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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]

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]

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]

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]

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: 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: 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]

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]

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]