Search

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 proposes a computational simulation procedure for simulating chemical dissolution-front instability problems, in which radially divergent flow is involved in fluid-saturated porous media. In the proposed computational simulation procedure, a combination of the finite element and finite difference methods is used to simulate a chemical dissolution-front instability problem involving radially divergent flow, while a new algorithm is used to apply a small perturbation to the problem. Particular attention is paid on simulating low-order modes of an unstable circular chemical dissolution-front propagating in a fluid-saturated porous medium, in which dissolvable materials only occupy a small part, so that the final porosity is remarkably smaller than unity when dissolvable materials are completely dissolved in the chemical dissolution system. To verify the proposed computational simulation procedure, analytical solutions for a benchmark chemical dissolution-front instability problem involving radially divergent flow are derived in a purely mathematical manner. The related computational simulation results have demonstrated that: (1) the proposed computational simulation procedure is correct and useful for simulating chemical dissolution-front instability problems, which are associated with both stable and unstable chemical dissolution systems involving radially divergent flow in fluid-saturated porous media; (2) the simulated shapes of the second-order, third-order and fifth-order modes associated with an unstable chemical dissolution-fronts are respectively an ellipse, a star of three angles and a star of five angles in the unstable chemical dissolution system involving radially divergent flow in the fluid-saturated porous medium; (3) although the heterogeneity of a porous medium can affect the propagation speed of a chemical dissolution-front, it does not affect the low-order mode shape in the unstable chemical dissolution system involving radially divergent flow in the fluid-saturated heterogeneous porous medium. [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 solve chemical dissolution-front instability problems, which are nonlinearly coupled by subsurface pore-fluid flow, reactive mass transport and porosity evolution processes in fluid-saturated porous media, through using two different computational schemes. In the first computational scheme, porosity, pressure of the pore-fluid and concentration of the solute are used as fundamental unknown variables to describe a chemical dissolution system, so that it can be named as the PPC scheme. In the second computational scheme, porosity, velocity of the pore-fluid and concentration of the solute are used as fundamental unknown variables to describe a chemical dissolution system, so that it can be named as the PVC scheme. Since the finite element equations of a chemical dissolution-front instability problem on the basis of using the PPC scheme is available, the main focus of this study is on deriving the finite element equations of a chemical dissolution-front instability problem on the basis of using the PVC scheme. In particular, analytical solutions for the property matrices of a four-node rectangular element have been derived and used in both the PVC scheme and the PPC scheme. Through comparing the computational simulation results obtained from using both the PPC scheme and the PVC scheme, it has demonstrated that: (1) if the chemical dissolution system is in a stable state, then the PPC scheme is superior to the PVC scheme because the PPC scheme uses less computational efforts than the PVC scheme; (2) if the chemical dissolution system is in an unstable state, then the PVC scheme is superior to the PPC scheme because the PVC scheme yields more accurate computational simulation results than the PPC scheme. [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]

This article presents an accurate porosity‐velocity‐concentration approach, in which porosity, pore‐fluid velocity and the concentration of dissolvable substances in the pore fluid are selected as four primary unknown variables for solving reactive mass transport problems involving chemical dissolution in fluid‐saturated porous media with arbitrarily initial porosity distributions. The first advantage of using the proposed approach is that since pore‐fluid velocity, instead of pore‐fluid pressure, is selected as the primary unknown variable to describe the pore‐fluid flow process, the pore‐fluid velocity obtained from the proposed approach is more accurate than that obtained from the numerical simulation, in which pore‐fluid pressure is selected as the primary unknown variable to describe the pore‐fluid flow. The second advantage of using the proposed approach is that because the property matrices of a four‐node rectangular element are precisely calculated in a purely mathematical way, the overall accuracy of numerical solutions can be ensured. After the proposed approach is verified by a benchmark problem, it has been applied for solving reactive mass transport problems involving chemical dissolution in fluid‐saturated porous media with three different kinds of initial porosity distributions. It has been demonstrated that: (1) the proposed approach can produce highly‐accurate numerical solutions for solving reactive mass transport problems involving chemical dissolution in fluid‐saturated porous media with arbitrarily initial porosity distributions; (2) the initial porosity distribution in a porous medium can have remarkable effects on the reactive mass transport process in the porous medium; (3) the porosity and dimensionless concentration fronts propagate from the entrance to the exit of the problem domain, which is identical to the pore‐fluid flow direction. [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]

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]

This paper primarily deals with the computational aspects of chemical dissolution-front instability problems in two-dimensional fluid-saturated porous media under non-isothermal conditions. After the dimensionless governing partial differential equations of the non-isothermal chemical dissolution-front instability problem are briefly described, the formulation of a computational procedure, which contains a combination of using the finite difference and finite element method, is derived for simulating the morphological evolution of chemical dissolution fronts in the non-isothermal chemical dissolution system within two-dimensional fluid-saturated porous media. To ensure the correctness and accuracy of the numerical solutions, the proposed computational procedure is verified through comparing the numerical solutions with the analytical solutions for a benchmark problem. As an application example, the verified computational procedure is then used to simulate the morphological evolution of chemical dissolution fronts in the supercritical non-isothermal chemical dissolution system. The related numerical results have demonstrated the following: (1) the proposed computational procedure can produce accurate numerical solutions for the planar chemical dissolution-front propagation problem in the non-isothermal chemical dissolution system consisting of a fluid-saturated porous medium; (2) the Zhao number has a significant effect not only on the dimensionless propagation speed of the chemical dissolution front but also on the distribution patterns of the dimensionless temperature, dimensionless pore-fluid pressure, and dimensionless chemical-species concentration in a non-isothermal chemical dissolution system; (3) once the finger penetrates the whole computational domain, the dimensionless pore-fluid pressure decreases drastically in the non-isothermal chemical dissolution system. [ABSTRACT FROM AUTHOR]

This paper deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including medium anisotropic effects. Since a general anisotropic medium can be described as an orthotropic medium in the corresponding principal directions, a two-dimensional orthotropic porous medium is considered to derive the analytical solution for the critical condition, which is used to judge whether or not the chemical dissolution front can become unstable during its propagation. 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 medium permeability anisotropic 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 including medium anisotropic effects. The related theoretical and numerical results demonstrated that: (1) a decrease in the medium anisotropic permeability factor (or ratio), which is defined as the ratio of the principal permeability in the transversal direction to that in the longitudinal direction parallel to the pore-fluid inflow direction, can stabilize the chemical dissolution front so that it becomes more difficult for a planar chemical-dissolution front to evolve into different morphologies in the chemical dissolution system; (2) the medium anisotropic permeability ratio can have significant effects on the morphological evolution of the chemical dissolution front. When the Zhao number of the chemical dissolution system is greater than its critical value, the greater the medium anisotropic permeability ratio, the faster the irregular chemical-dissolution front grows. [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]

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: 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]

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]

This article deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including solute dispersion effects. Since the solute equilibrium concentration is much smaller than the molar density of the dissolvable mineral in a mineral dissolution system, a limit case, in which the ratio of the solute equilibrium concentration (in the pore fluid) to the molar density of the dissolvable mineral (in the solid matrix of the porous medium) approaches zero, is considered in the theoretical analysis. Under this assumption, the critical condition under which a planar chemical-dissolution front becomes unstable has been mathematically derived when solute dispersion effects are considered. The present theoretical results clearly demonstrated that: (1) the propagation speed of a planar chemical-dissolution front in the case of considering solute dispersion effects is the same as that when solute dispersion effects are neglected. This indicates that solute dispersion does not affect the propagation speed of the planar chemical-dissolution front in a fluid-saturated porous medium. (2) The consideration of solute dispersion can cause a significant increase in the critical Zhao number, which is used to judge whether or not a planar chemical-dissolution front may become unstable in the fluid-saturated porous medium. This means that the consideration of solute dispersion can stabilize a planar chemical-dissolution front, because an increase in the critical Zhao number reduces the likelihood of the planar chemical-dissolution front instability in a fluid-saturated porous medium. In addition, the present results can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of chemical dissolution fronts in two-dimensional fluid-saturated porous media. [ABSTRACT FROM AUTHOR]

• 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]

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 model three-dimensional convective pore-fluid flow in fluid-saturated porous media when they are heated from below. In particular, we employ the particle-tracking technique to mimic the trajectories of particles in three-dimensional fluid flow problems. The related numerical results demonstrated that: (1) The progressive asymptotic approach procedure, which was previously developed for the finite element modelling of two-dimensional convective pore-fluid flow problems, is equally applicable to the finite element modelling of three-dimensional convective pore-fluid flow in fluid-saturated porous media heated from below. (2) The perturbation of gravity at different planes has a significant effect on the pattern of three-dimensional convective pore-fluid flow and therefore, may influence the pattern of orebody formation and mineralization in three-dimensional hydrothermal systems. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

• To consider a reactive mass transport problem of two different porosity regions in porous media. • To derive theoretical solutions for the acid concentration in the left region of constant porosity. • To derive numerical solutions for the acid concentration in the right region of variable porosity. Reactive mass transport is a common phenomenon associated with groundwater pollution in the field of groundwater hydrology. For a reactive mass transport problem involving two different porosity regions, in which the porosity of the fluid-saturated porous medium has a constant distribution in the left region and an exponential distribution in the right region, theoretical solutions for both dimensional and dimensionless acid concentrations have been derived mathematically in the left region by using the interface condition substitution strategy. The fundamental idea behind this strategy is that the boundary condition at the entrance of the left region and the mathematical governing equation of the right region at the interface location between the left and right regions can be used to determine two independent constants involved in the theoretical solutions for the dimensional and dimensionless acid concentrations in the left region of the reactive mass transport system. Since both the acid concentration and its first derivative are known at the left boundary (i.e. the interface location) of the right region, it is possible to derive analytical expressions for the numerical solution (e.g. the finite element solution) in the right region by using the point-by-point marching strategy. The related theoretical results have demonstrated that the porosity distribution pattern in the right region of the system can have a significant influence on the dimensionless acid concentration distribution in the whole system, so that it affects not only the chemical dissolution front instability, but also the reactive mass transport process in an underground water system. [ABSTRACT FROM AUTHOR]