Comparative study of gravity-driven discharge from reservoirs with translationally invariant and fractal pore networks

Balankin, Alexander S.; Morales-Ruiz, Leobardo; Matías-Gutierres, Sergio; Susarrey-Huerta, Orlando; Samayoa, Didier; Patiño-Ortiz, Julián

doi:10.1016/j.jhydrol.2018.08.052

Cited by 3 publications

(1 citation statement)

References 37 publications

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“…The peculiar properties of standard Sierpi ński carpets and cubes and Menger sponges remain an active topic of research (see Refs. [151][152][153][154][155][156][157][158][159][160] and references therein).…”

Section: The Standard Sierpiński Carpetsmentioning

confidence: 99%

A Brief Survey of Paradigmatic Fractals from a Topological Perspective

Ortíz

Martínez-Cruz

et al. 2023

Fractal Fract

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The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a fractal dimension D which exceeds the topological dimension d. In this regard, we point out that the constitutive inequality D>d can have either a geometric or topological origin, or both. The main topological features of fractals are their connectedness, connectivity, ramification, and loopiness. We argue that these features can be specified by six basic dimension numbers which are generally independent from each other. However, for many kinds of fractals, the number of independent dimensions may be reduced due to the peculiarities of specific kinds of fractals. Accordingly, we survey the paradigmatic fractals from a topological perspective. Some challenging points are outlined.

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Section: The Standard Sierpiński Carpetsmentioning

confidence: 99%

A Brief Survey of Paradigmatic Fractals from a Topological Perspective

Ortíz

Martínez-Cruz

et al. 2023

Fractal Fract

Self Cite

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Torricelli’s Law in Fractal Space–Time Continuum

Samayoa,

Alvarez-Romero,

Jiménez-Bernal

et al. 2024

Mathematics

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A new formulation of Torricelli’s law in a fractal space–time continuum is developed to compute the water discharge in fractal reservoirs. Fractal Torricelli’s law is obtained by applying fractal continuum calculus concepts using local fractional differential operators. The model obtained can be used to describe the behavior of real flows, considering the losses in non-conventional reservoirs, taking into account two additional fractal parameters α and β in the spatial and temporal fractal continuum derivatives, respectively. This model is applied to the flows in reservoirs with structures of three-dimensional deterministic fractals, such as inverse Menger sponge, Sierpinski cube, and Cantor dust. The results of the level water discharge H(t) are presented as a curve series, showing the impact and influence of fluid flow in naturally fractured reservoirs that posses self-similar properties.

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Optimization of the Water Reticulation System at Bulawayo Mining Company (BMC), Zimbabwe

Ngoroyemoto¹,

Sabao²,

Maganga³

et al. 2022

Malaysian J. Sci. Adv. Tech.

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Bulawayo Mining Company (BMC) is estimated to lose millions of dollars in potential profit over a period of its documented life of mine (LOM) which is nine years as at May 2019. The projected loss is attributed to the time value of money emanating from the extension of the Life Of Mine due to mining inefficiencies. These inefficiencies are due to poor management of the water management system that plays a key role in the mining cycle. This project was done to make a quantitative analysis of BMC underground water management system in order to establish the bottlenecks and use this knowledge to optimize an efficient Water Reticulation System (WRS). Erratic water supply has an implication of disrupting the mining cycle as most of the operations rely on water; therefore, the supply of water is of great significance. In an effort to resolve the problem of erratic water supply, experiments were conducted to ascertain the quantity of water demanded in contrast with the supply. New Visual basic computer program (WaterCal) that can calculate the optimum WRS parameters as well as simulating real conditions through extrapolation was developed. Algorithm based on fluid mechanics laws and theorems was integrated in the application thereby simplifying the mine design and planning process. It was strongly recommended that the mine should consider using computer solutions in future designs of Water Reticulation Systems such as the WaterCal Windows Application. The pipe size is supposed to be increased from 50mm to 100mm. The mine should also adopt the use of flow meters and pressure gauges to effectively monitor and control the reticulation system effectively.

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Comparative study of gravity-driven discharge from reservoirs with translationally invariant and fractal pore networks

Cited by 3 publications

References 37 publications

A Brief Survey of Paradigmatic Fractals from a Topological Perspective

A Brief Survey of Paradigmatic Fractals from a Topological Perspective

Torricelli’s Law in Fractal Space–Time Continuum

Optimization of the Water Reticulation System at Bulawayo Mining Company (BMC), Zimbabwe

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