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Keywords = inflow profile conformance

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13 pages, 6867 KiB  
Article
A Closed-Form Solution for Water Inflow into Deeply Buried Arched Tunnels
by Yunbo Wei, Qiang Chang and Kexun Zheng
Water 2025, 17(14), 2121; https://doi.org/10.3390/w17142121 - 16 Jul 2025
Viewed by 202
Abstract
The analytical solutions for groundwater inflow into tunnels are usually developed under the condition of circular tunnels. However, real-world tunnels often have non-circular cross-sections, such as arched, lens-shaped, or egg-shaped profiles. Accurately assessing water inflow for these diverse tunnel shapes remains challenging. To [...] Read more.
The analytical solutions for groundwater inflow into tunnels are usually developed under the condition of circular tunnels. However, real-world tunnels often have non-circular cross-sections, such as arched, lens-shaped, or egg-shaped profiles. Accurately assessing water inflow for these diverse tunnel shapes remains challenging. To address this gap, this study developed a closed-form analytical solution for water inflow into a deeply buried arched tunnel using the conformal mapping method. When the tunnel circumference degenerates to a circle, the analytical solution degenerates to the widely used Goodman’s equation. The solution also showed excellent agreement with numerical simulations carried out using COMSOL. Based on the analytical solution, the impact of various factors on water inflow Q was further discussed: (1) Q decreases as the boundary distance D increases. And the boundary inclination angle (απ/2) significantly affects Q only when the boundary is close to the tunnel (D<20); (2) Q increases quickly with the upper arc radius r1, while it shows minimal variation with the change in the lower arc radius r2. The findings provide a theoretical foundation for characterizing water inflow into arched tunnels, thereby supporting improved tunnel planning and grouting system design. Full article
(This article belongs to the Topic Water Management in the Age of Climate Change)
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14 pages, 2445 KiB  
Article
A Theoretical Analysis of Profile Conformance Improvement Due to Suspension Injection
by Konstantin Mikhailovich Fedorov, Alexander Yanovich Gilmanov, Alexander Pavlovich Shevelev, Alexander Vyacheslavovich Kobyashev and Denis Alekseevich Anuriev
Mathematics 2021, 9(15), 1727; https://doi.org/10.3390/math9151727 - 22 Jul 2021
Cited by 8 | Viewed by 1895
Abstract
This study is focused on a solution for the problem of suspension penetration in a porous formation. Such a solution forms the basis of injection profile diversion technology for oil reservoir sweep improvement. A conventional model of deep-bed suspension flow was used to [...] Read more.
This study is focused on a solution for the problem of suspension penetration in a porous formation. Such a solution forms the basis of injection profile diversion technology for oil reservoir sweep improvement. A conventional model of deep-bed suspension flow was used to describe the suspension injection process. The suspension slug was followed by water injection, and the inflow injection profile before and after treatment was investigated. For the first time, the criteria that determine the effectiveness of the inflow profile improvement process are introduced. The effect of the suspension filtration coefficient on the particle penetration depth was studied. A specific filtration coefficient value for the maximum penetration depth was achieved. The obtained analytical solution was generalized on multi-reservoir strata with poor interlayer crosslinking. The efficiency of profile conformance improvement was described by the differences in the root-mean-square deviations of the inflow velocities in interlayers from mean values before and after the treatment. It was shown that the complex criterion of suspension treatment efficiency should include a reduction in total injectivity. An increase in suspension slug volume improves the injectivity profile but decreases the total injectivity of an injector. Full article
(This article belongs to the Special Issue Mathematical Models of Multiphase Flows in Porous Media)
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