Coupled Thermo-Hydro-Mechanical Analysis

1. Coupled Thermo-Hydro-Mechanical Analysis Daniel Swenson Shekhar Gosavi Ashish Bhat Kansas State University Mechanical and Nuclear Engineering Department Manhattan, KS, 66506, USA e-mail: swenson@ksu.edu

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) n m

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) = 275.5 ˚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. 31.7 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 • 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 • Stress-Strain • Effective Stress

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.)