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

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

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

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

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)

Fluid Mass Balance

Change in Hydraulic Properties Porosity Permeability Capillary Pressure

Discretization Fluid Flow [IFDM] TOUGH2 Mesh

Discretization (Contd.) Momentum [FEM] Cartesian Dual

Dual Mesh TOUGH2 Mesh Cartesian Dual TOUGH2 Cell Center FEM Node

Solution Technique Newton-Raphson (TOUGH2) Jacobian Representation

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

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

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

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

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

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.

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

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)

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

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

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

Mass Balance (Contd.) Solid Solid Density where

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

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

Momentum Conservation General Static Equilibrium Equation Neglecting inertial terms

Jacobian Modifications Individual Term Fluid Flow

Jacobian Modifications (Contd.) Stress Equilibrium

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

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

Effective Stress Law Effective Stress Stress-Strain

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

Sample Problem (contd.)