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

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. Numerical modeling experts always say finely discretizing space as many nodes achieves accurate simulation of groundwater flow in aquifers. However, it takes unnecessary addition to computational cost with applying a large number of orthogonal nodes to discretize the circular rim of a well and the ring‐shaped skin zone around the well. The radius rwof a well is usually 0.1 m. The inner radius of the skin zone equals rw; the other outer radius rsusually falls in 1 m. Our example demonstrates the number of the orthogonal nodes is about 600 if rw= 0.1 m, rs= 1 m, and the well rim is discretized as four nodes, but the prediction of a conventional model is incorrect. This study introduces a new groundwater flow model. The model allows orthogonal 5 × 5 nodes to discretize a well rim and its surrounding skin zone, which is practical at low computational cost. This new model is applied to two field constant‐rate pumping tests in which a well extracts groundwater with a constant volumetric rate. Results suggest the predicted water level by the new model approaches the measured water level in the tests. The model may serve as a useful alternative for groundwater pumping and simulations. Two novel analytical models are proposed for flow due to constant rate pumping at a two‐zone double‐porosity confined aquiferOne model named as two‐zone model is built by applying flow equations to both skin and formation zonesA new source term is introduced in the other model, called as source‐term model, to reflect the effects of the skin and wellbore storage Two novel analytical models are proposed for flow due to constant rate pumping at a two‐zone double‐porosity confined aquifer One model named as two‐zone model is built by applying flow equations to both skin and formation zones A new source term is introduced in the other model, called as source‐term model, to reflect the effects of the skin and wellbore storage