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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 dynamic mechanism for destruction of the North China Craton (NCC) has been extensively discussed. Numerical simulation is used in this paper to discuss the effect of mantle upward throughflow (MUT) on the lithospheric heat flux of the NCC. Our results yield a three-stage destruction of the NCC lithosphere as a consequence of MUT variation. (1) In Late Paleozoic, the elevation of MUT, which was probably caused by southward and northward subduction of the paleo-Asian and paleo-Tethyan oceans, respectively, became a prelude to the NCC destruction. The geological consequences include a limited decrease of the lithospheric thickness, an increase of heat flux, and a gradual enhancement of the crustal activity. But the tectonic attribute of the NCC maintained a stable craton. (2) During Late Jurassic-Early Cretaceous, the initial velocity of the MUT became much faster probably in response to subduction of the Pacific Ocean; the conductive heat flux at the base of the NCC lithosphere gradually increased from west to east; and the lithospheric thickness was significantly decreased. During this stage, the heat flux distribution was characterized by zonation and partition, with nearly horizontal layering in the lithosphere and vertical layering in the underlying asthenosphere. Continuous destruction of the NCC lithosphere was associated with the intense tectono-magmatic activity. (3) From Late Cretaceous to Paleogene, the velocity of MUT became slower due to the retreat of the subducting Pacific slab; the conductive heat flux at the base of lithosphere was increased from west to east; the distribution of heat flux was no longer layered. The crust of the western NCC is relatively hotter than the mantle, so-called as a ‘hot crust but cold mantle’ structure. At the eastern NCC, the crust and the mantle characterized by a ‘cold crust but hot mantle.’ The western NCC (e.g., the Ordos Basin) had a tectonically stable crust with low thermal gradients in the lithosphere; whereas the eastern NCC was active with a hot lithosphere. The numerical results show that the MUT is the main driving force for the NCC destruction, whereas the complex interaction of surrounding plates lit a fuse for the lithospheric thinning. [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]

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]

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 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]

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]

The finite element method is used to simulate coupled problems, which describe the related physical and chemical processes of ore body formation and mineralization, in geological and geochemical systems. The main purpose of this paper is to illustrate some simulation results for different types of modelling problems in pore-fluid saturated rock masses. The aims of the simulation results presented in this paper are: (1) getting a better understanding of the processes and mechanisms of ore body formation and mineralization in the upper crust of the Earth; (2) demonstrating the usefulness and applicability of the finite element method in dealing with a wide range of coupled problems in geological and geochemical systems; (3) qualitatively establishing a set of showcase problems, against which any numerical method and computer package can be reasonably validated. [Copyright &y& Elsevier]