Evaluation of modified Hantush's function

TL;DR

This paper introduces a modified Hantush function for heat conduction modeling that accounts for groundwater flow, providing exact and approximate formulas useful for designing borehole systems and analyzing aquifers.

Contribution

It presents a new modified Hantush function E, with exact and approximate expressions, for improved modeling of heat conduction with groundwater flow effects.

Findings

High accuracy of approximations verified against exact values.

Approximate formulas are suitable for different parameter regimes.

Potential applications in borehole design and aquifer analysis.

Abstract

It is pointed out that Hantush's \emph{M} function, commonly used in groundwater pumping modeling, is identical to the function known in the problems of heat conduction in the ground. A modified Hantush function $E$ used in the steady-state solutions for heat conduction that take into account advection due to groundwater flow around borehole heat exchangers (BHEs) is introduced. New exact representation and two-types of approximate expressions for this two-parametric function \emph{E} are presented: one is suitable for small values of a parameter and the other for its large values. High accuracy of the approximate formulae is verified by comparison with the exact values provided by modified Hantush's function $E$ in those validity domains. These analytical expressions can be used for designing complex borehole configurations and may be potentially useful in steady-state analysis of partially penetrated wells (PPWs) in leaky aquifer.