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Hydrothermal ore‐forming systems usually involve coupled processes among pore‐fluid flow, heat transfer, mass transport and chemical reactions in fluid‐saturated porous media. The finite element method (FEM) has provided a powerful tool to solve hydrothermal ore‐forming problems associated with pore‐fluid convective flow. Depending on different interests of research, a hydrothermal ore‐forming system may be simulated at two different length‐scale models, such as a regional (i.e., large length‐scale) model or a deposit (i.e., small length‐scale) model. However, there is an unsolved issue to guarantee the consistency between the applied boundary conditions to a deposit model and the predicted results, at exactly the same location as the boundary of the deposit model, from using the regional model. This paper proposes a FEM‐based dual length‐scale simulation procedure to address this issue. In the proposed procedure, a regional model of coarse mesh is first simulated by the FEM. Since a deposit model is located within the regional model, the applied boundary conditions to the deposit model of fine mesh can be determined from the simulation results of the regional model, so that the consistency can be guaranteed at the common boundary between the deposit model and the regional model. Main outcomes of this study have demonstrated that: (1) the proposed FEM‐based dual length‐scale simulation procedure is suitable and applicable for solving coupled problems involving pore‐fluid flow, heat transfer, mass transport and chemical reactions in fluid‐saturated porous media; (2) the proposed procedure is predictive because it is unnecessary to know the location of an ore deposit prior to the simulation of a hydrothermal ore‐forming system; (3) the boundary condition of a deposit model of fine mesh is consistent with the simulation results obtained from the regional model of coarse mesh, so that the reliability of the simulation results obtained from the deposit model can be ensured. [ABSTRACT FROM AUTHOR]

Skarn-hosted deposits are commonly recognized as the consequence of magma intrusion within the Earth's upper crust. The Ergu Pb-Zn deposit can be regarded as a typical skarn-hosted deposit in the hydrothermal ore-forming system within the central Lesser Xing'an Range (LXR), Heilongjiang, China. Although extensive studies were conducted to understand the ore-forming system associated with the Ergu Pb-Zn deposit through using the traditional geoscience methods, the ore-forming process involved in this deposit has not been justified in a strictly scientific manner to date. In this paper, the hydrothermal ore-forming process of the Ergu Pb-Zn deposit is computationally simulated through using the dual length-scale approach associated with the finite element method (FEM). The related computational simulation results have demonstrated that: (1) the pore-fluid convection provides continuous ore-forming fluid and material sources for the Ergu Pb-Zn deposit at the quartz-Pb-Zn sulfide stage; (2) the convective flow of the pore fluid is the main dynamic mechanism, which controls the temperature, chemical species and pore-fluid velocity distributions in the Ergu Pb-Zn deposit; (3) the localized structure plays a key role in controlling the localized pore-fluid flow pattern, which can further control the location and formation of the orebody grade in the Ergu Pb-Zn deposit; (4) the dual length-scale approach associated with the FEM is very useful in dealing with the computational simulation of the hydrothermal ore-forming mechanism involved in the Ergu Pb-Zn deposit. [ABSTRACT FROM AUTHOR]

Hydrothermal ore‐forming systems usually involve coupled processes among pore‐fluid flow, heat transfer, mass transport and chemical reactions in fluid‐saturated porous media. The finite element method (FEM) has provided a powerful tool to solve hydrothermal ore‐forming problems associated with pore‐fluid convective flow. Depending on different interests of research, a hydrothermal ore‐forming system may be simulated at two different length‐scale models, such as a regional (i.e., large length‐scale) model or a deposit (i.e., small length‐scale) model. However, there is an unsolved issue to guarantee the consistency between the applied boundary conditions to a deposit model and the predicted results, at exactly the same location as the boundary of the deposit model, from using the regional model. This paper proposes a FEM‐based dual length‐scale simulation procedure to address this issue. In the proposed procedure, a regional model of coarse mesh is first simulated by the FEM. Since a deposit model is located within the regional model, the applied boundary conditions to the deposit model of fine mesh can be determined from the simulation results of the regional model, so that the consistency can be guaranteed at the common boundary between the deposit model and the regional model. Main outcomes of this study have demonstrated that: (1) the proposed FEM‐based dual length‐scale simulation procedure is suitable and applicable for solving coupled problems involving pore‐fluid flow, heat transfer, mass transport and chemical reactions in fluid‐saturated porous media; (2) the proposed procedure is predictive because it is unnecessary to know the location of an ore deposit prior to the simulation of a hydrothermal ore‐forming system; (3) the boundary condition of a deposit model of fine mesh is consistent with the simulation results obtained from the regional model of coarse mesh, so that the reliability of the simulation results obtained from the deposit model can be ensured. [ABSTRACT FROM AUTHOR]

Through using rigorously mathematical deductions, this article derives analytical solutions for chemical dissolution‐front instability (CDFI) problems, in which radially divergent flow is involved within fluid‐saturated porous media. Since the acid injection‐well to be considered is a circle of nonzero radius in the horizontal plane, a polar coordinate system is used to describe the coupled mathematical governing equations of the CDFI problem. To facilitate deriving analytical solutions, an appropriate mathematical transform is used to convert the coupled mathematical governing equations from a dimensional form into a dimensionless one. This enables the generalized linear stability approach to be utilized for deriving both analytical base and perturbation solutions for the CDFI problem involving radially divergent flow within a fluid‐saturated porous medium. Consequently, a theoretical criterion, which is usable for assessing the CDFI in the chemical dissolution system (CDS), is further established from the corresponding analytical perturbation solutions. The related theoretical results have demonstrated that: (1) the proposed theoretical criterion is useful and applicable for assessing the CDFI associated with radially divergent flow within fluid‐saturated porous media; (2) the permeability ratio between the downstream and upstream regions can affect significantly the critical Peclet number of a CDS associated with radially divergent flow; (3) the initial porosity can have remarkable effects on the critical Peclet number of a CDS associated with radially divergent flow; and (4) the difference between the final and initial porosities can also affect significantly the critical Peclet number of a CDS associated with radially divergent flow in the fluid‐saturated porous medium. [ABSTRACT FROM AUTHOR]

This paper deals with three fundamental issues associated with theoretical analyses of reactive infiltration instability (RII) problems in fluid‐saturated porous media. The first fundamental issue is to determine the spatial shapes of chemical dissolution‐fronts in the limit case of the mineral dissolution ratio approaching zero in both conventional time (daily life time) and unconventional time (abstract time) domains. The chemical dissolution‐front is commonly represented by the spatial shape of the porosity profile. The second fundamental issue is to conduct theoretical analyses of the RII problems associated with the mineral dissolution ratio approaching zero through directly solving dimensional mathematical governing equations in the conventional time domain. The third fundamental issue is to carry out theoretical analyses of the RII problems associated with the mineral dissolution ratio approaching zero through solving dimensionless mathematical governing equations in the unconventional time domain. Through purely mathematical deductions, it has been proven that: (1) the spatially sharp shape of a chemical dissolution‐front, which is theoretically predicted either at a much smaller timescale than the dissolution timescale associated with the daily life time or at a much larger timescale than the dissolution timescale associated with the daily life time, can be observed in the daily life time domain; (2) the theoretical instability criterion of an RII problem can be established directly at three different length‐scales in the daily life time domain; and (3) although the spatial shape of a chemical dissolution‐front at the dissolution timescale associated with the daily life time cannot be observed in the daily life time domain, the theoretical instability criterion of an RII problem at the dissolution timescale associated with the daily life time can be established when a physically consistent mathematical transform is used in the theoretical analysis. [ABSTRACT FROM AUTHOR]

Structural deformation regimes in the upper crust of the Earth can have significant effects on the distributions of pore-fluid flow in existing fissured and fractured zones, which are surrounded by fluid-saturated porous rocks. Based on the modern mineralization theory, mineralization distributions in ore-forming systems depend strongly on the distributions of pore-fluid flow velocity. Therefore, different structural deformation regimes associated with mineralization systems can remarkably affect mineralization distributions in existing fissured and fractured zones. This article utilizes a computational simulation approach, which is rigorously developed on the basis of fundamental scientific laws and principles, to solve coupled rock deformation, porosity–permeability evolution and pore-fluid flow problems, which are deeply involved in rock deformation driven mineralization systems. In particular, the porosity and permeability variations, which are caused by rock deformation, and often neglected in the previous studies of solving mineralization problems, are explicitly considered in the computational simulation approach of this study. The proposed approach is verified through a benchmark problem and, moreover, it was employed to examine how different structural deformation regimes can affect the mineralization distributions in existing fissured and fractured zones within the surrounding fluid-saturated porous rocks through using a generic model, which can be viewed as a representation of a generalized and simplified geological model. Main results obtained from this study have demonstrated the following conclusions: (1) consideration of porosity–permeability variations can have significant impacts on the computational simulation solutions of coupled rock deformation, porosity–permeability evolution and pore-fluid flow problems in fluid-saturated porous rocks; (2) different structural deformation regimes can have a significant effect on the mineralization enrichment distributions in ore-forming systems consisting of fluid-saturated porous rocks; (3) there are two favorable mineralization enrichment environments associated with compressional and extensional deformation regimes in ore-forming systems involving permeable fractured zones or faults. [ABSTRACT FROM AUTHOR]

Purpose: The objective of this paper is to establish a solution strategy for obtaining dual solutions, namely trivial (conventional) and nontrivial (unconventional) solutions, of coupled pore-fluid flow and chemical dissolution problems in heterogeneous porous media. Design/methodology/approach: Through applying a perturbation to the pore-fluid velocity, original governing partial differential equations of a coupled pore-fluid flow and chemical dissolution problem in heterogeneous porous media are transformed into perturbed ones, which are then solved by using the semi-analytical finite element method. Through switching off and on the applied perturbation terms in the resulting perturbed governing partial differential equations, both the trivial and nontrivial solutions can be obtained for the original governing partial differential equations of the coupled pore-fluid flow and chemical dissolution problem in fluid-saturated heterogeneous porous media. Findings: When a coupled pore-fluid flow and chemical dissolution system is in a stable state, the trivial and nontrivial solutions of the system are identical. However, if a coupled pore-fluid flow and chemical dissolution system is in an unstable state, then the trivial and nontrivial solutions of the system are totally different. This recognition can be equally used to judge whether a coupled pore-fluid flow and chemical dissolution system involving heterogeneous porous media is in a stable state or in an unstable state. The proposed solution strategy can produce dual solutions for simulating coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media. Originality/value: A solution strategy is proposed to obtain the nontrivial solution, which is often overlooked in the computational simulation of coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media. The proposed solution strategy provides a useful way for understanding the underlying dynamic mechanisms of the chemical damage effect associated with the stability of structures that are built on soil foundations. [ABSTRACT FROM AUTHOR]

This paper deals with how to implement perturbations in the computational simulations of chemical dissolution‐front instability (CDFI) problems in fluid‐saturated porous media. On the basis of theoretical analysis, it is found that the application of a perturbation to the chemical dissolution front is equivalent to the application of an alternative perturbation to the dimensionless pore‐fluid normal velocity (relative to the planar chemical dissolution front) in the chemical dissolution zone, where the chemical dissolution front is located. This avoids the difficulty to find the spatial coordinates of the chemical dissolution front locations in the computational simulations of CDFI problems. Based on this new finding, a novel algorithm for implementing perturbations in the computational simulations of CDFI problems is proposed. The key point of the proposed algorithm is that the perturbed pore‐fluid normal velocity (relative to the planar chemical dissolution front) is used to directly replace the original pore‐fluid normal velocity (relative to the planar chemical dissolution front) in the related mathematical governing equations (MGEs), so that the proposed algorithm works for the porosity‐velocity‐concentration scheme when it is used to solve CDFI problems in fluid‐saturated porous media. In addition, the related theoretical analysis in this study has answered the previous unanswered question why the application of a perturbation to porosity works in the porosity‐pressure‐concentration scheme but does not work in the porosity‐velocity‐concentration scheme for solving the same CDFI problems in fluid‐saturated porous media. Through solving two illustrative examples with two different distributions of initial porosity, in which one is homogeneous and another is heterogeneous in the chemical dissolution system, the validity and usefulness of the proposed algorithm for implementing perturbations in the computational simulations of CDFI problems have been demonstrated. [ABSTRACT FROM AUTHOR]

Purpose: The objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media. Design/methodology/approach: The porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem. Findings: The direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media. Originality/value: Analytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation. [ABSTRACT FROM AUTHOR]

[Display omitted] • To computationally simulate the ore-forming process in the Luziyuan deposit. • To determine the boundary conditions of the deposit model in a scientific way. • To identify the controlling ore-forming mechanism in the Luziyuan deposit. • To use computational simulations for identifying the location of an ore deposit. The giant Luziyuan Pb-Zn deposit is a typical hydrothermal ore-forming deposit in the southern Baoshan block of SE Tibet. Although extensive studies were conducted to understand the ore-forming system associated with the Luziyuan Pb-Zn deposit through using the traditional geoscience methods, the ore-forming process involved in this deposit has not been justified in a strictly scientific manner to date. In this paper, the hydrothermal ore-forming process of the Luziyuan Pb-Zn deposit is computationally simulated through using the dual length-scale approach associated with the finite element method (FEM). In the dual length-scale approach, the FEM is first used to simulate the regional model of a large length-scale in the geological region where the Luziyuan Pb-Zn deposit is located. Afterward, the FEM is then used to simulate the deposit model of the Luziyuan Pb-Zn deposit. Particularly, the boundary conditions of the deposit model are consistently determined from using the computational simulation results of the regional model. The related numerical results demonstrated that: (1) the pore-fluid convection provides a continuous source of ore-forming fluid and ore-forming material for the Luziyuan Pb-Zn deposit; (2) the convective pore-fluid flow is the main dynamic mechanism, which controls the temperature, pore-fluid velocity and chemical species distribution in the Luziyuan Pb-Zn deposit; (3) the localized structure is the main controlling factor for the localized pore-fluid flow pattern, which further controls the formation and location of the orebody in the Luziyuan Pb-Zn deposit; (4) the dual length-scale approach associated with the FEM is very useful for simulating the hydrothermal ore-forming process of the Luziyuan Pb-Zn deposit. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a semianalytical approach for solving first‐order perturbation (FOP) equations, which are used to describe dissolution‐timescale reactive infiltration instability (RII) problems in fluid‐saturated rocks. The proposed approach contains two parts because the chemical dissolution reaction divides the whole problem domain into two subdomains. In the first part, the interface‐condition substitution strategy is used to derive the analytical expressions of purely mathematical solutions for the FOP equations in the upstream subdomain, where the dissolution chemical reaction is ceased and the FOP equations are weakly coupled. In the second part, the finite element method (FEM) is used to derive the analytical expressions of numerical solutions for the FOP equations in the downstream subdomain, where the dissolution chemical reaction needs to be considered and the FOP equations are strongly coupled so that it is impossible to derive purely mathematical solutions for them. Particular attention is paid to the development of the element‐by‐element forward marching strategy, which is associated with the use of the FEM for solving this new kind of scientific problem. The related analytical results demonstrated that (1) both the dynamic characteristic of a reactive infiltration system and the dimensionless wavenumber can have pronounced influences on the distribution of the FOP dimensionless acid concentration within the entire domain of the dissolution‐timescale RII problems in fluid‐saturated rocks and (2) the FOP dimensionless acid concentration distribution exhibits two significantly different patterns in the upstream and downstream subdomains of the dissolution‐timescale RII system. [ABSTRACT FROM AUTHOR]

Summary: A theoretical study of reactive infiltration instability is conducted on the dissolution timescale. In the present theoretical study, the transient behavior of a dissolution‐timescale reactive infiltration system needs to be considered, so that the upstream region of the chemical dissolution front should be finite. In addition, the chemical dissolution front of finite thickness should be considered on the dissolution timescale. Owing to these different considerations, it is very difficult, even in some special cases, to derive the first‐order perturbation solutions of the reactive infiltration system on the dissolution timescale. To overcome this difficulty, an interface‐condition substitution strategy is proposed in this paper. The basic idea behind the proposed strategy is that although the first‐order perturbation equations in the downstream region cannot be directly solved in a purely mathematical manner, they should hold at the planar reference front, which is the interface between the upstream region and the downstream region. This can lead to two new equations at the interface. The main advantage of using the proposed interface‐condition substitution strategy is that through using the original interface conditions as a bridge, the perturbation solutions for the dimensionless acid concentration, dimensionless Darcy velocity, and their derivatives involved in the two new equations at the interface can be evaluated just by using the obtained analytical solutions in the upstream region. The proposed strategy has been successfully used to derive the dimensionless growth rate, which is the key issue associated with the theoretical study of dissolution‐timescale reactive infiltration instability in fluid‐saturated porous rocks. [ABSTRACT FROM AUTHOR]

Abstract Convective seepage flow plays a key role not only in naturally forming mineral deposits and oil reservoirs, but also in the carbon-dioxide sequestration in fluid-saturated rocks. This paper presents a steady-state numerical solver, which is based on the finite element method (FEM) and progressive asymptotic approach procedure (PAAP), to solve steady-state convective seepage flow problems in fluid-saturated heterogeneous rocks. Although this kind of flow problem is commonly solved by using transient-state numerical solvers, the use of the proposed steady-state numerical solver, which is the main characteristic of this study, can have certain advantages. After the proposed steady-state numerical solver is verified by a benchmark testing problem, for which analytical solutions are available for comparison, it is further applied to simulate steady-state convective seepage flow in the Australia North West Shelf basin, which is composed of naturally-formed heterogeneous porous rocks. Through the simulated numerical results, it can be found that: (1) compared with the analytical solutions of the benchmark testing problem, the use of the steady-state numerical solver can produce correct and accurate numerical simulation results for dealing with convective seepage flow problems in fluid-saturated heterogeneous rocks. (2) The main advantage of using the steady-state numerical solver is to avoid the need of considering initial conditions of the problem, which are commonly difficult to be determined because the convective seepage flow within the upper crust is a past event in geology. (3) In the Australia North West Shelf basin, the convective seepage flow and temperature distribution patterns depend strongly on both the permeability contrast of the faults and the basin geometry (including the layer structures and fault locations) in the computational model. Highlights • To present and verify the numerical method for modeling large-scale convective seepage flow in heterogeneous rocks. • To simulate large-scale convective seepage flow in the Australia North West Shelf basin. • Rock permeability heterogeneity can affect large-scale convective seepage flow and temperature patterns. • Basin geometry can also affect large-scale convective seepage flow and temperature patterns. [ABSTRACT FROM AUTHOR]

The MADS-box transcription factors have garnered substantial attention due to their crucial involvement in various biological processes, particularly in flower organogenesis. A comprehensive investigation into the MADS-box genes remains lacking in loquat (Eriobotrya japonica Lindl.). In the current study, to preliminarily explore the potential candidate genes related to flower and fruit development, a genome-wide analysis was carried out to identify and characterize the MADS-box gene family in loquat. Among the 125 identified EjMADS-box members, 49 genes belonged to type Ⅰ, which were subsequently assigned to three subfamilies: Mα (25 genes), Mβ (10 genes), and Mγ (14 genes). Additionally, 76 genes fell under type II, which were categorized into two groups: MIKCC (70 genes) and MIKC* (6 genes). Through the collinearity analysis and comparison of the gene numbers between loquat and other Rosaceae genomes, it was revealed that the type Ⅱ MADS-box members were expanded in Maloideae after a whole genome duplication. The gene expression analysis utilizing various tissues during flower development revealed that the expression patterns of the ABCDE model homologs were conserved in loquat. In addition, several candidate genes potentially involved in flower bud differentiation (EjMADS107/109) and fruit expansion (EjMADS24/46/49/55/61/67/77/86) were identified. This analysis could serve as a fundamental basis for investigating the molecular functions of the MADS-box genes in the development of flowers as well as fruits in loquat. [ABSTRACT FROM AUTHOR]

Mountain topography can cause both pressure-gradient driven advective flow and temperature-gradient driven convective flow. Compared with the pressure-gradient driven advective flow, the temperature-gradient driven convective flow can last long enough to enable the hydrothermal ore-forming system to reach a steady state. This paper is focused on the numerical modeling of a hydrothermal ore-forming system, in which the temperature-gradient driven convective flow is the main driving force of orebody formation and mineralization. A generic model, which can be viewed as a generalized geological model, is used in the numerical modeling. To simulate the chemical aspects of the hydrothermal ore forming system, a simplified chemical process associated with the Broken Hill type Pb-Zn deposit is considered in this study. The related numerical results demonstrated that: (1) The mountain topography plays an important role in controlling Pb and Zn mineralization distribution patterns in a hydrothermal ore-forming system; (2) The mixing of the reactive sulfide and sulfate fluids can be enhanced by the temperature-gradient driven convective flow; (3) If the duration of mineralization time is known, then the computed mineral precipitation rate can be used to predict the average (weight) grade of a mineral in the hydrothermal ore-forming system. Similarly, if the average (weight) grade of a mineral is known from a mining site, then the computed mineral precipitation rate can be used to estimate the duration of mineralization time in the hydrothermal ore-forming system. [ABSTRACT FROM AUTHOR]

Reaction-infiltration instability, in which chemical reactions can dissolve minerals and therefore create preferential pore-fluid flow channels in fluid-saturated rocks, may play an important role in controlling groundwater quality in groundwater hydrology. Although this topic has been studied for many years, there is a recent debate, which says that the use of large-density asymptotics in the previous studies is invalid. However, there is a crucial conceptual mistake in this debate, which leads to results and conclusions that are inconsistent with the fundamental laws of physics. It is well known that in terms of distance, time and velocity, there are only two independent variables. But they are treated as three independent variables, a procedure that is the main source of the physically unrealistic results and conclusions in the debate. In this paper, we will discuss the results and conclusions related to the debate, with emphasis on the issues leading to the corresponding errors. In particular, we demonstrate that there is an unappreciated constraint condition between the dimensional/dimensionless distance, time and velocity in the debate. By using this constraint condition, it can be confirmed that as the ratio of the reactant concentration in the incoming fluid stream to the mineral concentration approaches zero, the dimensionless transport parameter, H , automatically approaches infinity. Therefore, it is further confirmed that the previous work conducted by Chadam and others remains valid. [ABSTRACT FROM AUTHOR]

The use of the asymptotic limit can greatly simplify the theoretical analysis of chemical dissolution front instabilities in fluid-saturated rocks and therefore make it possible to obtain mathematical solutions, which often play a crucial role in understanding the propagation behavior of chemical dissolution fronts in chemical dissolution systems. However, there has been a debate in recent years that the asymptotic limit of the acid dissolution capacity (i.e., the acid dissolution capacity number approaching zero) alone cannot lead to a sharp dissolution front of the Stefan type in the acidization dissolution system, in which the dissolvable minerals of carbonate rocks are chemically dissolved by the injected acid flow. The acid dissolution capacity number is commonly defined as the ratio of the volume of the carbonate rock dissolved by an acid to that of the acid. In this paper, we use four different proof methods, including (i) direct use of the fundamental concepts; (ii) use of the mathematical governing equations of an acidization dissolution system; (iii) use of the different time scaling approach; and (iv) use of a moving coordinate system approach, to demonstrate that the asymptotic limit of the acid dissolution capacity can indeed lead to sharp dissolution fronts of the Stefan type in acidization dissolution systems on a much larger time scale (than the dissolution time scale). Our new finding is that on the reaction time scale, the condition of the conventional time derivative of porosity approaching zero alone can ensure that the acidization dissolution front has a sharp shape of the Stefan type. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Acid dissolution capability plays a considerable role in controlling the propagation of an acid-dissolution front in the carbonate rocks that are saturated by pore fluids. This capability can be represented by a dimensionless number, known as the acid dissolution capability number, by which we mean the quotient of the volume of an acid-dissolved carbonate rock divided by that of the acid itself. This paper aims primarily to investigate why and how the acid dissolution capacity can affect the behaviors of the acid-dissolution front propagation in the carbonate rocks that are saturated by pore fluids. If the acid dissolution capacity number is a nonzero finite number, as in a general case, then the computational simulation method needs to be employed to get numerical solutions for the acid-dissolution system. The relevant computational simulation results have demonstrated that: (1) with an increase in the value of the Zhao number (namely another dimensionless number), which is used to denote the dynamic characteristics of an acid-dissolution system, the acid-dissolution front becomes more unstable in the corresponding supercritical acid-dissolution system. (2) When the acid dissolution capacity number is small enough, the propagating speed of a planar acid-dissolution front in the corresponding subcritical acid-dissolution system is linearly dependent on the acid dissolution capacity number, indicating that the smaller the acid dissolution capacity, the slower the propagating speed of a planar acid-dissolution front in the corresponding subcritical acid-dissolution system. (3) With a decrease in the acid dissolution capacity number, the acid-dissolution front can exhibit more unstable behavior in the corresponding supercritical acid-dissolution system. [ABSTRACT FROM AUTHOR]

Pore-fluid flow associated with seepage instabilities can play an important role in controlling large mineralisation patterns within the upper crust of the Earth. To demonstrate this process, two kinds of seepage instability problems in fluid-saturated porous rocks are considered in this paper. The first kind of seepage instability problem is caused by the temperature-induced buoyancy of pore fluid, so that it can be called the buoyancy-driven seepage instability problem, while the second kind of seepage instability problem is caused by chemical dissolution reactions that are commonly encountered in the upper crust of the Earth, so that it can be called the chemical-dissolution-driven seepage instability problem. After the mathematical governing equations of and computational methods for these two kinds of seepage instability problems are introduced, two numerical examples are used to elucidate how and why these two kinds of seepage instabilities can provide favorable places for the formation of large mineralisation patterns within the upper crust of the Earth. The related computational simulation results have demonstrated that: (1) the convective pore-fluid flow caused by the buoyancy-driven seepage instability not only can dissolve minerals at the lower part of the upper crust, but also can transport the dissolved minerals from the lower part to the upper part of the upper crust, resulting in large mineralisation patterns near the surface of the Earth's upper crust. (2) The chemical-dissolution-driven seepage instability in fluid-saturated porous rock can provide some favorable places, such as finger-like channels created by porosity enhancement in the porous rock, for the formation of large mineralisation patterns within the upper crust of the Earth. [ABSTRACT FROM AUTHOR]

Because dissolution of rocks may create and enhance groundwater flow channels, the chemical dissolution-front instability (CDFI) can control the quality of groundwater. This paper presents the theoretical analyses of porosity-permeability relationship effects on the CDFI in water-saturated porous rocks. Since the CDFI in a water-rock reaction system can be assessed by comparing the comprehensive dimensionless dynamic characteristic (CDDC) number with the corresponding critical CDDC number of the geochemical dissolution system, it is necessary to investigate theoretically how different porosity-permeability relationships can affect the CDDC number and critical CDDC number of a water-rock reaction system. With the commonly-used Kozeny–Carman (KC) formula taken as a reference porosity-permeability formula, the permeability variation indicator (PVI), which is defined as the ratio of the permeability obtained from any porosity-permeability formula to that obtained from the KC formula, is proposed to reflect the effect of the porosity-permeability formula on the CDFI in a water-rock reaction system. The theoretical results demonstrated that: (1) since the porosity-permeability formula with a higher PVI can result in a stronger Darcy flow velocity, it may have a significant influence on the CDFI in the water-rock reaction system. (2) With an increase in the PVI of a porosity-permeability formula, there is a decrease in the critical CDDC number of the water-rock reaction system. This means that the porous rock with a higher PVI can enable the CDFI to take place much easier in the water-rock reaction system. (3) The use of the porosity-permeability formula with a higher PVI can also cause an increase in both the dimensionless growth rate of a perturbation and the propagation speed of the chemical dissolution front in the water-rock reaction system. [ABSTRACT FROM AUTHOR]

Distribution of the mineral precipitation region (in blue) and dissolution region (in red). [Display omitted] • To examine potential dynamic mechanisms for controlling mineralization patterns. • To propose a semi-analytical approach for coupled flow and heat transfer problems. • To precisely simulate coupled flow and heat transfer in permeable horizontal layers. • To investigate porosity structure effects on hydrothermal mineralization patterns. The porosity structures of a permeable rock can have remarkable effects on pore-fluid flow within the rock. According to the modern mineralization theory, the mineralization pattern in a hydrothermal ore-forming system is strongly dependent on the pore-fluid flow velocity, so that different porosity structures of a permeable rock can affect significantly hydrothermal mineralization patterns within the permeable layers consisting of fluid-saturated porous rocks. This paper presents a semi-analytical approach, in which pore-fluid velocity is directly used as fundamental primary variables in the governing equations of the problem and the property matrices of finite elements are analytically evaluated in a purely mathematical manner, to ensure the high accuracy of the obtained pore-fluid velocity, which is involved in controlling mineralization patterns in hydrothermal ore-forming systems. After the proposed semi-analytical approach is verified through comparing the numerical solution with the analytical solution for a benchmark problem, it has been used to investigate how different porosity structures can affect the hydrothermal mineralization patterns within permeable horizontal layers consisting of fluid-saturated porous rocks through using a generic model, which can be viewed as the representation of a generalized and simplified geological model. Main outcomes of this study have demonstrated that: (1) the proposed semi-analytical approach can produce highly-accurate numerical solutions for solving coupled pore-fluid flow and heat transfer problems in fluid-saturated porous rocks with different porosity structures; (2) the different porosity structure within a permeable horizontal layer consisting of fluid-saturated porous rocks can have a significant effect on the hydrothermal mineralization pattern of the permeable horizontal layer; (3) layered pore-fluid vertical velocity focusing may take place within a permeable horizontal layer involving a heterogeneous porosity structure. [ABSTRACT FROM AUTHOR]

Temporal-spatial distributions of geochemical data in geoinformatics are very important for mineral exploration in the upper crust of the Earth and for the treatment of geoenvironmental issues such as CO 2 sequestration in geological formations. To understand ore-forming processes associated with mineral exploration, it is necessary to acquire geochemical information regarding orebody formation and mineralization in hydrothermal systems within the upper crust of the Earth in the past. On the contrary, to generate a safe design for CO 2 sequestration in a geological formation, it is necessary to predict the composition of geochemical environment after CO 2 sequestration and test such predictions through acquiring geochemical information in the future, so that the safety and feasibility of the design can be adequately assessed. The computational simulation approach is used, in this paper, to facilitate and guide these acquisition procedures. To demonstrate the feasibility and usefulness of the computational simulation approach in this aspect, a simplified ore-forming system associated with the Australian Broken Hill Pb and Zn mine, which belongs to a natural system, and a fluid-rock reaction system involving CO 2 sequestration in a geological formation, which belongs to a man-made system, are considered to model geochemical information. The related computational simulation results demonstrate that the computational simulation method is not only applicable for simulating the ore-forming processes in hydrothermal systems within the upper crust of the Earth, but also useful for acquiring both the ancient geochemical information associated with ore-forming systems and the future geochemical information associated with geoenvironmental systems. [ABSTRACT FROM AUTHOR]

This paper mainly deals with the theoretical aspects of chemical dissolution-front instability problems in two-dimensional fluid-saturated porous media under non-isothermal conditions. In the case of the mineral dissolution ratio (that is defined as the ratio of the dissolved-mineral equilibrium concentration in the pore fluid to the molar concentration of the dissolvable mineral in the solid matrix of the fluid-saturated porous medium) approaching zero, the corresponding critical condition has been mathematically derived when temperature variation effects are considered. As a complementary tool, the computational simulation method is used to simulate the morphological evolution of chemical dissolution fronts in two-dimensional fluid-saturated porous media under non-isothermal conditions. The related theoretical and numerical results have demonstrated that: (i) a temperature increase in a non-isothermal chemical dissolution system can have some influence on the propagation speed of the planar chemical dissolution front in the system. Generally, the chemical dissolution front in the non-isothermal chemical dissolution system propagates slower than that in the counterpart isothermal chemical dissolution system when the temperature of the non-isothermal chemical dissolution system is higher than that of the counterpart isothermal chemical dissolution system; (ii) a temperature increase in the non-isothermal chemical dissolution system can stabilize the chemical dissolution front propagating in the system, because it can cause a decrease in the Zhao number of the system but does not affect the critical Zhao number of the system; and (iii) the temperature gradient in the upstream direction of a chemical dissolution front is smaller than that in the downstream direction of the chemical dissolution front when the non-isothermal chemical dissolution system is supercritical. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Numerical modeling has now become an indispensable tool for investigating the fundamental mechanisms of toxic nonaqueous phase liquid (NAPL) removal from contaminated groundwater systems. Because the domain of a contaminated groundwater system may involve irregular shapes in geometry, it is necessary to use general quadrilateral elements, in which two neighbor sides are no longer perpendicular to each other. This can cause numerical errors on the computational simulation results due to mesh discretization effect. After the dimensionless governing equations of NAPL dissolution problems are briefly described, the propagation theory of the mesh discretization error associated with a NAPL dissolution system is first presented for a rectangular domain and then extended to a trapezoidal domain. This leads to the establishment of the finger-amplitude growing theory that is associated with both the corner effect that takes place just at the entrance of the flow in a trapezoidal domain and the mesh discretization effect that occurs in the whole NAPL dissolution system of the trapezoidal domain. This theory can be used to make the approximate error estimation of the corresponding computational simulation results. The related theoretical analysis and numerical results have demonstrated the following: (1) both the corner effect and the mesh discretization effect can be quantitatively viewed as a kind of small perturbation, which can grow in unstable NAPL dissolution systems, so that they can have some considerable effects on the computational results of such systems; (2) the proposed finger-amplitude growing theory associated with the corner effect at the entrance of a trapezoidal domain is useful for correctly explaining why the finger at either the top or bottom boundary grows much faster than that within the interior of the trapezoidal domain; (3) the proposed finger-amplitude growing theory associated with the mesh discretization error in the NAPL dissolution system of a trapezoidal domain can be used for quantitatively assessing the correctness of computational simulations of NAPL dissolution front instability problems in trapezoidal domains, so that we can ensure that the computational simulation results are controlled by the physics of the NAPL dissolution system, rather than by the numerical artifacts. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Based on the particle simulation method, a thermo-mechanical coupling particle model is proposed for simulating thermally-induced rock damage. In this model, rock material is simulated as an assembly of particles, which are connected to each other through their bonds, in the case of simulating mechanical deformation, but connected to each other through thermal pipes in the case of simulating heat conduction. The main advantages of using this model are that: (1) microscopic parameters of this model can be directly determined from the related macroscopic ones; (2) the temperature-dependent elastic modulus and strength are considered in an explicit manner, so that thermally-induced rock damage can be realistically simulated in a thermo-mechanical coupling problem. The related simulation results from an application example have demonstrated that: (1) the proposed model can produce similar behaviors to those observed in experiments; (2) the final failure is initiated from the outer surface of the testing sample and propagates toward the borehole; (3) microscopic crack initiation and propagation processes can be reasonably simulated at the cooling stage. [Copyright &y& Elsevier]

SUMMARY This paper presents an instability theory that can be used to understand the fundamental behavior of an acidization dissolution front when it propagates in fluid-saturated carbonate rocks. The proposed theory includes two fundamental concepts, namely the intrinsic time and length of an acidization dissolution system, and a theoretical criterion that involves the comparison of the Zhao number and its critical value of the acidization dissolution system. The intrinsic time is used to determine the time scale at which the acidization dissolution front is formed, while the intrinsic length is used to determine the length scale at which the instability of the acidization dissolution front can be initiated. Under the assumption that the acidization dissolution reaction is a fast process, the critical Zhao number, which is used to assess the instability likelihood of an acidization dissolution front propagating in fluid-saturated carbonate rocks, has been derived in a strictly mathematical manner. Based on the proposed instability theory of a propagating acidization dissolution front, it has been theoretically recognized that: (i) the increase of the mineral dissolution ratio can stabilize the acidization dissolution front in fluid-saturated carbonate rocks; (ii) the increase of the final porosity of the carbonate rock can destabilize the acidization dissolution front, while the increase of the initial porosity can stabilize the acidization dissolution front in fluid-saturated carbonate rocks; (iii) the increase of the mineral dissolution ratio can cause an increase in the dimensionless propagation speed of the acidization dissolution front; (iv) the increase of the initial porosity can enable the acidization dissolution front to propagate faster, while the increase of the final porosity can enable the acidization dissolution front to propagate slower in the acidization dissolution system. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Highlights: [•] To derive analytical solutions for NAPL dissolution problems with radial flow. [•] Three key factors can affect the propagating speed of an NAPL dissolution front. [•] Three key factors can also affect the location and breakthrough time of an NAPL dissolution front. [•] The Zhao number can be used to represent the overall hydrodynamic characteristic of a NAPL dissolution system. [•] Several key factors can also affect the distribution pattern and evolution of the NAPL dissolution front. [Copyright &y& Elsevier]

Abstract: Since the generalized transfer matrix method overcomes the intrinsic instability of the Thomson–Haskell transfer matrix method for both high frequencies and/or thick layers, it can produce stable and accurate solutions for the dynamic analysis of viscoelastic media as well as anisotropic media. This paper extends the generalized transfer matrix method to the dynamic analysis of multilayered poroelastic media. Main improvements include the presentation of the concisely explicit general solutions for the dynamic analysis of multilayered poroelastic media and the derivation of an analytical inversion of 8×8 order layer matrix corresponding to the general solutions. The explicit solutions are valid for the dynamic analysis of one-dimensional, two-dimensional and three-dimensional poroelastic medium problems. In addition, an efficient recursive scheme is proposed for accurate determination of the equivalent interface sources for multilayered poroelastic media due to excitation by a source at an arbitrary depth. For the dynamic analysis of multilayered poroelastic media, the generalized transfer matrix method recursively transfers both the interface stiffness matrix and equivalent source starting from the bottom half space to the top layer, without resort to the numerical solution of the assembled global equations as the exact stiffness matrix method does. While keeping the simplicity of the Thomson–Haskell transfer matrix method, the generalized transfer matrix method is both accurate and stable. The related numerical examples have demonstrated that the generalized transfer matrix method is an alternative approach to conducting the dynamic analysis of multilayered poroelastic media. [Copyright &y& Elsevier]

This paper presents a numerical procedure for computational modeling of moving interfaces between fluid and porous medium domains. To avoid the direct description of the interface boundary conditions at the interface between the fluid and porous medium domains, Darcy's law is used to simulate fluid flows in both the fluid and porous medium domains. For the purpose of effectively simulating the fluid flow using Darcy's law, the artificial permeability of the fluid domain is used to establish a permeability ratio between the artificial permeability in the fluid domain and the real permeability in the porous medium domain. Using the proposed permeability ratio, the ratio of fluid pressure gradient in the porous medium domain to that in the fluid domain can be appropriately simulated. To verify the proposed numerical procedure, analytical solutions have been derived for a benchmark problem, which can be simulated using the proposed numerical procedure. Comparison of the numerical solutions with the derived analytical solutions has demonstrated the correctness and accuracy of the proposed numerical procedure. Through applying the proposed numerical procedure to several examples associated with the fluid-porous medium interface propagation problems, the related numerical solutions have demonstrated that: (1) the proposed numerical procedure is capable of simulating the morphological instability of the fluid-porous medium interface in a coupled fluid flow-chemical dissolution system when the system is in a supercritical state; and (2) the permeability ratio can have a considerable effect on the evolved morphologies of the fluid-porous medium interface in the coupled fluid flow-chemical dissolution system. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an efficient time-integration method for obtaining reliable solutions of the transient nonlinear dynamic problems and of the stiff systems in structural engineering. This method employs the backward Euler formulae for evaluating both displacements and velocities of structures. It is a self-starting, two-step, second-order accurate algorithm with the same computational effort as the trapezoidal rule. The evaluations of the stability and accuracy of the proposed method are also given in this paper. With some numerical damping introduced, the proposed method remains stable in large deformation and long time range solutions even when the trapezoidal rule fails. Meanwhile, the proposed method has the following characteristics: (1) it is applicable to linear as well as general nonlinear analyses; (2) it does not involve additional variables (e.g. Lagrange multipliers) and artificial parameters; (3) it is a single-solver algorithm at the discrete time points with symmetric effective stiffness matrix and effective load vectors; and (4) it is easy to implement in an existing computational software. Some numerical results indicate that the proposed method is a powerful tool with some notable features for practical nonlinear dynamic analyses. [Copyright &y& Elsevier]

Abstract: The main purpose of this paper is to investigate the effects of different domain shapes in general and trapezoidal domain shape in particular on the morphological evolution of nonaqueous phase liquid (NAPL) dissolution fronts in two-dimensional fluid-saturated porous media. After the governing equations of NAPL dissolution problems are briefly described, the numerical procedure consisting of a combination of the finite element and finite difference methods is used to solve these equations. The related numerical simulation results have demonstrated that: (1) domain shapes have a significant effect on both the propagating speed and the morphological evolution pattern of a NAPL dissolution front in the fluid-saturated porous medium; (2) an increase in the divergent angle of a trapezoidal domain can lead to a decrease in the propagating speed of the NAPL dissolution front; (3) the morphological evolution pattern of the NAPL dissolution front in a rectangular domain is remarkably different from that in a trapezoidal domain of a large divergent angle; (4) for a rectangular domain, the simplified dispersion model, which is commonly used in the theoretical analysis and numerical simulation, is valid for solving NAPL dissolution instability problems in fluid-saturated porous media; and (5) compared with diverging flow (when the trapezoidal domain is inclined outward), converging flow (when the trapezoidal domain is inclined inward) can enhance the growth of NAPL fingers, indicating that pump-and-treat systems by extracting contaminated groundwater might enhance NAPL dissolution fingering and lead to less uniform dissolution fronts. [Copyright &y& Elsevier]

SUMMARY This paper presents a systematic and efficient method, namely the generalized transfer matrix method, for evaluating the dispersion curves and eigenfunctions of surface waves in multilayered azimuthally anisotropic half-space. Apart from avoiding the well-known numerical difficulties associated with the existing Thomson-Haskell method, the generalized transfer matrix method possesses the robust determination of independent polarization vectors by using the singular value decomposition (SVD) approach, the explicit inversion of the 6 × 6 eigencolumn matrix without any resort to numerical inversion and the efficient computation of eigenfunctions for layered azimuthally anisotropic media. By means of straightforward transformations, the generalized transfer matrix method leads to a twofold recursive algorithm: (1) for the recursive computation of phase velocities it starts from the bottom half-space to the top layer and (2) for the recursive solution of eigenfunctions it starts from the top layer to the bottom half-space. While keeping the simplicity of the Thomson-Haskell transfer matrix method, the generalized transfer matrix method is of unconditional stability and computational efficiency. The related numerical examples demonstrate that the generalized transfer matrix method is a powerful and robust tool for simulating the propagation of elastic surface waves in the layered azimuthally anisotropic half-space. [ABSTRACT FROM AUTHOR]

In dealing with chemical-dissolution-front propagation problems in fluid-saturated porous media, the chemical dissolution front represented by the porosity of the medium may have a very steep slope (i.e., a very large porosity gradient) at the dissolution front, depending on the mineral dissolution ratio that is defined as the equilibrium concentration of the dissolved minerals in the pore-fluid to the solid molar density of the dissolvable minerals in the solid matrix. When the mineral dissolution ratio approaches zero, the theoretical value of the porosity gradient tends to infinity at the chemical dissolution front. Even for a very small value of the mineral dissolution ratio, which is very common in geochemical systems, the porosity gradient can be large enough to cause the solution hard to converge when the conventional finite element method is used to solve a chemical dissolution problem in a fluid-saturated porous medium where the pore-fluid is compressible. To improve the convergent speed of solution, a porosity-gradient replacement approach, in which the term involving porosity-gradient computation is replaced by a new term consisting of pore-fluid density-gradient and pressure-gradient computation, is first proposed and then incorporated into the finite element method in this study. Through comparing the numerical results obtained from the proposed approach with the theoretical solutions for a benchmark problem, it has been demonstrated that not only can the solution divergence be avoid, but also the accurate simulation results can be obtained when the proposed porosity-gradient replacement approach is used to solve chemical-dissolution-front propagation problems in fluid-saturated porous media including pore-fluid compressibility. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a general discussion on some fundamental issues associated with the current research status in the field of computational hydrodynamics of mineralization. Based on the scientific characteristics of mineral forming systems within the upper crust of the Earth, the fundamental issues under consideration include: (1) simulation of multi-process aspects of a mineral forming system; (2) simulation of multi-scale aspects of a mineral forming system; (3) simulation of fluid convection associated with a mineral forming system; (4) simulation of fluid focusing and mixing associated with a mineral forming system; and (5) simulation of reactive mass transport associated with a mineral forming system. After the current status of each fundamental issue is briefly summarized, the future development in the field of computational hydrodynamics of mineralization is discussed on the basis of further improving the treatments of the fundamental issues considered in this investigation. [Copyright &y& Elsevier]

Abstract: The main purpose of this paper is to simulate computationally the kinematical motion of the frictional drill-bit of an automatic mining machine in the underground consisting of cemented granular materials. Although the finite element method has become a powerful tool for the design and analysis of many kinds of engineering products, it cannot be used, both effectively and efficiently, for dealing with the frictional drill-bit design problem that involves discrete-mechanics characteristics in nature. Thus, the particle simulation method is employed for mimicking the kinematical motion of a frictional drill-bit, which is fundamental to the design of an automatic mining machine in cemented granular materials. In order to simulate the driving force mechanism of a frictional drill-bit, both the designed velocity and the actual velocity concepts of the frictional drill-bit are proposed. This enables the particle simulation method to be used as a potential tool for the design of an automatic mining machine, which can be used as a new mining technology in some particular mining environments. To illustrate the usefulness and applicability of the proposed driving mechanism associated with the particle simulation method, it has been used for mimicking the frictional drill-bit movement of an automatic mining machine in cemented granular materials under several working conditions. The related computational simulation results have demonstrated that (1) the particle simulation method, together with the proposed driving mechanism of a frictional drill-bit, can provide a useful tool for the design of an automatic mining machine and (2) the vibrating frequency of a frictional drill-bit may have considerable effects on the motion of the frictional drill-bit in the underground consisting of cemented granular materials. [Copyright &y& Elsevier]

Abstract: This paper presents a time-dependent semi-analytical artificial boundary for numerically simulating elastic wave propagation problems in a two-dimensional homogeneous half space. A polygonal boundary is considered in the half space to truncate the semi-infinite domain, with an appropriate boundary condition imposed. Using the concept of the scaled boundary finite element method, the wave equation of the truncated semi-infinite domain is represented by the partial differential equation of non-constant coefficients. The resulting partial differential equation has only one spatial coordinate variable and time variable. Through introducing a few auxiliary functions at the truncated boundary, the resulting partial differential equations are further transformed into linear time-dependent equations. This allows an artificial boundary to be derived from the time-dependent equations. The proposed artificial boundary is local in time, global at the truncated boundary and semi-analytical in the finite element sense. Compared with the scaled boundary finite element method, the main advantage in using the proposed artificial boundary is that the requirement for solving a matrix form of Lyapunov equation to obtain the unit-impulse response matrix is avoided, so that computer efforts are significantly reduced. The related numerical results from some typical examples have demonstrated that the proposed artificial boundary is of high accuracy in dealing with time-dependent elastic wave propagation in two-dimensional homogeneous semi-infinite domains. [ABSTRACT FROM AUTHOR]

Abstract: Mass and energy should be conservative in nature and ore forming systems within the upper crust of the earth are no exception. Thus, the mass conservation law is valid not only for a closed system, but for an open system as well. In the latter case, exchange between the system and its surroundings must be considered. Based on the mass conservation law, this paper considers a number of different roles of geofluid flow in ore forming systems. Due to the concurrence of these roles, interactions between fluid flow, heat transfer, mass transport and chemical reactions need to be considered in a comprehensive manner. Through theoretical analysis and computational simulations of several typical generic models for ore forming systems, it can be demonstrated that for an ore forming system in chemical equilibrium, the aqueous species of which are produced by the chemical dissolution reactions, the approximate form (i.e. the rock alteration index and the improved rock alteration index) of the mineralization rate can be used to predict mineralization patterns in the ore forming system. However, for a chemically non-equilibrated ore forming system, the detailed interaction between solute advection, solute diffusion/dispersion and chemical kinetics needs to be considered to determine potential mineralization patterns in the ore forming system. [Copyright &y& Elsevier]

Abstract: For a three-dimensional vertically-oriented fault zone, we consider the coupled effects of fluid flow, heat transfer and reactive mass transport, to investigate the patterns of fluid flow, temperature distribution, mineral alteration and chemically induced porosity changes. We show, analytically and numerically, that finger-like convection patterns can arise in a vertically-oriented fault zone. The onset and patterns of convective fluid flow are controlled by the Rayleigh number which is a function of the thermal properties of the fluid and the rock, the vertical temperature gradient, and the height and the permeability of the fault zone. Vigorous fluid flow causes low temperature gradients over a large region of the fault zone. In such a case, flow across lithological interfaces becomes the most important mechanism for the formation of sharp chemical reaction fronts. The degree of rock buffering, the extent and intensity of alteration, the alteration mineralogy and in some cases the formation of ore deposits are controlled by the magnitude of the flow velocity across these compositional interfaces in the rock. This indicates that alteration patterns along compositional boundaries in the rock may provide some insights into the convection pattern. The advective mass and heat exchanges between the fault zone and the wallrock depend on the permeability contrast between the fault zone and the wallrock. A high permeability contrast promotes focussed convective flow within the fault zone and diffusive exchange of heat and chemical reactants between the fault zone and the wallrock. However, a more gradual permeability change may lead to a regional-scale convective flow system where the flow pattern in the fault affects large-scale fluid flow, mass transport and chemical alteration in the wallrocks. [Copyright &y& Elsevier]

Abstract: A new finite element scheme is proposed, in this paper, for solving two-dimensional wave propagation problems in multilayered soils resting on a rigid base. The multilayered soils are treated as multiple horizontal layers of lateral infinite extension in geometry. Since these horizontal layers can be truncated by two artificially truncated vertical boundaries, two high-order artificial boundary conditions are applied for propagating the incoming waves from the interior domain into the far field of the system. Both the semi-analytical method and the truncated boundary migration procedure are used to derive the high-order artificial boundary conditions, which are comprised of a physically meaningful dashpot and a generalized energy absorber. The main advantage of using the proposed finite element scheme is that the derived artificial boundary condition can be straightforwardly implemented in the finite element analysis, without violating the band/sparse structure of the conventional finite element equation. The related numerical examples have demonstrated that the proposed finite element scheme is of high accuracy in dealing with wave propagation problems in multiple horizontal layers. [Copyright &y& Elsevier]

Abstract: When the particle simulation method is used to simulate large length-scale problems, such as crustal length-scale problems in the field of geology, it is necessary to include gravity effect into the particle model. To consider gravity effect appropriately, there is a minimum value requirement for the contact stiffness of a particle so that unexpected particle overlap can be avoided. This minimum value is called the critical contact stiffness of a particle due to gravity effect. Using the vertical force equilibrium condition of a particle at the bottom of a two-dimensional particle model, a theoretical formula has been successfully derived for determining the critical contact stiffness of the particle in this paper. For the two-dimensional particle model consisting of circular particles of unit thickness, there is a relationship between the critical contact stiffness of a particle and the critical elastic modulus of the particle material when a linear-elastic-contact model between any two particles is used. Since the elastic moduli of most crustal rocks are greater than the corresponding critical elastic modulus of the particle material, it has been theoretically demonstrated that the particle simulation method, which is based on the linear-elastic-contact model between any two particles, is suitable for simulating gravity effect within the particle model of a large length-scale. The related simulation results have demonstrated the usefulness of the particle simulation method for simulating spontaneous crack generation patterns within brittle crustal rocks. [Copyright &y& Elsevier]

• To study mathematical transform on analyzing chemical-dissolution front instability. • Two different mathematical transforms were considered in the study. • Mathematical transforms have no effect on the dispersion equation of the system. • Mathematical transforms affect evolution patterns in the system of a finite domain. Reactive mass transport, in which chemical dissolution front may become unstable, is a common phenomenon in the field of groundwater hydrology. The use of mathematical transforms can convert many scientific and engineering problems from the conventional time–space domain into a generalized time–space domain, so that analytical solutions, which are impossible to be directly obtained in the conventional time–space domain, can be derived in the generalized time–space domain. The theoretical analysis and computational simulation of dissolution-timescale chemical dissolution-front instability within fluid-saturated porous media is no exception. To investigate how different mathematical transforms can affect the theoretical analyses and computational simulation of chemical dissolution-front instability within fluid-saturated porous media, two different approaches are considered to select mathematical transforms in this study. In the first approach, the mathematical transform mainly consists of a much larger timescale than the dissolution timescale and a length-scale that is independent of the mineral dissolution ratio (MDR), while in the second approach, the mathematical transform mainly consists of the dissolution timescale and the MDR-dependent length-scale. The related theoretical and computational results have demonstrated that: (1) the use of two different mathematical transforms has no effect on the analytical solution to the dispersion equation of a chemical dissolution-front instability problem in the original physical time–space domain. (2) The use of different mathematical transforms may have significant effects on computationally simulating the evolution patterns of unstable chemical dissolution-front in finite space domains, which are filled with fluid-saturated porous media. (3) If the mathematical transform is appropriately selected, then the dissolution-timescale chemical dissolution-front instability problem in fluid-saturated porous media is mathematically solvable. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, theoretical and numerical methods are used to investigate pore-fluid flow focused temperature distribution patterns around geological faults and cracks of any length-scales in hydrothermal systems. If the far field inflow is uniform and the long axis of an elliptical fault of any length-scale is parallel to the far field inflow direction, a complete set of analytical solutions has been presented for the pore-fluid velocity, stream function and excess pore-fluid pressure around the elliptical fault embedded in fluid-saturated porous media. Because the analytical solutions are explicitly expressed in the conventional Cartesian coordinate system, not only can they be used to gain a theoretical insight into the pore-fluid flow patterns around geological faults and large cracks, but also they can be used as valuable benchmark solutions for validating any numerical methods. After a finite element computational model is validated by comparing the numerical solutions with the present analytical solutions, it is used to investigate pore-fluid flow focused heat transfer around geological faults in hydrothermal systems. Some interesting conclusions in relation to the effects of geological faults on pore-fluid flow focused heat transfer have been made through both the theoretical and the numerical analyses. [Copyright &y& Elsevier]

Abstract: The particle simulation method is used in this paper to explicitly simulate spontaneous crack generation in brittle crustal rocks. Although the method was previously used to simulate crack generation in small-scale laboratory specimens and mining sites, it has seldom been used to simulate spontaneous crack generation in large-scale geological systems. If a geological system can be treated as a quasi-static one, the mechanical response of the system should be independent of the loading rate. Based on this understanding, we have compared the commonly-used continuous loading procedure with a newly-proposed discontinuous loading procedure, which is independent of the loading rate within the elastic range of a particle system. The use of the discontinuous loading procedure enables the macroscopic elastic modulus of a two-dimensional particle system to be directly evaluated from the particle stiffness. However, the particle-size sensitivity analysis of at least two different models needs to be conducted for dealing with the particle size-dependent issue when the particle simulation method is applied to solve crack generation problems in geological systems. Through the phenomenological modeling of spontaneous crack generation problems, it has been demonstrated that the particle simulation method is useful for simulating spontaneous crack generation phenomena at geological length scales. [Copyright &y& Elsevier]

Large cracks and faults play an important and diverse role in controlling pore-fluid flow patterns in pore-fluid-saturated porous rocks. Examples of fault-related fluid flow include (1) geological structural controls on groundwater flow and contaminant transport, (2) formation and localization of some valuable mineral deposits around and within fault zones, (3) impacts of heterogeneous fault zone hydraulic properties on the formation and location of petroleum reservoirs through fault sealing, compartmentalization and variability in pore-fluid flow pathways and (4) induced rupture and failure processes by the interaction between material deformation and pore-fluid flow around faults through cycles of brittle deformation and seismicity. In this paper, theoretical and numerical methods are used to investigate pore-fluid flow patterns around and within large cracks and faults in pore-fluid-saturated porous rocks. Although considerable numerical investigations have been carried out on the flow pattern around large cracks and faults, a full set of exact analytical solutions in the case of a fault having any finite but non-zero permeability is not yet available due to mathematical difficulties in solving the related partial differential equations in a conventional Cartesian coordinate system. For the purpose of deriving a full set of exact analytical solutions, large cracks and faults are treated as elliptic inclusions, in which both the aspect ratio of an elliptic crack and the permeability ratio of the crack to its surrounding rock are used to represent the hydrodynamic property contrast of the elliptic crack. It is assumed that the pore-fluid flow in the far field away from the elliptic crack is uniform and that the long axis of the elliptic crack is inclined to the inflow direction in the undisturbed far field. Under these assumptions, a full set of analytical solutions has been derived for the pore-fluid velocity, stream function and excess pore-fluid pressure around and within an inclined elliptic crack in pore-fluid-saturated porous rocks. To overcome mathematical difficulties in describing and satisfying interface conditions between the elliptic crack and its surrounding rocks, analytical solutions are firstly derived in an elliptical coordinate system, and then explicitly expressed, through rigorous inverse mappings, in the conventional Cartesian coordinate system using elementary functions. This allows the present analytical solutions not only to be used to produce theoretical understanding of the pore-fluid flow pattern around and within a large crack, but also to be used as valuable benchmark solutions for validating any numerical methods. After a finite element computational model is validated by comparing the numerical solutions with the present analytical ones, it is used to investigate pore-fluid flow patterns around and within two parallel inclined cracks in pore-fluid-saturated porous rocks. Some conclusions in relation to the effects of inclined large cracks on pore-fluid flow patterns are made through both the theoretical and the numerical analyses. [ABSTRACT FROM AUTHOR]

Abstract: Chemical reaction patterns are strongly dependent on flow rates, solute diffusion/dispersion and chemical kinetics. Since ore body formation is closely associated with chemical reaction patterns, it is important to investigate an interaction between solute advection, solute diffusion/dispersion and chemical kinetics due to two fluids mixing and focusing around faults in fluid-saturated porous rocks. Therefore, the concept of the equilibrium length due to either solute advection or solute diffusion/dispersion is presented. For a permeable fault with a given chemical reaction, there exists an optimal flow rate so that chemical equilibrium may be attained between two fluids mixing and focusing within the fault. However, for rapid and parallel flows, such as those caused by the lithostatic pressure gradient, it may be impossible for a chemical reaction to reach an equilibrium state within a permeable vertical fault, if two fluids are not well mixed before entering the fault. [Copyright &y& Elsevier]

Abstract: Numerical methods are used to simulate the double-diffusion driven convective pore-fluid flow and rock alteration in three-dimensional fluid-saturated geological fault zones. The double diffusion is caused by a combination of both the positive upward temperature gradient and the positive downward salinity concentration gradient within a three-dimensional fluid-saturated geological fault zone, which is assumed to be more permeable than its surrounding rocks. In order to ensure the physical meaningfulness of the obtained numerical solutions, the numerical method used in this study is validated by a benchmark problem, for which the analytical solution to the critical Rayleigh number of the system is available. The theoretical value of the critical Rayleigh number of a three-dimensional fluid-saturated geological fault zone system can be used to judge whether or not the double-diffusion driven convective pore-fluid flow can take place within the system. After the possibility of triggering the double-diffusion driven convective pore-fluid flow is theoretically validated for the numerical model of a three-dimensional fluid-saturated geological fault zone system, the corresponding numerical solutions for the convective flow and temperature are directly coupled with a geochemical system. Through the numerical simulation of the coupled system between the convective fluid flow, heat transfer, mass transport and chemical reactions, we have investigated the effect of the double-diffusion driven convective pore-fluid flow on the rock alteration, which is the direct consequence of mineral redistribution due to its dissolution, transportation and precipitation, within the three-dimensional fluid-saturated geological fault zone system. [Copyright &y& Elsevier]

The convective instability of pore-fluid flow in inclined and fluid-saturated three-dimensional fault zones has been theoretically investigated in this paper. Due to the consideration of the inclined three-dimensional fault zone with any values of the inclined angle, it is impossible to use the conventional linear stability analysis method for deriving the critical condition (i.e., the critical Rayleigh number) which can be used to investigate the convective instability of the pore-fluid flow in an inclined three-dimensional fault zone system. To overcome this mathematical difficulty, a combination of the variable separation method and the integration elimination method has been used to derive the characteristic equation, which depends on the Rayleigh number and the inclined angle of the inclined three-dimensional fault zone. Using this characteristic equation, the critical Rayleigh number of the system can be numerically found as a function of the inclined angle of the three-dimensional fault zone. For a vertically oriented three-dimensional fault zone system, the critical Rayleigh number of the system can be explicitly derived from the characteristic equation. Comparison of the resulting critical Rayleigh number of the system with that previously derived in a vertically oriented one has demonstrated that the characteristic equation of the Rayleigh number is correct and useful for investigating the convective instability of pore-fluid flow in the inclined three-dimensional fault zone system. The related numerical results from this investigation have indicated that: (1) the convective pore-fluid flow may take place in the inclined three-dimensional fault zone; (2) if the height of the fault zone is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone stabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; (3) if the thickness of the stratum is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone destabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; and that (4) the shape of the inclined three-dimensional fault zone may affect the convective instability of pore-fluid flow in the system. [Copyright &y& Elsevier]

An equivalent algorithm is proposed to simulate thermal effects of the magma intrusion in geological systems, which are composed of porous rocks. Based on the physical and mathematical equivalence, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with a physically equivalent heat source. From the analysis of an ideal solidification model, the physically equivalent heat source has been determined in this paper. The major advantage in using the proposed equivalent algorithm is that the fixed finite element mesh with a variable integration time step can be employed to simulate the thermal effect of the intruded magma solidification using the conventional finite element method. The related numerical results have demonstrated the correctness and usefulness of the proposed equivalent algorithm for simulating the thermal effect of the intruded magma solidification in geological systems. [Copyright &y& Elsevier]

We use the finite element method to solve coupled problems between pore-fluid flow and heat transfer in fluid-saturated porous rocks. In particular, we investigate the effects of both the hot pluton intrusion and topographically driven horizontal flow on the distributions of the pore-flow velocity and temperature in large-scale hydrothermal systems. Since general mineralization patterns are strongly dependent on distributions of both the pore-fluid velocity and temperature fields, the modern mineralization theory has been used to predict the general mineralization patterns in several realistic hydrothermal systems. The related numerical results have demonstrated that: (1) The existence of a hot intrusion can cause an increase in the maximum value of the pore-fluid velocity in the hydrothermal system. (2) The permeability of an intruded pluton is one of the sensitive parameters to control the pore-fluid flow, heat transfer and ore body formation in hydrothermal systems. (3) The maximum value of the pore-fluid velocity increases when the bottom temperature of the hydrothermal system is increased. (4) The topographically driven flow has significant effects on the pore-fluid flow, temperature distribution and precipitation pattern of minerals in hydrothermal systems. (5) The size of the computational domain may have some effects on the pore-fluid flow and heat transfer, indicating that the size of a hydrothermal system may affect the pore-fluid flow and heat transfer within the system. [Copyright &y& Elsevier]

Using the operator splitting method, the non-reflecting artificial boundary condition, which has the same form as those originally presented by Hagstrom and Hariharan [Appl. Numer. Math. 27 (1998) 403] as well as Thompson et al. [Comput. Meth. Appl. Mech. Engrg. 191 (2001) 311], is re-derived in this paper to deal with transient scalar wave propagation problems in a two-dimensional homogeneous half space. In particular, the original non-reflecting artificial boundary condition is extended to approximately solve transient scalar wave propagation problems in a two-dimensional layered half space, which has a far field consisting of non-homogeneous materials. The proposed non-reflecting artificial boundary condition can be decomposed into three types of elements: physically meaningful springs and dashpots as well as the generalized energy absorbers, which represent the effects of incident waves at previous time instants on the truncated artificial boundary. Due to the meaningfulness in physics, the proposed non-reflecting artificial boundary is straightforwardly applied to the finite element analysis of wave propagation problems in infinite media. The related numerical results from three application examples have demonstrated the effectiveness, efficiency and usefulness of the proposed non-reflecting artificial boundary in dealing with scalar wave propagation problems in two-dimensional homogeneous and layered half spaces. [Copyright &y& Elsevier]