Computational Geosciences Research Articles

Correlation between the surface morphology of the intrusions and the formation of mineralization within skarn deposits: A numerical simulation study of the Qiaomaishan skarn Cu deposit, Middle and Lower Yangtze River Metallogenic Belt, China

Skarn deposits are high grade hydrothermal deposits distributed throughout the world, containing multiple mineral resources. However, the formation of skarn deposits is extremely complex, hindering our in-depth understanding of these deposits with high economic value. The Qiaomaishan Cu deposit is a typical skarn deposit located in the Liqiao-Tongshan orefield, Middle-Lower Yangtze River Metallogenic Belt (MLYRMB). This study applied numerical simulation approach to quantitatively describe the formation of copper mineralization within the Qiaomaishan skarn deposit, and explored the correlation between the surface morphology of intrusion and the formation of mineralization. This numerical model links five main processes related to ore formation within hydrothermal ore-forming system and their complex coupled relationship, namely chemical reactions, heat conduction, rock deformation, fluid migration, and materials diffusion. Results show that rough surface morphology of the intrusions is an ore controlling factor within the Qiaomaishan skarn deposit. The uneven surface of the intrusions greatly affects the time spent in cooling, thereby affecting the generation and spatial distribution of chalcopyrite. The concave part of the surface of the intrusions lives a longer cooling period (1000–2500 years) than the convex part (110–160 years) from 310 to 260 °C, which directly causes the difference in the temporal-spatial distribution of chalcopyrite. Results also show that the factors involved in prospectivity modeling must undergo strict conditional independence analysis, and numerical simulation method can be used to effectively achieve this goal. However, there are also some problems unsolved, such as difficulties caused by lack of data and oversimplified ore-forming chemical reactions. Future development of both geological research and modification of the law of mass action will undoubtedly improve the accuracy and practicability of numerical simulation and our understanding of the Qiaomaishan as well as other skarn deposit, providing information for mineral deposit research from the perspective of computational geoscience.

Editorial of Special Issue “Advances and Applications in Computational Geosciences”

In geoscientific fields, mathematical modelling, numerical analysis, visualization, simulation, and other computational techniques have become necessary to improve our understanding of phenomena and evolution of the Earth [...]

Earthcasting: Geomorphic Forecasts for Society

AbstractOver the last several decades, the study of Earth surface processes has progressed from a descriptive science to an increasingly quantitative one due to advances in theoretical, experimental, and computational geosciences. The importance of geomorphic forecasts has never been greater, as technological development and global climate change threaten to reshape the landscapes that support human societies and natural ecosystems. Here we explore best practices for developing socially relevant forecasts of Earth surface change, a goal we are calling “earthcasting”. We suggest that earthcasts have the following features: they focus on temporal (∼1–∼100 years) and spatial (∼1 m–∼10 km) scales relevant to planning; they are designed with direct involvement of stakeholders and public beneficiaries through the evaluation of the socioeconomic impacts of geomorphic processes; and they generate forecasts that are clearly stated, testable, and include quantitative uncertainties. Earthcasts bridge the gap between Earth surface researchers and decision‐makers, stakeholders, researchers from other disciplines, and the general public. We investigate the defining features of earthcasts and evaluate some specific examples. This paper builds on previous studies of prediction in geomorphology by recommending a roadmap for (a) generating earthcasts, especially those based on modeling; (b) transforming a subset of geomorphic research into earthcasts; and (c) communicating earthcasts beyond the geomorphology research community. Earthcasting exemplifies the social benefit of geomorphology research, and it calls for renewed research efforts toward further understanding the limits of predictability of Earth surface systems and processes, and the uncertainties associated with modeling geomorphic processes and their impacts.

Polytopic discontinuous Galerkin methods for the numerical modelling of flow in porous media with networks of intersecting fractures

We present a numerical approximation of Darcy's flow through a porous medium that incorporates networks of fractures with non empty intersection. Our scheme employs PolyDG methods, i.e. discontinuous Galerkin methods on general polygonal and polyhedral (polytopic, for short) grids, featuring elements with edges/faces that may be in arbitrary number (potentially unlimited) and whose measure may be arbitrarily small. Our approach is then very well suited to tame the geometrical complexity featured by most of applications in the computational geoscience field. From the modelling point of view, we adopt a reduction strategy that treats fractures as manifolds of codimension one and we employ the primal version of Darcy's law to describe the flow in both the bulk and in the fracture network. In addition, some physically consistent conditions couple the two problems, allowing for jump of pressure at their interface, and they as well prescribe the behaviour of the fluid along the intersections, imposing pressure continuity and flux conservation. Both the bulk and fracture discretizations are obtained employing the Symmetric Interior Penalty DG method extended to the polytopic setting. The key instrument to obtain a polyDG approximation of the problem in the fracture network is the generalization of the concepts of jump and average at the intersection, so that the contribution from all the fractures is taken into account. We prove the well-posedness of the discrete formulation and perform an error analysis obtaining a priori hp-error estimates. All our theoretical results are validated performing preliminary numerical tests with known analytical solution.

A Graph Clustering Approach to Localization for Adaptive Covariance Tuning in Data Assimilation Based on State-Observation Mapping.

An original graph clustering approach for the efficient localization of error covariances is proposed within an ensemble-variational data assimilation framework. Here, the localization term is very generic and refers to the idea of breaking up a global assimilation into subproblems. This unsupervised localization technique based on a linearized state-observation measure is general and does not rely on any prior information such as relevant spatial scales, empirical cutoff radii or homogeneity assumptions. Localization is performed via graph theory, a branch of mathematics emerging as a powerful approach to capturing complex and highly interconnected Earth and environmental systems in computational geosciences. The novel approach automatically segregates the state and observation variables in an optimal number of clusters, and it is more amenable to scalable data assimilation. The application of this method does not require underlying block-diagonal structures of prior covariance matrices. To address intercluster connectivity, two alternative data adaptations are proposed. Once the localization is completed, a covariance diagnosis and tuning are performed within each cluster, whose contribution is sequentially integrated into the entire covariance matrix. Numerical twin experiment tests show the reduced cost and added flexibility of this approach compared to global covariance tuning, and more accurate results yielded for both observation- and background-error parameter tuning.

Numerical simulation study on ore-forming factors of the Gejiu ore deposit, China

The Gejiu superlarge tin polymetallic mining area in Yunnan hosts the largest tin-copper polymetallic ore field worldwide. The output of tin and copper provides power for the development of the country. Therefore, the study of mineralization is very important. But the geological structure is diverse, and the mineralization of different geological structures is different. In this study, the geological characteristics, tectonics, mineralogy, and geochemistry of these typical magmatic hydrothermal deposits were analyzed, various geological structures are studied, and the finite-element method was used to simulate the mineralization of chalcopyrite in the study area. Finally, the results are validated against the instance area. The numerical results show that the hydrothermal flow is the main factor controlling the mineralization. The pore fluid flow is driven by the temperature gradient. Favorable metallogenic areas are located in faults, between horizontal strata, and at intersections of faults. In the future, by simulating the metallogenic region and studying the metallogenic structure, the locations of ore bodies can be predicted. Our research confirms the results of the coupled model in the field of emerging computational geoscience and provides insights into the mineralization process.

International Conference «Marchuk Scientific Readings 2020» (MSR-2020), dedicated to the 95th anniversary of the birthday of Academician Guri I. Marchuk

PrefaceThese Conference Proceedings contain the selected papers of the International Conference «Marchuk Scientific Readings 2020» (MSR-2020) held on October 19 - 23, 2020, in Akademgorodok, Novosibirsk, Russia.The conference is dedicated to the 95th anniversary of the birthday of Academician Guri I. Marchuk. He was the founder and the first Director of the Computer Centre of the Siberian Branch of the USSR Academy of Sciences (currently, the Institute of Computational Mathematics and Mathematical Geophysics SB RAS). In different periods, he was the Chairman of the Siberian Branch of the USSR Academy of Sciences, Chairman of the USSR State Committee for Science and Technology, the last President of the USSR Academy of Sciences, Chairman of the Council of the USSR Academy of Sciences for Space. Hero of Socialist Labour and Lenin Prize winner, Academician Guri I. Marchuk was an outstanding scientist, recognized specialist in computational mathematics and mathematical modelling, nuclear reactor theory, atmospheric physics and geophysics, space, and environmental sciences, medicine, and immunology. He authored more than 350 scientific papers and monographs.Academician Marchuk was a distinguished organizer of science. He created a huge scientific school and was actively working on the introduction of scientific achievements to industry. Guri I. Marchuk made a significant contribution to the development of nuclear reactor technology. He was one of the pioneers of space exploration, the organizer of the international project “World ocean”, international systems for remote sensing of the Earth from space and space station flights to Venus.The purpose of the «Marchuk Scientific Readings» conference series is to gather specialists in numerical analysis, applied mathematics, mathematical modelling, computational technologies, information systems, artificial intelligence, and machine learning to discuss, identify and systematize current results, applications, and promising directions in computational mathematics and computer science.The conference program included 31 plenary, 298 oral, and 46 poster presentations. They were presented in 11 sections and two mini-symposia.The conference sections were:• Numerical solution of differential and integral equations• Computational algebra and approximation methods• Numerical statistical modeling and Monte-Carlo methods• Mathematical geophysics• Mathematical models of atmospheric physics, ocean and environment• Programming• Supercomputer computations• Inverse problems• Informational and computational systems• Machine learning and artificial intelligence methods• Computer biology, medicine and biotechnologyTwo mini-symposia were held:• Computational geosciences across the scales• Particle-based methods: numerical aspects and modern applicationsAll contributions selected for publication in this volume have been peer-reviewed according to rigorous international standards. We are grateful to the reviewers for maintaining the manuscripts’ standards and quality throughout the reviewing process. However, the authors take full responsibility for the content of their papers.The event was organized by the Institute of Computational Mathematics and Mathematical Geophysics SB RAS and Novosibirsk State University. It was supported by the Russian Foundation for Basic Research (under project 20-01-20025) and the Siberian Branch of the Russian Academy of Sciences. We gratefully acknowledge all our sponsors.EditorsCorresponding Member of the RAS Gennady A. MikhailovCorresponding Member of the RAS Sergey I. KabanikhinProfessor Yurii M. LaevskiiProfessor Vladimir V. PenenkoProfessor Boris M. GlinskyPh.D. Alexey V. Penenko

Effects of Fe3+ on Dissolution Dynamics of Carbonate Rocks in a Shallow Burial Reservoir

Dissolution of carbonates in acidic fluids, which has attracted much research attention in recent years, is of great significance for the formation of high-quality reservoirs. The dissolution stage under low temperature and low pressure in shallow burial is one of the most important processes of reservoir dissolution and transformation. However, the dissolution dynamics of carbonate rocks in shallow burial and their formation have been controversial for a long time, and there are still disputes in the dissolution processes about how associated minerals and accessory minerals (e.g., pyrite) in carbonate reservoirs influence the formation of secondary pores. Additional metal ions in acidic fluids can change fluid properties and dissolution processes, and consequently affect reservoir quality. However, there are few laboratory studies done on the effect of associated minerals on the dissolution dynamics of carbonates. To clarify the specific impact of Fe-bearing associated minerals and Fe3+ on the dissolution of carbonates in shallow burial reservoirs, six samples of typical carbonate rocks in the Zigui area of Hubei Province, China were studied. The dissolution kinetics of carbonates in dilute hydrochloric acid and sulfuric acid solutions containing metal ions (Fe3+/Ca2+/Mn2+) at ambient temperature and pressure (T = 25 °C, P = 1 atm) were studied, by laboratory dissolution experiments combined with numerical simulations using PHREEQC. The results show that the Fe3+ is of great significance on the dissolution of carbonate rocks, while the influences of Ca2+ and Mn2+ are relatively weak. The dissolutions degrees of micritic limestone (ZG-L25), dolomitic limestone (ZG-L7) and dolomite (ZG-D9) were better than the other carbonates under the influence of metal ions (Fe3+/Ca2+/Mn2+) in acid solutions. Therefore, the dolomite reservoir of the Cambrian Qinjiamiao Formation, the dolomitic limestone reservoir of the Tianheban Formation and the limestone reservoir of the Triassic Daye Formation in the Zigui area are potential high-quality reservoirs. The carbonate reservoirs associated with Fe-bearing minerals were easier to dissolve and formed secondary pores under shallow burial. This process is beneficial to the formation of high-quality reservoirs. Moreover, the addition of Fe3+ into hydrochloric acid solution may be conducive to improving the reservoirs acidizing effect. Furthermore, the results gave innovative results from multiple perspectives of geo-material science and computational geosciences, which may provide new avenues for in-depth study of carbonate dissolution in shallow burial based on water–rock reaction, chemical dissolution, computational simulation, and geological background.

Translating novel HPC techniques into efficient geoscience solutions

Computational geoscience is an established field for better understanding and protecting our planet. It covers a wide range of different fields that are closely related to Earth systems. As a popular research area that largely relies on high performance computing, the efficient translation of novel techniques from computer science to practical geoscience solutions has emerged as an important and challenging problem. Based on a series of efforts in conducting interdisciplinary research in computer science and geoscience, this paper summarizes the measures we have taken and the lessons we have learned to successfully translate selected computational laboratory innovations into practical solutions.

Phase-field modeling of hydraulic fracture network propagation in poroelastic rocks

Modeling of hydraulic fracturing processes is of great importance in computational geosciences. In this paper, a phase-field model is developed and applied for investigating the hydraulic fracturing propagation in saturated poroelastic rocks with pre-existing fractures. The phase-field model replaces discrete, discontinuous fractures by continuous diffused damage field, and thus is capable of simulating complex cracking phenomena such as crack branching and coalescence. Specifically, hydraulic fracturing propagation in a rock sample of a single pre-existing natural fracture or natural fracture networks is simulated using the proposed model. It is shown that distance between fractures plays a significant role in the determination of propagation direction of hydraulic fracture. While the rock permeability has a limited influence on the final crack topology induced by hydraulic fracturing, it considerably impacts the distribution of the fluid pressure in rocks. The propagation of hydraulic fractures driven by the injected fluid increases the connectivity of the natural fracture networks, which consequently enhances the effective permeability of the rocks.

Altered mineral segmentation in thin sections using an incremental-dynamic clustering algorithm

Intelligent mineral segmentation in thin section images of rocks still remains a challenging task in modern computational mineralogy. The objective of the paper is segmenting minerals in geological thin section’s images with special attention on altered mineral segmentation. In this paper, an efficient incremental-dynamic clustering algorithm is developed for segmentation of minerals in thin sections containing altered and non-altered minerals. In the clustering algorithm, there is no need for determining the number of clusters (minerals) existed in thin section images, and also it is able to deal with color changing and non-evident boundaries in altered minerals. We have solved two main existing limitations: segmentation of mineral pixels that are frequently labeled as background pixels, and segmentation of thin sections containing altered minerals. Moreover, we created an open database (Alborz Mineralogical Database), as a benchmark database in computational geosciences regarding image studies of mineral. The proposed method is validated based on the results provided by the segmentation maps, and experimental results indicate that the proposed method is very efficient and outperforms previous segmentation methods for altered minerals in thin section images. The proposed method can be applied in mining engineering, rock mechanics engineering, geotechnique engineering, mineralogy, petrography, and applications such as NASA’s Mars Rover Explorations (MRE).

Certified reduced basis method in geosciences

One of the biggest challenges in Computational Geosciences is finding ways of efficiently simulating high-dimensional problems. In this paper, we demonstrate how the RB method can be gainfully exploited to solve problems in the Geosciences. The reduced basis method constructs low-dimensional approximations to (high-dimensional) solutions of parametrized partial differential equations. In contrast to other widely used geoscientific reduction techniques, the reduced basis method reduces the Galerkin approximation space, and not the physical space and is consequently much less restrictive. Another advantage of the method is that for the problems considered in this paper, the method provides a bound to the error in the reduced order approximation, thus permitting an objective evaluation of the approximation quality. Using a geothermal conduction problem, we demonstrate that depending on the model, we obtain a maximum speed-up of three orders of magnitude with an approximation error that is very small in comparison with typical measurement errors. This significant reduction of the cost of the forward simulation allows performing uncertainty quantification, inversions, and parameter studies for larger and more complex models than currently possible.

Numerical Simulation of Non-Equilibrium Isochoric Phase Transitions in Hydrocarbon Mixtures

Numerical simulations of phase behavior in multicomponent hydrocarbon mixtures is an essential part of petroleum reservoir engineering practice. Almost all industry-adopted models are based on equilibrium assumptions. The condition of Gibbs energy minimum, or equality of chemical potentials, combined with the equation of state (EoS), e.g. the Peng-Robinson EoS, for each phase and with balance conditions for concentrations are used to compute phase mole fractions and compositions (component concentrations in the phases). However, experimental and field data show that in a number of important real situations equilibrium assumptions are not valid. In the previous study of Indrupskiy et al. (Computational Geosciences, 21(5), 2017) a unified model and numerical algorithms were presented for isothermal non-equilibrium phase behavior simulations in petroleum engineering applications. The model is based on the relaxation equation for the component chemical potentials difference between phases. It was verified on field data; however, only integral behavior of the system (a gas-condensate reservoir) was available to be matched. In the current study, we extended the non-equilibrium model to isochoric processes and developed a numerical algorithm which allowed to perform direct simulation of laboratory experiments with a multicomponent hydrocarbon mixture and validate the non-equilibrium model. The experimental data were successfully matched with the model simulations. The model and algorithm are suitable for equilibrium and non-equilibrium isochoric phase behavior simulations with synthetic and real multicomponent hydrocarbon mixtures (oils and gas-condensates).

Numerical simulation of hydrothermal mineralization associated with simplified chemical reactions in Kaerqueka polymetallic deposit, Qinghai, China

Abstract The Kaerqueka polymetallic deposit, Qinghai, China, is one of the typical skarn-type polymetallic ore deposits in the Qimantage metallogenic belt. The dynamic mechanism on the formation of the Kaerqueka polymetallic deposit is always an interesting topic of research. We used the finite difference method to model the mineralizing process of the chalcopyrite in this region with considering the field geological features, mineralogy and geochemistry. In particular, the modern mineralization theory was used to quantitatively estimate the related chemical reactions associated with the chalcopyrite formation in the Kaerqueka polymetallic deposit. The numerical results indicate that the hydrothermal fluid flow is a key controlling factor of mineralization in this area and the temperature gradient is the driving force of pore-fluid flow. The metallogenic temperature of chalcopyrite in the Kaerqueka polymetallic deposit is between 250 and 350 °C. The corresponding computational results have been verified by the field observations. It has been further demonstrated that the simulation results of coupled models in the field of emerging computational geosciences can enhance our understanding of the ore-forming processes in this area.

Genesis of the Angeer Yinwula Pb–Zn deposit, Inner Mongolia, China: constraints from fluid inclusions, C–H–O–S–Pb isotope systematics, and zircon U–Pb geochronology

The Angeer Yinwula Pb–Zn deposit of Inner Mongolia, China, is located in the Erlianhot–Dongwuqi metallogenic belt, which is considered to be the eastern part of the Central Asian Orogenic Belt. We used the ore geology, fluid inclusion, isotopes, and zircon U–Pb geochronology to elucidate the genesis and tectonic setting of the deposit. The deposit belongs to the moderate-temperature hydrothermal-vein type, and most of the ore bodies occurred in the quartz diorite intrusions and silty slate country rocks of the Devonian Angeer Yinwula Group. Fluid inclusion petrography and microthermometry results show that the inclusions that developed in the different mineralization stages changed from the LV type (vapor-rich two-phase) + S type (daughter-mineral-bearing three-phase) + VL type (liquid-rich two-phase) to the VL type + LV type and eventually evolved into the VL type, and the ore-forming fluids changed from a moderate-temperature and moderate- to high-salinity, boiling fluid system to a low-temperature and low-salinity H2O–NaCl system. The isotope (C, H, O, S) characteristics suggest that the ore-forming fluids were derived from a magmatic source, and the lead was derived from a deep-seated mantle-derived magma and also included some crustal material. The LA–ICP–MS zircon U–Pb age of the quartz diorite is 152.0 ± 1.5 Ma, which is the best estimate for the age of mineralization of the deposit. Overall, we suggest that the deposit formed in a Late Jurassic Paleo-Pacific Plate subduction setting, although this hypothesis needs to be further tested by conducting computational simulations in the field of emerging computational geosciences.

Computational reproducibility in geoscientific papers: Insights from a series of studies with geoscientists and a reproduction study

ABSTRACTReproducibility is a cornerstone of science and thus for geographic research as well. However, studies in other disciplines such as biology have shown that published work is rarely reproducible. To assess the state of reproducibility, specifically computational reproducibility (i.e. rerunning the analysis of a paper using the original code), in geographic research, we asked geoscientists about this topic using three methods: a survey (n = 146), interviews (n = 9), and a focus group (n = 5). We asked participants about their understanding of open reproducible research (ORR), how much it is practiced, and what obstacles hinder ORR. We found that participants had different understandings of ORR and that there are several obstacles for authors and readers (e.g. effort, lack of openness). Then, in order to complement the subjective feedback from the participants, we tried to reproduce the results of papers that use spatial statistics to address problems in the geosciences. We selected 41 open access papers from Copernicus and Journal of Statistical Software and executed the R code. In doing so, we identified several technical issues and specific issues with the reproduced figures depicting the results. Based on these findings, we propose guidelines for authors to overcome the issues around reproducibility in the computational geosciences.

Time-space-domain mesh-free finite difference based on least squares for 2D acoustic-wave modeling

Finite-difference (FD) methods approximate derivatives through a weighted summation of function values from neighboring nodes. Traditionally, these neighboring nodes are assumed to be distributed regularly, such as in square or rectangular lattices. To improve geometric flexibility, one option is to develop FD in a mesh-free discretization, in which scattered nodes can be placed suitably with respect to irregular boundaries or arbitrarily shaped anomalies without coordinate transformation or forming any triangles or tetrahedra, etc. These mesh-free FDs have had successful applications, especially in computational geoscience. However, they are all space-domain FD schemes, in which FD coefficients are derived by approximating spatial derivatives individually in the space domain. For acoustic-wave modeling, it has been proven that space-domain FD methods normally have higher dispersion error than time-space-domain FD methods, which determine FD coefficients by approximating the time-space-domain dispersion relation. Now, we have developed a time-space-domain mesh-free FD based on minimizing the absolute error of the dispersion relation by least-squares (LS) for 2D acoustic-wave modeling. The matrix used to solve for FD coefficients in our method is determined by the spatial distribution of the nodes in a local FD stencil, whereas the temporal step size and velocity information are considered in the right side of the linear system. This feature of considering both spatial and temporal effects allows our proposed mesh-free LS-based FD to obtain greater temporal accuracy adaptive to different Courant-Friedrichs-Lewy parameters than pure space-domain mesh-free FDs. Under several 2D acoustic scenarios, the advantage was proven by comparing our method with radial-basis-function-generated FD, which is one of the most popular mesh-free FDs and has been applied in elastic wave modeling.

Selected contributions from the 14th European Conference on the Mathematics of Oil Recovery (ECMOR XIV)

The 14th European Conference on the Mathematics of Oil Recovery (ECMOR XIV) was held in Catania, a beautiful city lying between Mount Etna and the Mediterranean Sea on the magnificent island of Sicily (Italy) [1] from 9 to 11 September, 2014. ECMOR has been organized every even year since 1988 to provide a place where engineers and scientists from Academia and the oil and gas industry could meet to focus advancements on mathematical aspects of reservoir simulation and modelling. After ECMOR VI, held in Scotland in September 1998, the European Association of Geoscientists and Engineers (EAGE) included this event in its regular program. In Catania, a total of 88 oral presentations and 47 posters covered a wide range of topics and received attention from 185 attendees, a new record for ECMOR. The full list of papers presented at the conference can be found on the EAGE website (http://www. eage.org/event/index.php?eventid=1093&evp=12651), and all papers are electronically accessible via the EarthDoc online data base (http://earthdoc.eage.org/). This issue of Computational Geosciences presents 24 papers developed upon selected works from the Sicilian conference and that have been peer reviewed according to the journal’s policy. These papers address complex mathematical challenges arising from the need to meet the world energy demand in the next years, and provide evidences of the technical success of ECMOR XIV. I wish to congratulate the authors for

Computational Methods for Simulating Some Typical Problems in Computational Geosciences

The main purpose of this paper is to present computational methods for simulating some typical problems in the emerging computational geoscience field. Due to remarkable differences between engineering systems and Earth ones, existing computational methods, which are designed for solving engineering problems, cannot be directly used to solve geoscience problems without any modification. However, the fundamental philosophy of developing computational methods is applicable to the computational simulation of both geoscience and engineering problems. Because of their inherent approximation, computational methods must be verified before putting into application. After several computational methods and algorithms, which are developed for simulating some typical problems in the emerging computational geoscience field, are briefly introduced, a typical geoscience problem, known as the chemical dissolution-front instability problem in ore-forming systems of supercritical Zhao numbers, is selected to demonstrate how computational methods can be used to solve geoscience problems.

Simulating flows in multi-layered and spatially-variable permeability media via a new Gray Lattice Boltzmann model

The simulation of flow in porous and fibrous permeable media is of high importance in many scientific and industrial applications. Although the finite element models at the representative elementary volume scales are used to solve a huge amount of scientific and engineering problems, they are hardly used to efficiently simulate pore-fluid flow problems at the particle scales. This encourages the development of numerical models to match the needs of such studies. In this paper, we propose a new Gray Lattice Boltzmann numerical model for simulating fluid flow in permeable media. Unlike most previous models, our proposed model has the ability to simulate multi-layers and space-variable permeability while preserving the continuity of the macroscopic velocity field. The model is verified with the available analytical solutions and a derived analytical expression for the case of variable porosity. In addition, we examine the importance of introducing a transition layer with a defined porosity function near the boundaries and interfaces. If this layer exists in practice, then the numerical results reveal that it cannot be neglected, and its impact is significant on the obtained velocity distribution. Finally, in the light of the obtained results, we can state that the proposed model has great potential to simulate complex and heterogeneous media with smoothness and accuracy, so that it may enrich the research content of the emerging computational geosciences.