1. Recent research results on geothermal reservoir modelling
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
Good afternoon everyone, my name is Ji Zhang, I am a Phd student of Dr Huilin Xing, from Earth Systems Science Computational Centre, The University of Queensland. I am giving this talk on behalf of Huilin, who cannot be here today, and asked me to pass his apology for his absence.

2. Acknowledgement 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
Before I start my presentation, I would like to express my deep appreciations to

3. Outline
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
In today’s talk, first I will give a brief introduction of our self-developed finite element simulator ‘Pandas Thermo/Fluid’, from the big picture of the software, to the physical and mathematical equations and the numerical feathers. Then I will present some recent applications and results of modeling geothermal related problems with Pandas Thermo/Fluid.

4. Finite element method has its sound mathematical foundation and widely applied in various scientific and engineering fields, such as our in-house FEM program ‘PANDAS’.
PANDAS has the 5 key components for different physical problems:
ESyS_Crustal for the interacting fault system simulation;
PANDAS/Fluid for simulating the fluid flow in fractured porous media;
PANDAS/Thermo for the thermal analysis of metals and fractured porous media;
PANDAS/Pre and PANDAS/Post for conceptual modeling, mesh generation and visualisation.
It has been successfully applied for analysing many problems in mechanical engineering and crustal dynamics in various scales.
Recently we have started to develop our simulator towards multiphase fluid and heat flow in fractured porous medium and applied to geothermal reservoir modeling.

5. Automatic Meshing and Construction of 3D Reservoir Systems
Abstract geological models
(Data source: 3D geological model created with Geomodeller by
Helen Gibson of Intrepid Geoscience )
As the existence of two faults, a model with different geological objects is divided into three parts.
Mr Yan Liu will give a talk on this topic during the upcoming AGEC conference.
A well model with Tetrahedral mesh

6. Converted rock image with 3,871,488 grid points
Modelling fluid Flow in fractured medium using Lattice Boltzmann Method (LBM)
2D case
3D case
We also have student modeling fluid flow in fractured medium using Lattice Boltzmann Method in both 2d and 3d. Here is some preliminary results of LBM modeling of fluid infiltration to the fractured rock. The object of this study is to find out the relationship between the micro geometries and the macro phenomena in porous medium.
It is capable of simulating 2D/3D fluid flow in heterogeneous porous media with disordered microstructures under various conditions.
As more models are coupled with, PLBS will be deeply figuring out the relationship between micro geometries and macro phenomena. The usage of PLBS will be not only restricted for micro-scale simulation of porous media, but also effective to evaluate the material properties (i.e. permeability) in any complicated but with similar macro-scale structures.
Converted rock image with 3,871,488 grid points

7. Physical/mathematical equations of multiphase fluid/heat flow in porous medium
Mass balance equation
Momentum balance equation
Energy balance equation
Darcy’s law:
Under several assumptions, multiphase fluid/heat flow in porous medium can be described with 3 set of equations: the mass balance equation, the momentum balance equation and the energy balanced equation. In these equations, the main unknown variables are the fluid pressure, the saturation of each phases, the temperature and the fluid flow rate. Fluid properties such as density is dependent on pressure and temperature and cannot treated as constant parameters. Relative permeability are usually function of saturation. These can make the problem highly nonlinear.
Forchheimer(non-Darcy) equation:

8. Numerical solution feathers
Streamline upwind/Petrov-Galerkin (SUPG) finite element formulation with shock-capturing operator
We have put a lot of efforts to solve these nonlinear diffusion-convection PDEs. Numerical instabilities in solving problems with high Reynolds numbers and shocks or thin boundary layers are the most common difficulties.
The streamline-upwind/Petrov-Galerkin (SUPG) formulation is one of the most widely used stabilized methods in finite element computation of flow problems. Typically the SUPG formulation is used in combination with a shock-capturing term that provides additional stability near the shock fronts. This equation is a semi-discrete form of the solution algorithm.
This example shows how we overcome the oscillations at the shock front in a convection dominated problem. With traditional Galerkin finite element formulation, very large amount of wiggles exist at both sides of the shock front; with SUPG method, the wiggles are apparently depressed and only slightly exist at the upper front; by using SUPG method together with a shock-capturing term, the oscillation is totally eliminated. In practice, the shock front normally represents the phase interface, which is a very common difficulty to deal with multiphase problems.
Galerkin
SUPG
SUPG with
shock-capturing

9. Variable mesh support Newton-based nonlinear procedure
Support different 2D/3D meshes (triangle, quadrilateral, tetrahedron, hexahedron)
Newton-based iterative method for non-linear problems
We have developed our code to be compatible to various finite element meshes, such as the triangle and quadrilateral with and linear and quadratic functions, and 3d meshes such as the tetrahedron and hexahedron.
To deal with highly non-linear problems, we implemented Newton-based iterative solution procedure to deal with the nonlinear algebraic equations.

10. Non-Darcy flow
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
In porous medium, fluid flow normally obeys the Darcy flow equation, which gives a linear relationship of the flow velocity and the pressure gradient. It is well known that in the high flow rate regime, the Darcy flow equation is not application, the relationship between the flow velocity and the pressure gradient is nonlinear.
… …
It is widely accepted that the non-Darcy flow follows the Forchheimer equation, in which a drag force term was introduced by Forchheimer to extend the applicability of Darcy equation.

11. Variable thermodynamic properties - Water/CO2 Equation-of-State (EOS)
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
Thermodynamic properties of water are of vital importance to understand the physical-chemical and geological processes in the Earth and get accurate modeling results. We have implemented different Equation-of-State for both water and CO2 to model their multiphase flow behavior under geothermal conditions.
These pictures show the mobility of water and CO2 under different pressure and temperature conditions. We can see that both of them have complicated relationship with pressure and temperature. Numerical modeling of geothermal reservoirs is highly dependent on the availability and accuracy of fluid thermodynamic properties such as density and dynamic viscosity. So it is important to consider using variable fluid thermodynamic properties in our simulation. 11

12. Recent applications and results
Now I am going to show some recent applications and results of our geothermal modeling.

13. Fluid velocity evolution at early stage of a single channel flow
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
We started with a simple horizontal channel flow problem. The injection well is located at the left side, where 30 degree cold fluid is inject in. the production well is located at the right side, where the hot fluid is pumped out. The channel has a length of 500m and a vertical width of 0.01m. It is surrounded by hot rock matrix of 260 degrees. This picture shows the fluid velocity evolution at the very early stage of the channel flow. The injection well pressure is 44 Mpa, and constant pressure drop of 10 Mpa is set between the injection and production wells. As we can see, with the same pressure drop between injection well and production well, CO2 has high flow rate than water.
It is also can be seen that CO2 takes about 81 hours to reach the stable state, while water takes only less than 50 hours. The reason for longer stabilization time for CO2 is because it has larger ratio of fluid density to viscosity and larger compressibility (about 8 times of water) than water under reservoir pressure/temperature.
CO2
water

14. Drawdown test on a concentric well in a circular reservoir with non-Darcy flow effects
Parameters for the well drawdown test problem
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
Non-Darcy coefficient
1~2×107
m-1
Critical Forchheimer number
0.02
In petroleum and geothermal reservoir engineering, pressure and flow well tests are routinely conducted to determine formation permeability, porosity, total formation compressibility, skin factor and initial reservoir pressure.
The drawdown pressure test is a well-test which is performed to obtain permeability data for the reservoir formation. For a drawdown test, a well, initially at equilibrium conditions, is produced at a constant flow rate while the bottom hole pressure history is recorded.
Here we build a 2D model with fine mesh for the near well region to study the Darcy and non-Darcy flow behavior in pressure drawdown test.
1/12 of a circular reservoir model

15. Typical temperature/pressure starting conditions on water phase diagram for the drawdown tests
We choose several typical temperature/pressure starting conditions for the drawdown test. As we can see from the water phase diagram, 3 points are put in the liquid water region, and 3 points are choose in the vapor region and 1 point is choose as just above the saturaion line, thus during the drawdown test, phase change will happen.

16. Pressure drawdown tests with non-Darcy flow effects
Water dominated reservoir
Vapor dominated reservoir
These pictures show the pressure drawdown tests of different reservoir conditions.
The near-well final pressure is highly different between Darcy flow and non-Darcy flow. This shows the significance of considering the non-Darcy flow effect in modeling well performance in reservoir simulation.
It is also can be seen that the geothermal reservoir well performances of the water/vapor drawdown tests are strongly dependent on reservoir initial temperature.
2-phase reservoir

17. A conceptual fractured geothermal reservoir with 29 horizontal and 45 vertical channels
Hot
Water
Production
30ºC
Cold
Water
Injection
The 2nd application is a more complicated channel flow model, which represent a conceptual model of fractured geothermal reservoir. It has 29 horizontal channels and 45 vertical channels. It has a highly fracture zone in the middle and close to the injection well area and less fractured zone in the outside.
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

18. Heat flow – reservoir temperature change
This movie shows the reservoir temperature change with time. It clearly shows how the cold water and low temperature is spread out to the entire reservoir through the channels during 10 years production time. It is interesting to notice that several isolated island surround by channel flows can stay high temperature after 10 years. This is evident to show how important to use hydraulic stimulation to create more fractures before energy production. Supposed we can get this area fractured as this area, more energy will be extracted within a same production time.

19. Production well temperature monitoring
We can easily monitor the production fluid temperature and draw a temperature evolution history chart like this. It will give a clear concept of how the temperature drops at the production wells. If we give a minimum required temperature for energy production such as 100 degree. We can read the longevity of the geothermal reservoir.

20. Coupled multi-well heat/fluid flow
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: m x 3000 m x 1750 m) is designed and further analysis.
Microseismic data source:
Geodynamics Limited
Hydraulic stimulation is a basic concept of improving the residual permeability for the creation of an enhanced geothermal reservoir.
Reservoir permeability distribution can be calculated through the microseismic events recorded during a hydraulic stimulation process. As shown in this picture, the permeability is heterogeneous, with higher values in the red regions.
Based on the permeability distribution, a virtual 8-well geothermal reservoir with 1 injection well and 7 production wells is designed and further analysis as shown in this picture. The wells are well-distributed in the high permeability region.
Calculated permeability distribution
Designed multi-well system

21. Coupled multi-well flow
Fluid Flow velocity in multi-well reservoir (on a horizontal section)
Pressure distribution after 5 years
Temperature distribution after 40 years
We created 3D mesh to model the coupled multi-well flow with heterogeneous permeability.
This picture shows the fluid Flow velocity on a horizontal section.
This picture shows the pressure distribution after 5 years.
And this picture shows the temperature distribution after 40 years, as we can see the temperature decrease mostly in the high permeability region, due to the high fluid flow rate.

22. Conclusions 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

23. Thank you!