for thedetermination of the vertical distribution of hydraulic conductivity near the test well.The assumption of the uniform distribution of groundwater pressure head (uniformhead, hereinafter referred to as UH) along the test section is more close to realisticexperimental condition because there is vertical flow distribution which exists nearthe test section. However, this assumption creates a mixed boundary problem thatthere are two types of boundary on the border of the test well: a uniform headcondition is prescribed along the test section length and an impermeable boundarycondition is stipulated over the remaining part. In general, the mixed boundaryproblem cannot be directly solved by the integral transform method. This studyderives the semi-analytical solution at the Laplace domain of such a mixed boundaryproblem for the multilevel slug test in a confined aquifer by the Laplace transform andfinite Fourier cosine transform. In this method, the screen of the test section is evenlydiscretized into a finite number of segments, and each segment maintains the samegroundwater head but different wellbore flux. Then, the uniform head boundary isreplaced by a corresponding Neumann boundary in terms of wellbore flux that variesalong the test section, which means the mixed boundary is changed into ahomogeneous Neumann boundary. The modified model containing this homogeneousNeumann boundary can be solved by integral transform method. In addition, theuniform head boundary along the test section should be coupled with the groundwatermomentum conservation equation in test well when dealing with the oscillating reaction in the high permeability aquifer.After the semi-analytical solutions in low and high permeability confined aquiferare derived by UH method, writing the MATLAB code and the semi-analyticalsolution can be converted to numerical solution by inverse Laplace conversion via theinvlap.m program. Comparing the UH method with the model assumed that theuniform flux distributes along the test section (uniform flux，referred to as UF), theinfluence of the partially penetrating ratio and the aspect ratio on the difference of thetwo methods are discussed and it is analyzed that the UF method ignore the rechargeof the vertical flow of the upper and lower edge of the test section which leads to thedifference. The application scope of UH method is determined. The wellbore fluxdistribution along the test section and the groundwater flow field distribution near thetest well are obtained accurately by the UH method. The parametric sensitivity of thespecific storativity and the location of the test section are analyzed in the UH method,the influence mechanism of the two parametric are discussed at the same time.In the study, the field data of the multilevel slug test at the sites in FooyinUniversity, Kaohsiung, Taiwan are fitting by UH method to determine the hydraulicconductivity. The practicality of the UH method is verified.Compared the results tothe UF method, the relationship among the partially penetrating ratio, the aspect ratioand the deviation between the two method is discussed.