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

IF 4.6 1区 地球科学 Q2 ENVIRONMENTAL SCIENCES Water Resources Research Pub Date : 2024-10-14 DOI:10.1029/2024wr037472
Chen Wang, Chenchen Tong, Hund-Der Yeh, Ching-Sheng Huang
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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.
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双区双孔隙承压含水层恒速抽水的新分析方案:反映井皮和井筒存储影响的新源项
本研究针对双孔隙承压含水层中部分贯入井的恒定抽水速率开发了两个新的分析模型,同时考虑了表皮区和地层区。其中一个模型被称为双区模型,包含一个流动方程,用于描述水井周围表层的流动情况。另一个模型被称为源项模型,在表皮外缘引入了一个新的源项,以反映表皮和井筒存储的影响。这两种模型的分析解都是通过拉普拉斯变换和有限傅里叶余弦变换得出的。此外,还给出了源项模型的有限元解法。结果表明,当表皮宽度小于 1 米且影响半径超过表皮外缘时,源项模型适用于大多数油井。负表皮的时间缩减分布呈三驼峰形,有两个平坦阶段,而正表皮的时间缩减分布呈单调增长。源项模型采用正交 5 × 5 节点进行有限元近似,以离散化一口井及其相邻表皮。在两次现场恒速抽水试验中观察到的影响下,有限元解决方案与观测井测得的早期抽水数据一致。总之,本研究引入了一种新的双区流动建模方法,可在现场应用中找到实际效用。
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来源期刊
Water Resources Research
Water Resources Research 环境科学-湖沼学
CiteScore
8.80
自引率
13.00%
发文量
599
审稿时长
3.5 months
期刊介绍: Water Resources Research (WRR) is an interdisciplinary journal that focuses on hydrology and water resources. It publishes original research in the natural and social sciences of water. It emphasizes the role of water in the Earth system, including physical, chemical, biological, and ecological processes in water resources research and management, including social, policy, and public health implications. It encompasses observational, experimental, theoretical, analytical, numerical, and data-driven approaches that advance the science of water and its management. Submissions are evaluated for their novelty, accuracy, significance, and broader implications of the findings.
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