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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]

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]

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]

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

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: 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]

Numerical methods are used to solve double diffusion driven reactive flow transport problems in deformable fluid-saturated porous media. In particular, the temperature dependent reaction rate in the non-equilibrium chemical reactions is considered. A general numerical solution method, which is a combination of the finite difference method in FLAC and the finite element method in FIDAP, to solve the fully coupled problem involving material deformation, pore-fluid flow, heat transfer and species transport/chemical reactions in deformable fluid-saturated porous media has been developed. The coupled problem is divided into two sub-problems which are solved interactively until the convergence requirement is met. Owing to the approximate nature of the numerical method, it is essential to justify the numerical solutions through some kind of theoretical analysis. This has been highlighted in this paper. The related numerical results, which are justified by the theoretical analysis, have demonstrated that the proposed solution method is useful for and applicable to a wide range of fully coupled problems in the field of science and engineering. [ABSTRACT FROM AUTHOR]