A trigonometric interpolation approach to mixed-type boundary problems associated with permeameter shape factors

Abstract

[1] Hydraulic conductivity is a fundamental hydrogeological parameter, whose in situ measurement at a local scale is principally performed through injection tests from screened probes or using impermeable packers in screened wells. The shape factor F [L] is a proportionality constant required to estimate conductivity from observed flow rate to injection head ratios, and it depends on the geometric properties of the flow field. Existing approaches for determination of F are either based on geometric or mathematical simplifications and are limited to particular assumptions about the flow domain's external boundaries. The present work presents a general semianalytical solution to steady state axisymmetric flow problems, where external boundaries may be nearby and of arbitrary combinations of impermeable and constant head type. The inner boundary along the probe or well may consist of an arbitrary number of impermeable and constant head intervals resulting in a mixed-type boundary value problem, for which a novel and direct solution method based on trigonometric interpolation is presented. The approach is applied to generate practical nondimensional charts of F for different field and laboratory situations. Results show that F is affected by less than 5% if a minimum distance of 10 probe or well diameters is kept between the injection screen and a nearby boundary. Similarly, minimum packer lengths of two well diameters are required to avoid increasing F by more than 10%. Furthermore, F is determined for laboratory barrel experiments giving guidelines for achieving equal shape factors as in field situations without nearby boundaries. F for the theoretical case of infinitely short packers is shown to be infinitely large.