Analytical and Numerical Models in Geo-Energy

Topic Information

Dear Colleagues,

The development of geo-energy and the storage of carbon dioxide and hydrogen involve physical mechanisms such as fluid dynamics, thermodynamics and solid mechanics, etc. The governing equations are generally partial differential equations of parabolic, hyperbolic, or elliptic type. Analytical or semi-analytical methods are often used to solve situations which are based on ideal assumptions, typically computationally efficient. For practical or complex situations, numerical methods are widely used, and the work in numerical models is generally aimed at describing more complex mechanisms or using new discretization schemes or solver strategies to improve computational efficiency or accuracy. This Topic focuses on recent advances in analytical or numerical models in the field of geo-energy.

Dr. Xiang Rao
Dr. Hao Xiong
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Computation computation	1.9	3.5	2013	18.6 Days	CHF 1800
Mathematical and Computational Applications mca	1.9	-	1996	25.4 Days	CHF 1400
Mathematics mathematics	2.3	4.0	2013	18.3 Days	CHF 2600
Symmetry symmetry	2.2	5.4	2009	17.3 Days	CHF 2400
Energies energies	3.0	6.2	2008	16.8 Days	CHF 2600

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Published Papers (5 papers)

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20 pages, 3217 KiB  

Open AccessArticle

Evolution of Wellbore Pressure During Hydraulic Fracturing in a Permeable Medium

by Ali Lakirouhani

Mathematics 2025, 13(1), 135; https://doi.org/10.3390/math13010135 - 1 Jan 2025

Viewed by 751

Abstract

In hydraulic fracturing tests, the initial crack length and the compressibility of the injection system have a significant effect on the initiation and propagation of the fracture. Numerical or theoretical models that ignore the compressibility of the injection system are unable to accurately [...] Read more.

In hydraulic fracturing tests, the initial crack length and the compressibility of the injection system have a significant effect on the initiation and propagation of the fracture. Numerical or theoretical models that ignore the compressibility of the injection system are unable to accurately predict fracture behavior. In this paper, a 2D analytical/numerical model based on linear elastic fracture mechanics is presented for the initiation and propagation of hydraulic fracturing from two transversely symmetrical cracks in a borehole wall. It is assumed that the fracture is driven by compressible inviscid fluid in a permeable medium. To solve the problem, the governing equations are made dimensionless and the problem is solved in the compressibility–toughness-dominated propagation regime. According to the results, the initial crack length and the compressibility of the injection system have a significant effect on fracture initiation behavior. When the initial flaw length is small or compressibility effects are important, the initiation of the fracture is accompanied by instability and the occurrence of a sudden decrease in borehole pressure and a sudden increase in crack length. If the initial crack length is large or the compressibility effects are negligible, the crack propagation is stable. The leak-off coefficient has no effect on the pressure level required for crack propagation, but with an increase in leak-off, more time is required to reach the conditions for crack propagation. The results obtained in this paper provide good insights into the design of hydraulic fracturing processes. Full article

(This article belongs to the Topic Analytical and Numerical Models in Geo-Energy)

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16 pages, 6442 KiB  

Open AccessArticle

Finite Element Simulation of Stoneley Wave Propagation in Fracture Zones in Wells

by Xinghua Qi, Yuxuan Wei, Shimao Wang and Zhuwen Wang

Mathematics 2024, 12(22), 3511; https://doi.org/10.3390/math12223511 - 10 Nov 2024

Viewed by 905

Abstract

The formation and development of fractures increase reservoir heterogeneity and improve reservoir performance. Therefore, it is of great research value to accurately identify the development of fractures. In this paper, two- and three-dimensional models are constructed based on the finite element method and [...] Read more.

The formation and development of fractures increase reservoir heterogeneity and improve reservoir performance. Therefore, it is of great research value to accurately identify the development of fractures. In this paper, two- and three-dimensional models are constructed based on the finite element method and compared with the real axis integration method. The influence of different geometric parameters on the Stoneley wave amplitude is studied to assess the propagation of Stoneley waves in the fracture zone in the well. The results show a significant positive correlation between the width and number of fractures and the attenuation coefficient of Stoneley waves. The fracture angle has a negative correlation with the attenuation coefficient and lesser impact on Stoneley waves. In addition, Stoneley waves are less sensitive to changes in fracture location, while the sensitivity to fracture spacing is significant in the range of 50 cm to 75 cm. The main propagation depth of Stoneley waves occurs 20 cm from the wall of the well. Quantitative analyses of the fracture width, number, location, spacing, depth, and angle are conducted to determine the influence of the fracture parameters on the Stoneley wave attenuation coefficient, clarify Stoneley wave propagation in wells, and provide a theoretical basis for the accurate evaluation of fractures. Full article

(This article belongs to the Topic Analytical and Numerical Models in Geo-Energy)

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17 pages, 7148 KiB  

Open AccessArticle

Magnetotelluric Forward Modeling Using a Non-Uniform Grid Finite Difference Method

by Hui Zhang and Fajian Nie

Mathematics 2024, 12(19), 2984; https://doi.org/10.3390/math12192984 - 25 Sep 2024

Cited by 1 | Viewed by 951

Abstract

Magnetotelluric (MT) forward modeling is essential in geophysical exploration, enabling the investigation of the Earth’s subsurface electrical conductivity. Traditional finite difference methods (FDMs) typically use uniform grids, which can be computationally inefficient and fail to accurately capture complex geological structures. This study addresses [...] Read more.

Magnetotelluric (MT) forward modeling is essential in geophysical exploration, enabling the investigation of the Earth’s subsurface electrical conductivity. Traditional finite difference methods (FDMs) typically use uniform grids, which can be computationally inefficient and fail to accurately capture complex geological structures. This study addresses these challenges by introducing a non-uniform grid-based FDM for MT forward modeling. The proposed method optimizes computational resources by varying grid resolution, offering finer grids in areas with complex geology and coarser grids in more homogeneous regions. We apply this method to both typical synthetic models and a complex fault structure case study, demonstrating its capability to accurately resolve subsurface features while reducing computational costs. The results highlight the method’s effectiveness in capturing fine-scale details that are often missed by uniform grid approaches. The conclusions drawn from this study suggest that the non-uniform grid FDM not only improves the accuracy of MT modeling but also enhances its efficiency, making it a valuable tool for geophysical exploration in challenging environments. Full article

(This article belongs to the Topic Analytical and Numerical Models in Geo-Energy)

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16 pages, 5086 KiB  

Open AccessArticle

Driver Analysis and Integrated Prediction of Carbon Emissions in China Using Machine Learning Models and Empirical Mode Decomposition

by Ruixia Suo, Qi Wang and Qiutong Han

Mathematics 2024, 12(14), 2169; https://doi.org/10.3390/math12142169 - 11 Jul 2024

Cited by 1 | Viewed by 1065

Abstract

Accurately predicting the trajectory of carbon emissions is vital for achieving a sustainable shift toward a green and low-carbon future. Hence, this paper created a novel model to examine the driver analysis and integrated prediction for Chinese carbon emission, a large carbon-emitting country. [...] Read more.

Accurately predicting the trajectory of carbon emissions is vital for achieving a sustainable shift toward a green and low-carbon future. Hence, this paper created a novel model to examine the driver analysis and integrated prediction for Chinese carbon emission, a large carbon-emitting country. The logarithmic mean divisia index (LMDI) approach initially served to decompose the drivers of carbon emissions, analyzing the annual and staged contributions of these factors. Given the non-stationarity and non-linear characteristics in the data sequence of carbon emissions, a decomposition–integration prediction model was proposed. The model employed the empirical mode decomposition (EMD) model to decompose each set of data into a series of components. The various carbon emission components were anticipated using the long short-term memory (LSTM) model based on the deconstructed impacting factors. The aggregate of these predicted components constituted the overall forecast for carbon emissions. The result indicates that the EMD-LSTM model greatly decreased prediction errors over the other comparable models. This paper makes up for the gap in existing research by providing further analysis based on the LMDI method. Additionally, it innovatively incorporates the EMD method into the carbon emission study, and the proposed EMD-LSTM prediction model effectively addresses the volatility characteristics of carbon emissions and demonstrates excellent predictive performance in carbon emission prediction. Full article

(This article belongs to the Topic Analytical and Numerical Models in Geo-Energy)

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10 pages, 539 KiB  

Open AccessArticle

Geometric Stochastic Resonance in an Asymmetric T-Shaped Chamber

by Shouhui Duan, Bixuan Fan and Zhenglu Duan

Symmetry 2023, 15(12), 2183; https://doi.org/10.3390/sym15122183 - 11 Dec 2023

Cited by 1 | Viewed by 1169

Abstract

The investigation of a Brownian particle subjected to an AC force that diffuses within a T-shaped chamber was conducted. This T-shaped chamber is composed of a strip cavity and a trapezoidal cavity positioned below it. The interplay between the AC force and asymmetric [...] Read more.

The investigation of a Brownian particle subjected to an AC force that diffuses within a T-shaped chamber was conducted. This T-shaped chamber is composed of a strip cavity and a trapezoidal cavity positioned below it. The interplay between the AC force and asymmetric geometry creates a spatially bistable potential perpendicular to the AC force. With the assistance of noise, the particles can transition between two stable states and oscillate along the AC force at corresponding amplitudes at every spatially stable state. The asymmetric geometry facilitates the trapezoid cavity’s ability to more easily trap the Brownian particle than the upper strip cavity in the weak noise limit. Our observations reveal that proper noise can ensure the particle’s efficient trapping within the upper strip cavity and synchronization with the AC force, indicating the occurrence of geometric stochastic resonance. The T-shaped chamber serves as a simplified model, aiding in the further understanding of geometric stochastic resonance induced by irregular geometries and enabling the manipulation of microscopic particles in various small-scale systems. Full article

(This article belongs to the Topic Analytical and Numerical Models in Geo-Energy)

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