Coupled Thermo-Hydro-Mechanical Analysis

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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_at_ksu.edu

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

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

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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

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System Equations for Stress Coupling

• Conservation Equations
• Mass
• Energy
• Momentum
• Constitutive Equations
• Darcys law (Advective Flux)
• Ficks law (Diffusive Flux)
• Fourier law (Thermal)
• Terzaghis Principle (Effective Stress)

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Fluid Mass Balance
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Change in Hydraulic Properties

• Porosity

• Permeability

• Capillary Pressure

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Discretization

• Fluid Flow IFDM

• TOUGH2 Mesh

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Discretization (Contd.)

• Momentum FEM

• Cartesian Dual

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Dual Mesh

• TOUGH2 Mesh

• Cartesian Dual

TOUGH2 Cell Center
FEM Node
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Solution Technique

• Newton-Raphson (TOUGH2)

• Jacobian Representation

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Jacobian Modifications (Contd.)

• Solid-Fluid Coupling

• Volumetric Strain (IFDM)

n
m
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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

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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

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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

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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

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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.

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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

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Sample Problem

• Sample problem 5 from TOUGH2 users guide
• Well with inside diameter 0.2 m
• 500 m thick, two-phase reservoir
• Water at P 60 bars, TTsat(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)

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Sample Problem (contd.)

• Results obtained from the two runs plotted
• These trends match with those obtained in TOUGH2
  guide

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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

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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
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Mass Balance (Contd.)

• Solid

• Solid Density

where
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Mass Balance (Contd.)

• Fluid

TOUGH2
Skeleton
Solid Grains


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Energy Balance

• General

• Using Internal Energy
• Neglecting conversion of KE to IE

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Momentum Conservation

• General

• Static Equilibrium Equation
• Neglecting inertial terms

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Jacobian Modifications

• Individual Term

• Fluid Flow

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Jacobian Modifications (Contd.)

• Stress Equilibrium

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Constitutive Laws

• Darcys Law (Advection)

• Ficks Law (Diffusion)

• Fouriers Law (Heat Conduction)

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Jacobian Modifications (Contd.)

• Fluid-Solid Coupling

• Internal Forces Dual Mesh

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Effective Stress Law

• Effective Stress

• Stress-Strain

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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

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Sample Problem (contd.)