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.
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