Huilin Xing1*, Ji Zhang1, Yan Liu1, Jinfang Gao1, Doone Wyborn2 and Hans Muhlhaus1

1 Earth System Science Computational Centre, The University of Queensland, QLD 4072

2 Geodynamics Limited, PO BOX 2046, Milton Queensland QLD 4064

I would express my deep appreciations to

◦ ARC & Geodynamics Ltd for financial support through a

Linkage project: supercomputer simulation of hot fractured

rock geothermal reservoir systems (investigators: Xing,

Mühlhaus and Wyborn)

◦ Former developers of research code PANDAS at ESSCC,

which this work is built on

◦ Supervisors Dr Huilin Xing and Prof Hans Mühlhaus for this

exciting research topic and all the academic advices and

supports

Brief introduction of geothermal modeling using PANDAS/ThermoFluid◦ The big picture◦ Physical/mathematical equations◦ Numerical solution feathers

Recent applications and results◦ Well/channel flow in geothermal fields◦ Water/CO2 multiphase modeling◦ Non-Darcy flow in well tests◦ Geotechnical risk assessment: An open pit mining

site

A well model with Tetrahedral mesh

Abstract geological models (Data source: 3D geological model created with Geomodeller by

Helen Gibson of Intrepid Geoscience )

Mr Yan Liu will give a talk on this topic during the upcoming AGEC conference.

Converted rock image with 3,871,488 grid points

2D case 3D case

Mass balance equation

Momentum balance equation

Energy balance equation

( )( ) ( ) 0l l g g l gq q

t

v v

ggll SS

[ (1 ) ] ( ) ( ) ( ) 0r r l l l g g g m l l g gh h h h K T q h q ht

v v

ZgPk

ZgPk

ggg

rgggll

l

rlll

KKvv ;Darcy’s law:

Pk

v v vForchheimer(non-Darcy) equation:

Streamline upwind/Petrov-Galerkin (SUPG) finite element formulation with shock-capturing operator

Galerkin SUPG SUPG with shock-capturing

Support different 2D/3D meshes (triangle, quadrilateral, tetrahedron, hexahedron)

Newton-based iterative method for non-linear problems

For high flow rate, the Darcy flow equation is not applicable

Non-Darcy flow behavior in the fracture dominated reservoir has long been reported in petroleum/gas reservoirs, as well as the geothermal reservoirs

Well tests are widely used to study reservoir characteristics. Fluid flow behavior in the near-well region is significantly impacted by the non-Darcy flow due to high flow rate in this region.

The fluid flow follows the Forchheimer equation

Pk

v v v

Thermodynamic properties of water are of vital importance to understand the physical-chemical and geological processes in the Earth and get accurate modeling results

The most accepted IAPWS-95 formulation is implemented into Pandas as thermodynamic properties of water

SWEOS, an Equation of State (EOS) for CO2 which was originally

developed by Span and Wagner (1996) is also adopted to calculate CO2

properties

of water

of CO2

Injection well pressure is 44MPa, constant pressure drop of 10MPa is set between the injection well and production well.

•L=500m, D=15m, H=0.01m•Initial rock matrix is 260 degrees•The inflow water is 30 degrees

CO2

water

Parameter Value Unit

Reservoir radius 500 m

Well radius 0.05 M

Well production rate per unit depth 1.57×10-4 Kg s -1

Porosity 0.2

Fluid density 1,000 kg m-3

Fluid viscosity 1×10-3 Pa s

Fluid compressibility 5×10-10 Pa-1

Fracture permeability 1×10-12 m2

Rock matrix permeability 1×10-16 m2

Non-Darcy coefficient 1~2×107 m-1

Critical Forchheimer number 0.02

1/12 of a circular reservoir model

Parameters for the well drawdown test problem

Triple Point

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

200 250 300 350 400 450 500 550 600Temperature (K)

Pre

ssu

re (

ba

r)

Vapor

Solid

Liquid

630Bar

40Bar

A B C

D E F

A - Water, 60°CB - Water, 160°CC - Water, 260°CD - Vapor, 260°CE - Vapor, 280°CF - Vapor, 300°CG - 2 Phase, 300°C

90Bar G

550

560

570

580

590

600

610

620

630

640

0 1 2 3 4 5

Time (Day)

Pro

duct

ion

wel

l pre

ssur

e (B

ar)

Darcy flow, T=60ºCDarcy flow, T=160ºCDarcy flow, T=260ºCForchheimer flow, T=60ºCForchheimer flow, T=160ºCForchheimer flow, T=260ºC

0

5

10

15

20

25

30

35

40

45

0 0.5 1 1.5 2 2.5 3 3.5

Time (Day)

Pro

duct

ion

wel

l pre

ssur

e (B

ar)

Darcy flow, T=260ºCDarcy flow, T=280ºCDarcy flow, T=300ºCForchheimer flow, T=260ºCForchheimer flow, T=280ºCForchheimer flow, T=300ºC

70

75

80

85

90

95

0 0.5 1 1.5 2 2.5 3 3.5

Time (Day)

Pro

duct

ion

wel

l pre

ssur

e (B

ar) Darcy flow Forchheimer flow

Water dominated reservoir Vapor dominated reservoir

2-phase reservoir

30ºCColdWaterInjection

Hot

Water

Production

Dimension of the entire region: 150m x 90m Channel width: 1.5m Hot Rock Zone: Impermeable, 250ºC of initial temperature Fractured Channel Zone: 30% of porosity; permeability 0.1 Darcy Injection Pressure: 700 bars; Injection Water Temperature: 30ºC Production Pressure: 630 bars

Temperature Drop of Prodution Outlets

0

50

100

150

200

250

300

0 1 2 3 4 5 6 7 8 9 10

Time (year)

Tem

pera

ture

(D

egre

e)

Outlet A

Outlet B

Outlet C

Reservoir permeability distribution can be calculated through the microseismic events recorded during a hydraulic stimulation process

Based on the permeability distribution, a virtual 8-well geothermal reservoir (1 injection well plus 7 production wells in a reservoir with the dimensions of Length x Width x Height: 4000 m x 3000 m x 1750 m) is designed and further analysis.

Calculated permeability distribution Designed multi-well system

Microseismic data source:Geodynamics Limited

H1H1

Fluid Flow velocity in multi-well reservoir (on a horizontal section)

Pressure distribution after 5 yearsTemperature distribution after 40 years

Pandas/ThermoFluid has several sound feathers:◦ Outstanding background usage in mechanical engineering

and crustal dynamics modeling◦ Multiphase modeling with variable fluid thermodynamic

properties◦ Robust/accurate solution procedure with Streamline

Upwind/Petrov-Galerkin (SUPG) finite element formation and shock capturing technique

◦ Variable mesh type support◦ Newton-based iterative method for non-linear problems◦ Capable of modeling non-Darcy flow behavior

Pandas/ThermoFluid code is a valuable and versatile tool for geothermal reservoir modeling such as:◦ Well tests, well design, pressure/flow rate evaluation◦ Temperature change, geothermal field longevity estimation◦ Geothermal risk management strategies, geothermal

hazards prediction