Chongbin Zhao

Geodynamic modelling of the Century deposit, Mt Isa Province, Queensland

This paper is concerned with an example of quantitative modelling of orebody formation as a guide to reducing the risk for future mineral exploration. Specifically, the paper presents a detailed 3–D numerical model for the formation of the Century zinc deposit in northern Queensland. The model couples fluid flow with deformation, thermal transport and chemical reactions. The emphasis of the study is a systems approach where the holistic mineralising system is considered rather than concentrating solely on the mineral deposit. In so doing the complete plumbing system for mineralisation is considered with a view to specifying the critical conditions responsible for the ore deposit occurring where it does and having the size and metal grades that are observed. The numerical model is based on detailed geological, tectonic, isotopic and mineralogical data collected over the past 20 years. The conclusions are that the Century zinc deposit is located where it is because of the following factors: (i) a thermal anomaly is associated with the Termite Range Fault due to advection of heat from depth by fluid flow up the Termite Range Fault; (ii) bedding‐plane fissility in the shale rocks hosting the Century zinc deposit has controlled the wavelength and nature of D1 folding in the vicinity of the deposit and has also controlled increases in permeability due to hydrofracture of the shales; such hydrofracture is also associated with the production of hydrocarbons as these shales passed through the ‘oil‐window’; (iii) Pb–Zn leached from crustal rocks in the stratigraphic column migrated up along faults normal to the Termite Range Fault driven by topographic relief associated with inversion at the end of the Isan Orogeny; these fluids mixed with H2S derived at depth moving up the Termite Range Fault to mix with the crustal fluids to precipitate Pb–Zn in a plume downstream from the point of mixing. Critical factors to be used as exploration guides are high temperatures, carbonaceous fissile shales now folded into relatively tight D1 folds, fault‐controlled plumbing systems that enable fluid mixing, depletion of metals upstream of the deposit and,in particular,a very wide Fe‐depletion halo upstream of the deposit.

Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses

We present finite element simulations of temperature gradient driven rock alteration and mineralization in fluid saturated porous rock masses. In particular, we explore the significance of production/annihilation terms in the mass balance equations and the dependence of the spatial patterns of rock alteration upon the ratio of the roll over time of large scale convection cells to the relaxation time of the chemical reactions. Special concepts such as the gradient reaction criterion or rock alteration index (RAI) are discussed in light of the present, more general theory. In order to validate the finite element simulation, we derive an analytical solution for the rock alteration index of a benchmark problem on a two-dimensional rectangular domain. Since the geometry and boundary conditions of the benchmark problem can be easily and exactly modelled, the analytical solution is also useful for validating other numerical methods, such as the finite difference method and the boundary element method, when they are used to deal with this kind of problem. Finally, the potential of the theory is illustrated by means of finite element studies related to coupled flow problems in materially homogeneous and inhomogeneous porous rock masses.

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium

Application of coupled deformation, fluid flow, thermal and chemical modelling to predictive mineral exploration

Abstract The mineralisation process consists of complex interaction and feedback between mechanisms involving deformation, fluid flow, thermal transport and chemical reactions. Through quantitative modelling of specific regions with detailed structure and simple ‘what-if’ scenarios, we may explore and provide bounds for the various parameters involved in mineralisation and even determine parameters critical for predictive exploration.

Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe less than or equal to 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright (C) 1999 John Wiley & Sons, Ltd.

The influence of faulting on host-rock permeability, fluid flow and ore genesis of gold deposits: a theoretical 2D numerical model

Abstract Veins, ore deposits and faults are often spatially related. We quantitatively explore the coupled faulting-deformation-fluidflow-chemical reaction process resulting in this association. Our 2D numerical models focus on faulting-related deformation, dilation and permeability development, fluid flow patterns, and fluid focusing/mixing locations. The models provide insight into the transport of fluids through low-permeability rocks with isolated, but more permeable faults. Mineral precipitation patterns resulting from chemical reactions during the coupled processes are also computed. The results are relevant to understanding the relationship of gold ore deposits to faults.

Numerical modelling of double diffusion driven reactive flow transport in deformable fluid‐saturated porous media with particular consideration of temperature‐dependent chemical reaction rates

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 prop...

Finite element modeling of fluid–rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins

In order to use the finite element method for solving fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins effectively and efficiently, we have presented, in this paper, the new concept and numerical algorithms to deal with the fundamental issues associated with the fluid-rock interaction problems. These fundamental issues are often overlooked by some purely numerical modelers. (1) Since the fluid-rock interaction problem involves heterogeneous chemical reactions between reactive aqueous chemical species in the pore-fluid and solid minerals in the rock masses, it is necessary to develop the new concept of the generalized concentration of a solid mineral, so that two types of reactive mass transport equations, namely, the conventional mass transport equation for the aqueous chemical species in the pore-fluid and the degenerated mass transport equation for the solid minerals in the rock mass, can be solved simultaneously in computation. (2) Since the reaction area between the pore-fluid and mineral surfaces is basically a function of the generalized concentration of the solid mineral, there is a definite need to appropriately consider the dependence of the dissolution rate of a dissolving mineral on its generalized concentration in the numerical analysis. (3) Considering the direct consequence of the porosity evolution with time in the transient analysis of fluid-rock interaction problems; we have proposed the term splitting algorithm and the concept of the equivalent source/sink terms in mass transport equations so that the problem of variable mesh Peclet number and Courant number has been successfully converted into the problem of constant mesh Peclet and Courant numbers. The numerical results from an application example have demonstrated the usefulness of the proposed concepts and the robustness of the proposed numerical algorithms in dealing with fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins

A CONSISTENT POINT-SEARCHING ALGORITHM FOR SOLUTION INTERPOLATION IN UNSTRUCTURED MESHES CONSISTING OF 4-NODE BILINEAR QUADRILATERAL ELEMENTS

To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point-searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 td mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co ordinates of any point in a four-node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point-searching algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.

Effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in deformable fluid-saturated porous media heated from below

In this paper, a solution method is presented to deal with fully coupled problems between medium deformation, pore-fluid flow and heat transfer in fluid-saturated porous media having supercritical Rayleigh numbers. To validate the present solution method, analytical solutions to a benchmark problem are derived for some special cases. After the solution method is validated, a numerical study is carried out to investigate the effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in fluid-saturated media when they are heated from below. The related numerical results have demonstrated that: (1) medium thermoelasticity has a little influence on the overall pattern of convective pore-fluid flow, but it has a considerable effect on the localization of medium deformation, pore-fluid flow, heat transfer and mineralization in a porous medium, especially when the porous medium is comprised of soft rock masses; (2) convective pore-fluid flow plays a very important role in the localization of medium deformation, heat transfer and mineralization in a porous medium.