Bruce E. Hobbs

Numerical modelling of single-layer folding: clarification of an issue regarding the possible effect of computer codes and the influence of initial irregularities

The influence of initial perturbation geometry and material propel-ties on final fold geometry has been investigated using finite-difference (FLAC) and finite-element (MARC) numerical models. Previous studies using these two different codes reported very different folding behaviour although the material properties, boundary conditions and initial perturbation geometries were similar. The current results establish that the discrepancy was not due to the different computer codes but due to the different strain rates employed in the two previous studies (i.e. 10(-6) s(-1) in the FLAC models and 10(-14) s(-1) in the MARC models). As a result, different parts of the elasto-viscous rheological field were bring investigated. For the same material properties, strain rate and boundary conditions, the present results using the two different codes are consistent. A transition in Folding behaviour, from a situation where the geometry of initial perturbation determines final fold shape to a situation where material properties control the final geometry, is produced using both models. This transition takes place with increasing strain rate, decreasing elastic moduli or increasing viscosity (reflecting in each case the increasing influence of the elastic component in the Maxwell elastoviscous rheology). The transition described here is mechanically feasible but is associated with very high stresses in the competent layer (on the order of GPa), which is improbable under natural conditions

An equivalent algorithm for simulating thermal effects of magma intrusion problems in porous rocks

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.

A Segregated Algorithm for Simulating Chemical Dissolution Front Instabilities in Fluid-Saturated Porous Rocks

When fresh pore-fluid flow enters a solute-saturated porous medium, where the concentration of the solute (i.e. aqueous mineral) reaches its equilibrium concentration, the concentration of the aqueous mineral is diluted so that the solid part of the solute (i.e. solid mineral) is dissolved to maintain the equilibrium state of the solution. This chemical dissolution process can result in the propagation of a dissolution front within the fluid-saturated porous medium. Due to the dissolution of the solid mineral, the porosity of the porous medium is increased behind the dissolution front. Since a change in porosity can cause a remarkable change in permeability, there is a feedback effect of the porosity change on the pore-fluid flow, according to Darcy’s law. It is well known that because pore-fluid flow plays an important role in the process of reactive chemical-species transport, a change in pore-fluid flow can cause a considerable change in the chemical-species concentration within the porous medium (Steefel and Lasaga 1990, 1994, Yeh and Tripathi 1991, Raffensperger and Garven 1995, Shafter et al. 1998a, b, Xu et al. 1999, 2004, Ormond and Ortoleva 2000, Chen and Liu 2002, Zhao et al. 2005a, 2006c). This means that the problem associated with the propagation of a dissolution front is a fully coupled nonlinear problem between porosity, pore-fluid pressure and reactive chemical-species transport within the fluid-saturated porous medium. If the fresh pore-fluid flow is slow, the feedback effect of the porosity change is weak so that the dissolution front is stable. However, if the fresh pore-fluid flow is fast enough, the feedback effect of the porosity change becomes strong so that the dissolution front becomes unstable. In this case, a new morphology (i.e. dissipative structure) of the dissolution front can emerge due to the self-organization of this coupled nonlinear system. This leads to an important scientific problem, known as the reactive infiltration instability problem (Chadam et al. 1986, 1988, Ortoleva et al. 1987), which is closely associated with mineral dissolution in a fluid-saturated porous medium.

The Particle Simulation Method for Dealing with Spontaneous Crack Generation Problems in Large-Scale Geological Systems

Cracking and fracturing are one class of major failure mechanisms in brittle and semi-brittle materials. Crustal materials of the Earth can be largely considered as brittle rocks, and so cracking and fracturing phenomena are ubiquitous. Cracks created within the Earth’s crust often provide a very useful channel for mineral-bearing fluids to flow, particularly from the deep crust into the shallow crust of the Earth. If other conditions such as fluid chemistry, mineralogy, temperature and pressure are appropriate, ore body formation and mineralization can take place as a result of such fluid flow. Because of the ever-increasing demand for mineral resources in the contemporary world, exploration for new mineral resources has become one of the highest priorities for many industrial countries. For this reason, extensive studies (Garven and Freeze 1984, Yeh and Tripathi 1989, 1991, Steefel and Lasaga 1994, Raffensperger and Garven 1995, Zhao et al. 1997a, Schafer et al. 1998a, b, Zhao et al. 1998a, Xu et al. 1999, Zhao et al. 2000b, Schaubs and Zhao 2002, Zhao et al. 2002a, 2003e, 2005a) have been conducted to understand the detailed physical and chemical processes that control ore body formation and mineralization within the upper crust of the Earth. Thus, the numerical simulation of spontaneous crack generation in brittle rocks within the upper crust of the Earth has become an important research topic in the field of computational geoscience.

A Consistent Point-Searching Interpolation Algorithm for Simulating Coupled Problems between Deformation, Pore-Fluid Flow, Heat Transfer and Mass Transport Processes in Hydrothemal Systems

Over the past decade or so, many commercial computational codes have become available for solving a great number of practical problems in both scientific and engineering fields. Primary advantages of using commercial computational codes are: (1) built-in pre-processing and post-processing tools make it very easy and attractive to prepare, input and output data which are essential in a numerical analysis; (2) provision of movie/animation functions enables numerical results, the treatment of which is often a cumbersome and tedious task, to be visualised via clear and colourful images; (3) detailed benchmark solutions and documentation as well as many embedded robust solution algorithms allow the codes to be used more easily, correctly, effectively and efficiently for solving a wide range of practical problems. However, the main disadvantage of using commercial computational codes is that each code is often designed, within a certain limit, for solving some particular kinds of practical problems. This disadvantage becomes more and more obvious because the ever-increasing competitiveness in the world economy requires us to deal with more and more complicated and complex geoscience problems, which are encountered and not solved in the field of contemporary computational geoscience. There are three basic ways to overcome the above difficulties. The first is to develop some new commercial computational codes, which is time consuming and often not cost-effective for numerical analysts and consultants. The second is to extend an existing commercial computational code, which is usually impossible because the source code is often not available for the code users. The third is to use several existing commercial computational codes in combination. This requires development of a data translation tool to transfer data necessary between each of the codes to be used. Compared with the difficulties encountered in the first two approaches, the third one is more competitive for most numerical analysts and consultants.

A Decoupling Procedure for Simulating Fluid Mixing, Heat Transfer and Non-Equilibrium Redox Chemical Reactions in Fluid-Saturated Porous Rocks

Non-equilibrium redox chemical reactions of high orders are ubiquitous in fluid-saturated porous rocks within the crust of the Earth. They play a very important role in ore body formation and alteration closely associated with a mineralizing system. Since pore-fluid is a major carrier transporting chemical species from one part of the crust into another, the chemical process is coupled with the pore-fluid flow process in fluid-saturated porous rocks. In addition, if the rate of a chemical reaction is dependent on temperature, the chemical process is also coupled with the heat transfer process. When a pore-fluid carrying one type of chemical species meets with that carrying another type of chemical species, these two types of pore-fluids can mix together to allow the related chemical reaction to take place due to solute molecular diffusion/dispersion and advection. For these reasons, the resulting patterns of mineral dissolution, transportation, precipitation and rock alteration are a direct consequence of coupled processes between fluids mixing, heat transfer and chemical reactions in fluid-saturated porousrocks.

A Progressive Asymptotic Approach Procedure for Simulating Steady-State Natural Convective Problems in Fluid-Saturated Porous Media

In a fluid-saturated porous medium, a change in medium temperature may lead to a change in the density of pore-fluid within the medium. This change can be considered as a buoyancy force term in the momentum equation to determine pore-fluid flow in the porous medium using the Oberbeck-Boussinesq approximation model. The momentum equation used to describe pore-fluid flow in a porous medium is usually established using Darcy’s law or its extensions. If a fluid-saturated porous medium has the geometry of a horizontal layer, and is heated uniformly from the bottom of the layer, then there exists a temperature difference between the top and bottom boundaries of the layer. Since the positive direction of the temperature gradient due to this temperature difference is opposite to that of the gravity acceleration, there is no natural convection for a small temperature gradient in the porous medium. In this case, heat energy is solely transferred from the high temperature region (the bottom of the horizontal layer) to the low temperature region (the top of the horizontal layer) by thermal conduction. However, if the temperature difference is large enough, it may trigger natural convection in the fluid-saturated porous medium. This problem was first treated analytically by Horton and Rogers (1945) as well as Lapwood (1948), and is often called the Horton-Rogers-Lapwood problem.

An Equivalent Source Algorithm for Simulating Thermal and Chemical Effects of Intruded Magma Solidification Problems

Consideration of the effects of magma ascending and solidification is important to the further understanding of ore body formation and mineralization in the crust of the Earth. Although various possible fundamental mechanisms of magma ascending in the crust are proposed (Johnson and Pollard, 1973, Marsh 1982, Lister and Kerr 1991, Rubin 1995, Weinberg 1996, Bons et al. 2001), the development of numerical algorithms for simulating the proposed magma ascending mechanisms is still under-developed. For example, continuum-mechanics-based numerical methods have encountered serious difficulties in simulating the random generation and propagation of hydro-fractured cracks, the magma flow within these cracks, the solidification of the ascending magma due to heat losses to the surrounding rocks, and so forth.

Mineral systems, hydridic fluids, the Earth’s core, mass extinction events and related phenomena

We argue that hydridic fluids from the deep-earth are an important fluid type in mineral systems. The Carboniferous through Triassic interval of Earth history is used to illustrate our hypothesis that flux of hydridic fluid is a causative link between many earth processes such as mass extinction, evolution of ocean chemistry, climate change, anoxia, large-scale volcanism and mineral systems. The Earth’s core is considered the dominant reservoir of hydrogen. An enhanced flux of hydridic fluids mobilizes the mantle and sustains tectonism and metallogenesis over 100s of millions of years.