Bruce E Hobbs

The Commonwealth Scientific and Industrial Research Organisation | CSIRO

This paper investigates the near-field performance of chemical dissolution-front instability (CDFI) around a circular acid-injection-well in fluid-saturated porous media (FSPM) through using purely mathematical deductions. After the mathematical governing equations of the CDFI problem involving radially divergent flow are briefly described, both an...

Purpose 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. Design/methodology/approach Through applying a perturbation to the pore-fluid velo...

Through using rigorously mathematical deductions, this article derives analytical solutions for chemical dissolution‐front instability (CDFI) problems, in which radially divergent flow is involved within fluid‐saturated porous media. Since the acid injection‐well to be considered is a circle of nonzero radius in the horizontal plane, a polar coordi...

This paper proposes a computational simulation procedure for simulating chemical dissolution-front instability problems, in which radially divergent flow is involved in fluid-saturated porous media. In the proposed computational simulation procedure, a combination of the finite element and finite difference methods is used to simulate a chemical di...

This paper deals with three fundamental issues associated with theoretical analyses of reactive infiltration instability (RII) problems in fluid‐saturated porous media. The first fundamental issue is to determine the spatial shapes of chemical dissolution‐fronts in the limit case of the mineral dissolution ratio approaching zero in both conventiona...

This paper deals with how to solve chemical dissolution-front instability problems, which are nonlinearly coupled by subsurface pore-fluid flow, reactive mass transport and porosity evolution processes in fluid-saturated porous media, through using two different computational schemes. In the first computational scheme, porosity, pressure of the por...

The porosity structures of a permeable rock can have remarkable effects on pore-fluid flow within the rock. According to the modern mineralization theory, the mineralization pattern in a hydrothermal ore-forming system is strongly dependent on the pore-fluid flow velocity, so that different porosity structures of a permeable rock can affect signifi...

We consider the implications of adding a cap to the yield surface for elastic–plastic and elastic–visco-plastic solids with coupling between deformation, fluid flow and mineral reactions. For a suitable combination of (low) permeability and strain rate, opening-mode veins can form in compression. Such behaviour is enhanced by dissolution and by sim...

We describe the localized folding of thick layers embedded in a viscoelastic framework. Higher-order partial differential equations such as the Swift-Hohenberg equation are standard for modelling the folding process. Using a high-order shear theory, we modify the Swift-Hohenberg equation to describe the buckling of thick layers and consider the fol...

This paper deals with how to implement perturbations in the computational simulations of chemical dissolution‐front instability (CDFI) problems in fluid‐saturated porous media. On the basis of theoretical analysis, it is found that the application of a perturbation to the chemical dissolution front is equivalent to the application of an alternative...

Measuring the predictability and complexity of 2D data (image) series using entropy is an essential tool for evaluation of systems’ irregularity and complexity in remote sensing and geophysical mapping. However, the existing methods have some drawbacks related to their strong dependence on method parameters and image rotation. To overcome these dif...

The concept of fractal spatial distributions of mineralisation has been widely proposed since Mandelbrot (1965) who emphasised the stable Pareto-Lévy distribution as the relevant distribution. The concept of a fractal is used as a basis for estimating endowment and for erecting exploration models based on self-organised criticality. This paper expl...

Despite many studies of orogenic gold systems, the underlying processes involved in their formation and in defining their location and endowment remain enigmatic. This arises because such processes are multiscale and nonlinear so that patterns of alteration and mineralisation are apparently irregular and unpredictable. The goal of a nonlinear dynam...

The production of breccias and cataclasites is commonly proposed to result in power-law or log-normal probability distributions for fragment (grain) size. We show that in both natural and experimental examples, the common best fit probability distributions for the complete distributions are members of the Generalised Gamma (GG), Extreme Value (GEV)...

Purpose 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. Design/methodology/approach The porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unkn...

Chemical dissolution-front instability (CDFI) problems usually involve multiple temporal and spatial scales, as well as multiple processes. A key issue associated with solving a CDFI problem in a fluid-saturated rock is to mathematically establish a theoretical criterion, which can be used to judge the instability of a chemical dissolution-front (C...

This paper presents an accurate porosity‐velocity‐concentration approach, in which porosity, pore‐fluid velocity and the concentration of dissolvable substances in the pore fluid are selected as four primary unknown variables for solving reactive mass transport problems involving chemical dissolution in fluid‐saturated porous media with arbitrarily...

Reactive mass transport, in which chemical dissolution front may become unstable, is a common phenomenon in the field of groundwater hydrology. The use of mathematical transforms can convert many scientific and engineering problems from the conventional time-space domain into a generalized time-space domain, so that analytical solutions, which are...

Despite many decades of study, the genesis of orogenic gold deposits remains in debate. One aspect of this debate concerns the origin of the mineralising fluids. Two important constraints are that the fluids are sulphur and CO 2 bearing and that high fluid fluxes are maintained in a spatially localised environment for a relatively short period of t...

This paper presents a semianalytical approach for solving first‐order perturbation (FOP) equations, which are used to describe dissolution‐timescale reactive infiltration instability (RII) problems in fluid‐saturated rocks. The proposed approach contains two parts because the chemical dissolution reaction divides the whole problem domain into two s...

The relative strengths of constituent minerals in a deforming poly-mineralic rock depend on the grain size distributions of the various phases, the operating deformation mechanisms in those phases, and the topology of the microstructure. It is observed that more than one deformation mechanism operates, and the resulting constitutive relations (espe...

Reactive mass transport is a common phenomenon associated with groundwater pollution in the field of groundwater hydrology. For a reactive mass transport problem involving two different porosity regions, in which the porosity of the fluid-saturated porous medium has a constant distribution in the left region and an exponential distribution in the r...

This paper examines the rheological behaviour of power law viscous materials arising from mixtures of deformation mechanisms and/or different mineral assemblages. The mixing relation is based on classical thermodynamics mixing relations where the enthalpy of the mixture is the sum of the molar volume proportions of the individual molar enthalpies;...

This paper sets the historical context for the Journal of Structural Geology when it was first published in 1979. The major advances in Structural Geology over the past 40 years are then highlighted. Finally, ten Grand Challenges for the next decade are nominated.

This paper deals with how the purely mathematical approach can be used to solve transient-state instability problems of dissolution-timescale reactive infiltration (DTRI) in fluid-saturated porous rocks. Three key steps involved in such an approach are: (1) to mathematically derive an analytical solution (known as the base solution or conventional...

A theoretical study of reactive infiltration instability is conducted on the dissolution timescale. In the present theoretical study, the transient behavior of a dissolution‐timescale reactive infiltration system needs to be considered, so that the upstream region of the chemical dissolution front should be finite. In addition, the chemical dissolu...

Convective pore-fluid flow (CPFF) plays a critical role in generating mineral deposits and oil reservoirs within the deep Earth. Therefore, theoretical understanding and numerical modeling of the thermodynamic process that triggers and controls the CPFF are extremely important for the exploration of new mineral deposits and underground oil resource...

This paper presents a unified theory to deal with when, why and how a sharp acidization dissolution front (ADF), which is represented by the porosity distribution curve, can take place in an acidization dissolution system composed of fluid-saturated porous rocks. The theory contains the following main points: (1) A reaction rate of infinity alone c...

The goal of any nonlinear dynamical analysis of a data series is to extract features of the dynamics of the underlying physical and chemical processes that produce that spatial pattern or time series; a by-product is to characterise the signal in terms of quantitative measures. In this paper, we briefly review the methodology involved in nonlinear...

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 stead...

Worldwide, mineral exploration is suffering from rising capital costs, due to the depletion of readily recoverable reserves and the need to discover and assess more inaccessible or geologically complex deposits. For gold exploration, this problem is particular acute. We propose an innovative approach to mineral exploration and orebody characterisat...

Worldwide, mineral exploration is suffering from rising capital costs, due to the depletion of readily recoverable reserves and the need to discover and assess more inaccessible or geologically complex deposits. For gold exploration, this problem is particularly acute.We propose an innovative approach to mineral exploration and orebody characterisa...

Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them. The chemical dissolution-front instability problem in fluid-saturated porous rocks is no exception. Since this kind of instability problem has both the conventio...

Three-dimensional models of natural geological fold systems established by photogrammetry are quantified in order to constrain the processes responsible for their formation. The folds are treated as nonlinear dynamical systems and the quantification is based on the two features that characterize such systems, namely their multifractal geometry and...

In this reply we further demonstrate and confirm that the main conclusion (namely, that the asymptotic limit of the acid dissolution capacity can lead to sharp dissolution fronts) in our recent publication in this journal is correct and valid. The basis of the incorrect critique in the comment is whether or not a physically-consistent velocity scal...

Reactive transport, in which chemical dissolution reactions dissolve dissolvable materials in fluid-saturated porous rocks, is very common in groundwater pollution and geoenvironmental engineering. Because of coupled porosity evolution and mass transport processes on the dissolution time scale, analytical solutions for dissolution-timescale reactiv...

One aim of structural geology is to understand the processes that operate during deformation and metamorphism so that the conditions (P, T, strain-rates, stresses, rates of other processes such as grain-size reduction) that control these processes can be identified and quantified. In this paper we explore ways of quantifying the geometry of deforme...

Coupling between the physical processes intrinsic to a hydrothermal system can lead to episodic and chaotic behaviour. Such behaviour includes variations in both space and time of the temperature, fluid pressure and activity of H2S, which result in the deposition of alteration mineral assemblages, zoned pyrite and gold; these variations are multifr...

Mountain topography can cause both pressure-gradient driven advective flow and temperature-gradient driven convective flow. Compared with the pressure-gradient driven advective flow, the temperature-gradient driven convective flow can last long enough to enable the hydrothermal ore-forming system to reach a steady state. This paper is focused on th...

Episodic fluctuations in fluid pressure and temperature are characteristic of the behaviour of orogenic gold systems and are commonly attributed to processes external to the system, such as seismic events and associated adiabatic fault valve or suction pump/piston behaviour; any temperature changes are attributed to the adiabatic nature of the proc...

Reaction-infiltration instability, in which chemical reactions can dissolve minerals and therefore create preferential pore-fluid flow channels in fluid-saturated rocks, may play an important role in controlling groundwater quality in groundwater hydrology. Although this topic has been studied for many years, there is a recent debate, which says th...

The spatial distributions of mineralization and alteration in hydrothermal systems are complex and are often considered to be cryptic and problematic to quantify. We used wavelet analysis of conventional hyperspectral drillcore logs to demonstrate quantitatively that primary Au mineralization, common vein-hosted mineralogy (calcite and ankerite), h...

Orogenic gold systems are open, flow-controlled thermodynamic systems and generally occur in mid- to upper crustal environments where there is strong coupling between fluid flow and dilatant plastic deformation. This paper considers the principles involved in such coupling, with an emphasis on the elastic and plastic volume changes and their influe...

According to the Minerals Council Australia 44% of today’s exploration projects try to discover gold deposits–a consequence of the risen gold price. However, exploration of an optimal mineral deposit is expensive with respect with time and the equipment required. Expenditure costs are increasing and decrease the profitability of mining companies: r...

It is widely proposed that tectonic pressure (the difference between the mean stress and the pressure arising from a lithostatic load) is large, and has a significant influence on mineral phase equilibria in deforming metamorphic rocks. The implication/assertion is that the mean stress is equivalent to the thermodynamic pressure which characterises...

A recurring question in mineral exploration is to predict the spatial distribution of ore-bearing minerals, to determine both (i) the economic value of a prospective deposit, and (ii) the optimal locations for mineral discovery (Jébrak M, 1997). In hydrothermal gold deposits such as the Imperial deposit, in the Yilgarn of Western Australia, the gol...

The use of the asymptotic limit can greatly simplify the theoretical analysis of chemical dissolution front instabilities in fluid-saturated rocks and therefore make it possible to obtain mathematical solutions, which often play a crucial role in understanding the propagation behavior of chemical dissolution fronts in chemical dissolution systems....

The natural phenomenon associated with the chemical dissolution of dissolvable minerals of rocks can be employed to develop innovative technology in mining and oil extracting engineering. This paper presents a new alternative approach for theoretically dealing with chemical dissolution front (CDF) propagation in fluid-saturated carbonate rocks. Not...

Homogeneity and heterogeneity are two totally different concepts in nature. At the particle length scale, rocks exhibit strong heterogeneity in their constituents and porosities. When the heterogeneity of porosity obeys the random uniform distribution, both the mean value and the variance of porosities in the heterogeneous porosity field can be use...

How to build an ore body. Gold'17 Rotorua 2 How does one build an ore body? or How does one design and build a chemical reactor that is an orogenic gold system? 1. Location? Access to raw materials, feed stock and c energy? 2. What kind of reactor are we going to build? 3. What are the operating conditions for maximum yield? 4. How do I ensure stab...

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 ca...

We address the questions: are the temperature and thermodynamic pressure significantly different for thermodynamic equilibrium under hydrostatic versus non-hydrostatic stresses? Moreover, is the nature of the equilibrium state comprising the number of phases and their microstructure different? Only closed thermodynamic systems are considered involv...

Because dissolution of rocks may create and enhance groundwater flow channels, the chemical dissolution-front instability (CDFI) can control the quality of groundwater. This paper presents the theoretical analyses of porosity-permeability relationship effects on the CDFI in water-saturated porous rocks. Since the CDFI in a water-rock reaction syste...

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 cause...

The study of the evolution with time of nonlinear systems is called nonlinear dynamics. Examples in metamorphic geology are the buckling and boudinage of layers embedded in nonlinear materials, the behaviour of coupled mineral reactions and the formation of joint systems. Nonlinear systems evolve through a number of stages: (1) A uniform state beco...

The subject concerned with movements during a deformation history is called kinematics. In this chapter, we examine some common deformation histories in deformed rocks and discuss the advection of quantities through the deforming material in terms of the material time derivative. This highlights the need to distinguish between spatial and material...

This chapter is concerned with the transport of heat by conduction and thermal advection in deforming metamorphic rocks. We first consider the diffusion of heat governed by Fourier's Law of heat conduction and the heat conservation law. This enables the thermal diffusivity to be defined together with the characteristic time for heat conduction over...

This chapter considers the remaining pieces of information we need in order to examine the thermomechanics of a metamorphic system, namely, the nature of the material that is deformed. This means we need relations between the stress, the heat flow, the deformation gradient and the stretching tensor. These relations are called constitutive relations...

This chapter concerns the processes associated with the nucleation and growth of new mineral grains during deformation. Four end-member models are explored: (1) networked mineral reactions; (2) isochoric replacement of old grains involving stress-driven diffusion processes (‘pressure solution’); (3) classical nucleation and growth processes; and (4...

This chapter is concerned with the thermodynamics of systems not at equilibrium. Thermodynamics is the study of the flow of physical and chemical quantities (such as momentum, heat, fluid and chemical components) through or within a system driven by thermodynamic forces. These forces comprise gradients in deformation, the inverse of the temperature...

Mineral reactions are a fundamental component of the development of metamorphic rocks but the subject is commonly discussed without reference to deformation which ubiquitously accompanies the chemical processes. In this chapter we concentrate on the coupling between mineral reactions and deformation with particular reference to the controls that pr...

Microstructure has a first-order influence on the flow stress of polycrystalline aggregates. It controls the magnitude of the flow stress (as a function of grain size and shape), the anisotropy of elasticity and of flow stress, whether localisation will occur and the pattern of localisation. The development of crystallographic preferred orientation...

The two previous chapters discuss the geometry and the movements (flows) that are involved in the deformation of rocks. This chapter discusses two extra fundamental concepts that allow us to understand deforming systems. These are based on the observation that mass in a deforming closed system is neither destroyed nor created and that a system of f...

Visco-plastic flow is the rate- and temperature-sensitive deformation of solids. The behaviour is characterised by a yield or flow surface which marks the change over from elastic behaviour for stress states inside the surface to visco-plastic behaviour for stress states on the yield surface. The shape and size of the yield surface depends on both...

In this introductory chapter we present the basic framework and approach for the remainder of the book. We are concerned with the processes that operate during the deformation and metamorphism of the rocks that comprise the crust and uppermost mantle of the Earth and the mechanical principles that govern the behaviour and resulting geometry of thes...

This paper presents a numerical implementation of the coupled hydro-thermal-mechanical logic in the commercial code FLAC3D. The numerical model uses the Boussinesq approximation in which fluid density variations are neglected in all but the body force term of the equation of motion. The numerical solution is compared to an analytical solution (obta...

Temporal-spatial distributions of geochemical data in geoinformatics are very important for mineral exploration in the upper crust of the Earth and for the treatment of geoenvironmental issues such as CO2 sequestration in geological formations. To understand ore-forming processes associated with mineral exploration, it is necessary to acquire geoch...

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...

It is vital to interpret porphyroblast microstructures accurately relative to both one another and to external matrix structures when using them to reconstruct the tectono-metamorphic evolution of orogenic terranes. Misinterpretation may have profound implications for either the deformation component or the inferred metamorphic reactions resulting...

Hydrothermal mineralising systems are presented as large, open chemical reactors held far from equilibrium during their lifetime by the influx of heat, fluid and dissolved chemical species. As such they are nonlinear dynamical systems and need to be analysed using the tools that have been developed for such systems. Hy-drothermal systems undergo a...

A range of factors controls the location of hydrothermal alteration and gold mineralisation in the Earth’s crust. These include the broad-scale lithospheric architecture, availability of fluid sources, fluid composition and pH, pressure-temperature conditions, microscopic to macroscopic structural development, the distribution of primary lithologie...

Fabrics in deformed rocks can be thought of as resulting from iterative processes where the growth of one part of the fabric relies on a previous state of the system in order to evolve. In addition there are commonly competitive processes operating such as the competition between grain growth and the rate of supply of nutrients. Such iterative-comp...

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This chapter is concerned with damage evolution, both brittle and ductile. Damage is a term that describes any process that results in degradation of strength or load-bearing capacity and is expressed both as localised and distributed microfractures, intra- and intergranular voids, chemical damage, such as stress corrosion, grain size reduction, du...

This chapter is concerned with brittle deformation, a process whereby macroscopic deformations are achieved by fracturing at the crystal structure scale. The classical theories of Griffith and Barenblatt are treated with an emphasis on the energy associated with fracture. We concentrate on two aspects of fracture mechanics, namely, those processes...

This chapter introduces the geometrical concept of deformation and the associated concepts of strain and rotation. The geometrical description of deformation is independent of the applied forces, velocities and histories of these quantities. We consider the concept of the deformation gradient and how that quantity describes the changes in the posit...

The ability to understand and predict how thermal, hydrological, mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal–Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is...

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 concentr...

Ore-forming and geoenviromental systems commonly involve coupled fluid flow and chemical reaction processes. The advanced numerical methods and computational modelling have become indispensable tools for simulating such processes in recent years. This enables many hitherto unsolvable geoscience problems to be addressed using numerical methods and c...

Hydrothermal systems in the Earth's crust comprise fluid (of low pH) and thermal transport systems that can be tens of kilometres in height and a 100 km wide. They also transport precious metals and, under suitable conditions, concentrate these metals in relatively small ore bodies. Such systems represent an archetype example of fully couped fluid...

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 thr...

Structural Geology is a groundbreaking reference that introduces you to the concepts of nonlinear solid mechanics and non-equilibrium thermodynamics in metamorphic geology, offering a fresh perspective on rock structure and its potential for new interpretations of geological evolution. This book stands alone in unifying deformation and metamorphism...

This paper presents an instability theory that can be used to understand the fundamental behavior of an acidization dissolution front when it propagates in fluid‐saturated carbonate rocks. The proposed theory includes two fundamental concepts, namely the intrinsic time and length of an acidization dissolution system, and a theoretical criterion tha...

This paper deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including medium anisotropic effects. Since a general anisotropic medium can be described as an orthotropic medium in the corresponding principal directions, a two-dimensional orthotropic porous medium is...