Search results

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.

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.

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.

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.

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.

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.

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.

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.

Based on the asymptotic solution for predicted natural frequencies of a two‐dimensional elastodynamic problem from the finite element analysis, presents the concept of the asymptotic error, which is an approximate error but tends to the exact error when the characteristic length of elements approaches zero, and a practical error estimator. The present practical error estimator contains two criteria: one is the error estimator criterion, the other the finite element mesh design criterion. Using this practical error estimator, not only can the accuracy of a finite element solution for natural frequencies of a two‐dimensional elastodynamic problem be directly evaluated without any further finite element calculation, but also a new target finite element mesh for the desired accuracy of solution can be immediately designed from the relevant information of an original finite element solution. Generally, for the purpose of designing a new target finite element mesh, this original finite element solution is obtainable from a very coarse mesh of a few elements and usually does not satisfy the accuracy requirement. Since the new target finite element mesh could result in a finite element solution with a desire accuracy, the finite element solution so obtained can be used for a structural design in engineering practice. The related numerical results from vibration problems of three representative plates of different shapes under plane stress conditions have demonstrated the correctness and applicability of the present practical error estimator.

We present a numerical methodology for the study of convective pore‐fluid, thermal and mass flow in fluid‐saturated porous rock basins. In particular, we investigate the occurrence and distribution pattern of temperature gradient driven convective pore‐fluid flow and hydrocarbon transport in the Australian North West Shelf basin. The related numerical results have demonstrated that: (1) The finite element method combined with the progressive asymptotic approach procedure is a useful tool for dealing with temperature gradient driven pore‐fluid flow and mass transport in fluid‐saturated hydrothermal basins; (2) Convective pore‐fluid flow generally becomes focused in more permeable layers, especially when the layers are thick enough to accommodate the appropriate convective cells; (3) Large dislocation of strata has a significant influence on the distribution patterns of convective pore‐fluid flow, thermal flow and hydrocarbon transport in the North West Shelf basin; (4) As a direct consequence of the formation of convective pore‐fluid cells, the hydrocarbon concentration is highly localized in the range bounded by two major faults in the basin.

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.

We use the finite element method to model the heat transfer phenomenon through permeable cracks in hydrothermal systems with upward throughflow. Since the finite element method is an approximate numerical method, the method must be validated before it is used to solve any new kind of problem. However, the analytical solution, which can be used to validate the finite element method and other numerical methods, is rather limited in the literature, especially for the problem considered here. Keeping this in mind, we have derived analytical solutions for the temperature distribution along the vertical axis of a crack in a fluid‐saturated porous layer. After the finite element method is validated by comparing the numerical solution with the analytical solution for the same benchmark problem, it is used to investigate the pore‐fluid flow and heat transfer in layered hydrothermal systems with vertical permeable cracks. The related analytical and numerical results have demonstrated that vertical cracks are effective and efficient members to transfer heat energy from the bottom section to the top section in hydrothermal systems with upward throughflow.

The main purpose of this paper is to present and use the particle simulation method to explicitly simulate the spontaneous crack initiation phenomenon in brittle materials, and to compare the particle simulation results with experimental ones on the laboratory scale.

Using the particle simulation method, the brittle material is simulated as an assembly of particles so that the microscopic mechanism of inter‐ and intra‐particle crack initiation can be straightforwardly considered on the microscopic scale. A laboratory test has been conducted using a gypsum sample model to validate the particle simulation method for explicitly simulating the spontaneous crack initiation phenomenon.

The paper finds that in terms of simulating the macroscopic sliding surface along or around the contact plane between a block and its foundation, both the laboratory test and the particle simulation have produced consistent results. This indicated that the particle simulation method is capable of simulating macroscopic cracks through simulating conglomerations and accumulations of microscopic crack initiation within the brittle material. Compared with other numerical methods, the particle simulation method is more suitable for explicitly and effectively simulating spontaneous crack initiation problems on the microscopic scale in brittle materials.

The particle simulation method can be used to explicitly and effectively simulate the spontaneous crack initiation on the microscopic scale in brittle materials. It can be also used to simulate the macroscopic sliding surface along or around the contact plane between a block and its foundation. The experimental results of simulating the spontaneous crack initiation on the laboratory scale in brittle materials are very valuable for validating the numerical simulation results obtained not only from the particle simulation method, but also from other numerical simulation methods.

We present the finite element simulations of reactive mineral‐carrying fluids mixing and mineralization in pore‐fluid saturated hydrothermal/sedimentary basins. In particular we explore the mixing of reactive sulfide and sulfate fluids and the relevant patterns of mineralization for lead, zinc and iron minerals in the regime of temperature‐gradient‐driven convective flow. Since the mineralization and ore body formation may last quite a long period of time in a hydrothermal basin, it is commonly assumed that, in the geochemistry, the solutions of minerals are in an equilibrium state or near an equilibrium state. Therefore, the mineralization rate of a particular kind of mineral can be expressed as the product of the pore‐fluid velocity and the equilibrium concentration of this particular kind of mineral. Using the present mineralization rate of a mineral, the potential of the modern mineralization theory is illustrated by means of finite element studies related to reactive mineral‐carrying fluids mixing problems in materially homogeneous and inhomogeneous porous rock basins.

Extends the evolutionary structural optimization method to the solution for the natural frequency optimization of a two‐dimensional structure with additional non‐structural lumped masses. Owing to the significant difference between a static optimization problem and a structural natural frequency optimization problem, five basic criteria for the evolutionary natural frequency optimization have been established. The inclusion of these criteria into the evolutionary structural optimization method makes it possible to solve structural natural frequency optimization problems for two‐dimensional structures with additional non‐structural lumped masses. Gives two examples to demonstrate the feasibility of the extended evolutionary structural optimization method when it is used to solve structural natural frequency optimization problems.

In many scientific and engineering fields, large‐scale heat transfer problems with temperature‐dependent pore‐fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large‐scale heat transfer problems with temperature‐dependent pore‐fluid densities in the lithosphere and crust scales.

The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts.

From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive‐and‐advective lithosphere with variable pore‐fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere.

The present analytical solutions can be used to: validate numerical methods for solving large‐scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large‐scale heat transfer problems with temperature‐dependent fluid densities.