What is a numerical model and what is it good for? Outline ...In exploration, we are ONLY interested...

Enabling Technologies

Modelling Philosophy

predictive mineral discovery*Cooperative Research Centre

A legacy for mineral exploration science

A. Gradient inhydraulicpotential

B. Permeability

C. Solubilitysensitivity to P, T, C

D. Spatialgradient of P, T, C

E. Time (duration)

Key Parameter

is reflected in

ExplorationMineral System

scale-dependent translation

5 Questions1. Geodynamics2. Architecture3. Fluid

reservoirs4. Flow drivers &

pathways5. Deposition

Terrain Selection

Area Selection

Drill Targeting

What is a numerical model?

Numerical modeling is simply taking the equations that governa system and using them to simulate the changes in a systemwith math.

Always based on several assumptions

Create the most accurate model with the simplest equations

Why use numerical models?What factors control the formation of ore deposits

Test hypotheses derived from field observations

Explore the effects of changing rock properties and/or boundaryConditions

e.g. permeability or mechanical strengthe.g. orientation of the far-field principal stresses

understand interactions between geological processes

determine the response of the system to any given parameter(e.g. deformation, fluid flow, heat transfer)

Provide quantitative results

Identify critical geological processes

Translate all of the qualitative research understanding intoquantitative spatial prediction

Coupled Models

Proxies for earth processes – not replication

No code provides a proxy for all processes

Many codes evolved for different purposes (i.e. not for understanding earth processes)

Some basic parameters/relationships not well understood

All 3D models are boxes - boundary conditions critical

Formation of ore systems involves many complex interactionstime/length scale ≠ geological scale

So we need to couple codes which model different processes together

Coupled Models

FLAC3Dfully coupled deformation and fluid flowcan handle permeability and pore pressure changes produced by deformation-induced dilatancy

Coupled Models

FastFlohandles chemical reactions (equilibrium or kineticallycontrolled), mineral dissolution and precipitation, solute transport by advection and diffusion (with heat flow)

Deformation

Many ore deposits are structurally controlled

Create/destroy permeability

Pathways to fluids

Barriers/traps to fluids

Constitutive models: Elastic, plastic, viscous and combinationsof these

Modelling Deformation

Displacement vectors

Magnitudes of displacement vectors

Modelling Deformation

Simple Shearing of an Elastic Mohr-Coulomb Material.

If the material has non-associative constitutive behaviour, ie., the stress vector is not parallel to the plastic strain rate increment, then shear zones form spontaneously at yield (strain-hardening both+&-).

Contours of plastic strain-rate.

Fluid Flow

Darcy flow (laminar flow through porous media) is the mostrelevant processes (not on all scales!)

Darcy flow is driven by hydraulic head (i.e. fluid flows downenergy potential gradients

Permeability in many cases is the key property to determinewhere fluid flows in a hydrothermal system

Permeability is a material property, but can by modified bydeformation (destruction and creation of pore space) andchemical reaction (dissolution / precipitation)

Darcy’s Law

( )gPkq fρµ−∇−=

Fluid flux (m3/m2/s) = velocity x porosity

Permeability (m2)

Pressure gradient (Pa/m)

Fluid density (kg/m3)

Gravity (m/s2)Fluid viscosity (Pa s)

Flux = Rate x Driving Force

Fluid FLowWhat controls the driving force?

Deformation– Dilation– Compaction

Fluid production/consumption– Dehydration reactions– Cooling magma

Topography

Fluid density– Temperature– Pressure– Chemical composition (salinity)

( )gPkq fρµ−∇−=

Modelling Fluid Flow

Potential for mixing meteoric/basinal fluids with metamorphic fluids

Contours of shear strain + particle tracks

Downflow (due to extension)

Upflow (due to devol.)

Fluid moves towards shear zone – on edge of granite dome

Heat Transfer

Geologically relevant are only conduction and advection

Conduction is a diffusive process: ‘‘heat will flow from hot tocold’’

Advection is a transport process, whereby heat is transportedby a solid, fluid or gas

Advection is faster than diffusion

Normal geothermal gradient generally too small for convection(requires local heat source or high permeability)

Heat Transfer

Conduction

Diffusive process: “heat will flow from hot to cold”

Fourier’s law:

Geotherms are conductive

Heat Transfer

Advection

Heat is transported by a solid, fluid or gas

Heat Transfer

Convection

Density-driven flow

Density varies with P, T, and chemistry

HEAT( )gPkq fρµ

−∇−=

Modelling Convection

Transport

Molecular Diffusion is solute transport down a concentration gradient in chemical potential or concentrationSolute flux is directly proportional to the concentration gradient

Advection describes transport of solutes by movement of medium (e.g. fluid)

Dispersion describes the effect of an inhomogeneous flow field(heterogenity of porous media)

Reaction

KINETIC MODELS Mineral reactions fall into three groups:

(1) reaction rates may be so slow relative to the time period of interest that the reaction can be ignored altogether

(2) those in which the rates are fast enough to maintain equilibrium

(3) the remaining reactions. Only those require a kinetic description

Modelling Convection

Gold concentration

(g/tonne)

5 Processes – basic relationship

dtcccp

eee ... ⎟⎟⎠

⎞⎜⎜⎝

⎛∇

∂∂

+∇∂∂

∇= ∑∫ µκρ

Amount of material deposited at a particular point

Fluid viscosity

permeability

Fluid densitygravity

gradient in non-hydrostatic pressure

equilibrium solubility sensitivities with respect to T, P and c of other species

spatial gradients in T, p and cr

the time the system operates for

Current research issues

Accurate simulation of fracture porosity generation and fluidflow

Thermodynamic data for chemical modelling

Effective simulation of magma intrusion and wall rock effects

Geologically realistic consistency of models across all scales

Full coupling

Appropriate methodology

Appropriate constitutive model

Efficiency gains

Computation time

Parameter space exploration (inversion process)

Stability

Visualisation and interpretation

User interaction

Use in economic geology

In exploration, we are ONLY interested in prediction

So we observe patterns associated with known mineralisationand seek to find copies of them

NUMERICAL METHODS HELP TO UNDERSTAND PROCESSINTERACTION, AND TO MAKE PREDICTIONS ABOUT PHYSICALPROCESSES INTERACTING WITH COMPLEX GEOMETRIES

Convection cells and temperature contours

1 Enabling Technologies1 Enabling Technologies Numerical modelingNumerical modelingLaverton model concept

Laverton model geometry in FLAC3D

Laverton model faults

1 Enabling Technologies1 Enabling Technologies Numerical modelingNumerical modeling

Conclusion 2Conclusion 2

Under the effect of thrust loading from west, dilation is localized along the Bardoc shear and the lower part of the Ida fault, forming the dominant fluid transport channel.

Geometry of the modelGeometry of the model

Greenstones

Ida FaultBardoc Shear

140 km

ZuleikaFaultUpper Crust

Lower Crust

Model 1Model 1

• stratigraphic units + faults• no thrust loading• horizontal shortening

deformation

Dilation - Volumetric strain

Darcy Fluid Flow Vectors

Conclusion 1Conclusion 1

The Ida fault is the major channel for fluids to migrate upwards, but the Bardoc shear is also important.

Model 2Model 2

• stratigraphic units + faults• thrust loading

(the west margin)• horizontal shortening

deformation

Dilation - Volumetric strain

Darcy Fluid Flow Vectors

Darcy Fluid Flow

Vectors

(zoom-in view)

Model architectureModel architecture

Granite – old and cold

Greenstone

Conglomerate

Shale (turbidites)

(late)

Present-day erosion?

Rock propertiesRock properties

Medium

MediumHigh

LowVery

high Permeability

Strong

WeakModerate

Very wea

Strength (cohesion, friction

angle, tensile strength)

Results 1: Regional Results 1: Regional devolatilisationdevolatilisation

Heat from the base: T = 500 °C

Initialise with steady-state geotherm (30 °C/km at surface)

T = 25 °C

Results 1: Regional Results 1: Regional devolatilisationdevolatilisation

Results 2: Local Results 2: Local devolatilisationdevolatilisation

T = 25 °C

Late (low-Ca) granites: Initialised at 750 °C

Fluid flow directions Fluid flow directions after 1 after 1 MyrMyr

Regional heating: Still dehydrating, upward flow (max. 3 x 10-10 m3/m2/s)

Local heating: Cooling and retrogression, downward flow (max. 0.9 x 10-10 m3/m2/s)

Integrated fluid flux Integrated fluid flux after 1 after 1 MyrMyr

Regional heating

Max. = 1.04 x 104 m3/m2

Local heating

Max. = 3.49 x 103 m3/m2

Results 3: Results 3: Regional Regional devolatilisationdevolatilisation + extension+ extension

Heat from the base: T = 500 °C

T = 25 °C

Extend at strain rate ~8 x 10-15 s-1

Wallaby

Conceptual model

Model Conditions• Burial depth of around 8km• Pore fluid pressure initialised at around 0.7 x lithostatic(~ 140 Mpa)

• Insitu boundary stress applied at a ratio ofσ1 / σ2 = 1.2

σ3 / σ2 = 0.8

σ1 = 240 MPaσ2 = 200 MPaσ3 = 160 MPa

Software – UDEC and FLAC 3d Comparisons

1 Enabling Technologies 1 Enabling Technologies Mechanical modelingMechanical modeling

DeformationDeformation• Deformation of rock can create permeability (in solid rock) and destroy permeability (by enhancing compaction of unconsolidated sediment)

• Faults in mineral deposits often act as pathways to fluids, faults in hydrocarbon deposits often act as barriers to fluids

• The relation between stress and strain is described by a constitutive model

• Constitutive models: Elastic, plastic, viscous and combinations of these • Many ore deposits are structurally controlled• Important structures such as faults, jogs, and bends provide structural traps

• Focussing of metal laden fluids is an important issue in developing an ore deposit

DeformationDeformation• Elastic materials are characterized by reversible deformations upon unloading.

The stress-strain laws are linear and path-independent.

e.g. Hooke’s law

Stress = constant * strain

stress

strain

DeformationDeformationPlastic models potentially involve some degree of permanent, path-dependent deformations

non-linear stress-strain relations

Different models may be characterized by their yield function, hardening/softening functions and flow rule.

stress

strainStress = f(plastic strain)

MohrMohr--CoulombCoulombRepresentative forupper crustal rocks

ValidationPhysical versus numerical experiments.

Volumetric strain versus axial

Axial stress versus axial strain strain

GA 02/000

Fluid flowFluid flowDarcy Fluid Flow

Vectors

(zoom-in view)

What is a numerical model and what is it good for? Outline ...In exploration, we are ONLY interested...

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