1. Coupled Thermo-Hydro-Mechanical Analysis
Daniel Swenson
Shekhar Gosavi
Ashish Bhat
Kansas State University
Mechanical and Nuclear Engineering Department
Manhattan, KS, 66506, USA

2. Objective
To provide coupled thermal-hydraulic-mechanical analysis tools that enable quantitative understanding and prediction of thermal effects on flow in the reservoir.

3. Approach Couple deformation/stress analysis with TOUGH2
Couple wellbore model with TOUGH2
Apply these tools to the analysis of Coso injection

4. Status Implemented one way (forward) coupling
Implemented back coupling effect on hydraulic properties (porosity and permeability) without full Jacobian terms.
Now implementing full Jacobian solution
Expect to have working version first quarter of 2005

5. System Equations for Stress Coupling
Conservation Equations
Mass
Energy
Momentum
Constitutive Equations
Darcy’s law (Advective Flux)
Fick’s law (Diffusive Flux)
Fourier law (Thermal)
Terzaghi’s Principle (Effective Stress)

6. Fluid Mass Balance

7. Change in Hydraulic Properties
Porosity
Permeability
Capillary Pressure

8. Discretization
Fluid Flow [IFDM]
TOUGH2 Mesh

9. Discretization (Contd.)
Momentum [FEM]
Cartesian Dual

10. Dual Mesh
TOUGH2 Mesh
Cartesian Dual
TOUGH2 Cell Center
FEM Node

11. Solution Technique
Newton-Raphson (TOUGH2)
Jacobian Representation

12. Jacobian Modifications (Contd.)
Solid-Fluid Coupling
Volumetric Strain (IFDM) m n

13. Motivation for Coupling of Wellbore Model
Settings at Coso (EGS) site
Low permeability
Significant drawdown
Presence of two-phase flow and multiple feedzones
Our goal is to provide enhanced capability in TOUGH2 to-
Better model flow in geothermal systems containing inclined wells with multiple feedzones
account for varying flowing bottomhole pressure

14. HOLA wellbore Simulator
Multi-feedzone wellbore simulator for pure water
GWELL and GWNACL-extensions of HOLA
Can handle steady state, one-dimensional flow (single and two-phase) in the well with varying well-radius
2 approaches :
Option 1 (Wellhead-to-Bottomhole)
Option 2 (Bottomhole-to-Wellhead)
Simulates both production and injection

15. Background
Murray and Gunn (1993) – coupling between TETRAD and WELLSIM
Hadgu et al., (1995) – TOUGH2 and WFSA
Coupled wellbore flow option in TOUGH2
tables are generated for each well that are used for interpolation.
limited to single feedzone

16. Coupling of HOLA with TOUGH2
Some features of the coupled code are,
No change in TOUGH2 input file
‘H----’ type of record in GENER block indicates coupled simulation
Input file format for the well is in similar spirit of HOLA
Wellhead pressure as a time-dependent tabular data
Shut-in/Flowing option

17. Coupling of HOLA with TOUGH2 (Contd.)
PROCEDURE:
Read input file
Obtain required reservoir parameters
Call HOLA at the start of each new time-step
A positive(/negative) flowrate at a feedzone in HOLA is supplied as production(/injection) rate in the corresponding source/sink element in TOUGH2
Enthalpy of a producing element is calculated in TOUGH2, while for injection it comes from HOLA
Repeat steps (ii) to (v) for the next time-step with updated values of reservoir parameters.

18. Coupling of HOLA with TOUGH2 (Contd.)
Minimal changes made to TOUGH2
Issues in HOLA
Averaging of parameters in routine VINNA2
Relative permeability calculations
Instances of un-initialized variables being used
Division by zero
Inclined wells
Hard-coded simulation parameters

19. Sample Problem Sample problem 5 from TOUGH2 user’s guide
Well with inside diameter = 0.2 m
500 m thick, two-phase reservoir
Water at P = 60 bars, T=Tsat(P) = ˚C, Sg = 0.1
Wellhead pressure = 7 bars
feedzone depth =1000 m
1-D radial mesh, extends 10,000 m
Well Productivity Index = 4.64e-11
Simulation starts with a time-step of 1.e5 sec and ends at time, 1.e9 sec (approx years)

20. Sample Problem (contd.)
Results obtained from the two runs plotted
These trends match with those obtained in TOUGH2 guide

21. Current/Future Work
Revisit the convergence methodology implemented in HOLA
Extension to GWELL and GWNACL
Use the coupled code to better model the wells at Coso (EGS) site
Finished first half of 2005

22. Acknowledgements THANK YOU Karsten Pruess and Jonny Rutqvist, LBNL.
Teklu Hadgu, Sandia National Laboratories.
This work is supported by the U.S. Department of Energy, under DOE Financial Assistance Award DE-FC07-01ID14186.
THANK YOU

23. Mass Balance (Contd.)
Solid
Solid Density
where

24. Mass Balance (Contd.)
Fluid + +
TOUGH2 +
Skeleton +
Solid Grains

25. Energy Balance General Using Internal Energy
Neglecting conversion of KE to IE

26. Momentum Conservation
General
Static Equilibrium Equation
Neglecting inertial terms

27. Jacobian Modifications
Individual Term
Fluid Flow

28. Jacobian Modifications (Contd.)
Stress Equilibrium

29. Constitutive Laws Darcy’s Law (Advection) Fick’s Law (Diffusion)
Fourier’s Law (Heat Conduction)

30. Jacobian Modifications (Contd.)
Fluid-Solid Coupling
Internal Forces – Dual Mesh

31. Effective Stress Law
Effective Stress
Stress-Strain

32. TOUGH2 simulator
Numerical simulator for multi-phase fluid and heat flow in porous and fractured media.
A well is represented in a simplified manner
Well on deliverability model
fixed bottomhole pressure
production rate is calculated as,
Coupled wellbore option

33. Sample Problem (contd.)