New Analytical Solutions for Constant Rate Pumping in Two-Zone Double-Porosity Confined Aquifer: A New Source Term Reflecting Effects of Well Skin and Wellbore Storage

Abstract

This study develops two new analytical models for constant rate pumping at a partially penetrating well in a double-porosity confined aquifer, considering skin and formation zones. One model, referred to as the two-zone model, incorporates a flow equation to depict the flow in the skin around the well. The other model, named the source-term model, introduces a novel source term at the outer rim of the skin to reflect the effects of both the skin and wellbore storage. The analytical solutions for both models are derived by the Laplace transform and finite Fourier cosine transform. Additionally, a finite element solution for the source-term model is presented. Results suggest the source-term model is suitable to most wells when the width of the skin is less than 1 m and the radius of influence exceeds the outer rim of the skin. Temporal drawdown distribution for a negative skin exhibits a triple-humped shape with two flat stages, while that for a positive skin shows monotonous increase. The source-term model enables orthogonal 5 × 5 nodes for finite element approximation to discretize a well and its adjacent skin. The finite element solution aligns with early drawdown data measured at an observation well under the effects observed in two field constant rate pumping tests. In conclusion, this study introduces a novel approach to modeling two-zone flow, which may find practical utility in field applications.