Fluid-Mechanical Interaction

This section contains information regarding the modeling of fluid in 3DEC. This includes theory and practical considerations for modeling flow through blocks (“Matrix Fluid Flow), flow along fractures (“Joint Fluid Flow”), and flow of proppant (“Proppant”). In each section, examples and verification problems are presented.

Properties and units used in fluid flow analyses are given in “Fluid Flow Properties and Units”. Commands and FISH functions related to fluid flow modeling are …

• Introduction
• Pore Pressure and Effective Stress
  • Introduction
    • Definitions
    • Pore Pressure in 3DEC
    • A Note on Using the block water table Command
  • No Flow Example
• Matrix Fluid Flow
  • Introduction
  • 3DEC Fluid-Mechanical Formulation – Mathematical Description
    • Conventions and Definitions
    • Governing Differential Equations
    • Balance Laws
    • Constitutive Laws
  • Numerical Formulation
    • Introduction
    • Saturated Fluid Flow
      • Finite-Difference Approximation to Space Derivatives
      • Nodal Formulation of the Mass Balance Equation
      • Explicit Finite-Difference Formulation
    • Mechanical Timestep and Numerical Stability
    • Total Stress Correction
  • Properties and Units for Fluid Flow Analysis
    • Permeability Coefficient
    • Mass Density
    • Fluid Bulk Modulus
      • Fluid Modulus and Convergence
      • Fluid Modulus for Drained and Undrained Analyses
  • Porosity
  • Fluid-Flow Boundary Conditions, Initial Conditions, Sources, and Sinks
  • Calculation Modes for Fluid-Mechanical Interaction
    • Grid Not Configured for Fluid Flow
    • Grid Configured for Fluid Flow
    • Storage, Diffusivity, and Timestep
    • Flow-Only Calculation
      • Steady State
      • Transient
    • No Flow — Mechanical Generation of Pore Pressure
    • Coupled Flow and Mechanical Calculations
      • Fully Coupled Analysis
      • Uncoupled Analysis
    • Selection of a Modeling Approach for Fully Coupled Analysis
  • Verification Examples
    • Transient Groundwater Flow in a Confined Layer
    • One-Dimensional Consolidation
• Joint Fluid Flow
  • Introduction
  • Joint Hydraulics and Parallel Plate Model for Incompressible Flow
    • Range of Validity of Parallel Plate Model, Hydraulic Aperture, and Mechanical Aperture
  • Hydromechanically Coupled Fluid-Flow Formulation in Rock Masses
    • Effect of Pore Pressure on Deformation and Strength
    • Effect of Mechanical Deformation on Permeability
    • Effect of Deformation on Pore Pressures
  • 3DEC Joint Model
    • Constitutive Model and Relevant Properties
    • Degree of Saturation
    • Fluid Timestep Size and Numerical Stability
  • Calculation Modes and Commands for Fluid-Flow Analysis
    • Fluid-Only Analysis
    • One-Way Coupling
    • Undrained
    • Fully Coupled Hydromechanical Simulation
      • Definition of Fluid Properties
      • Solving for Initial State
      • Running the Coupled Solution
      • Example
      • Fast Flow
  • Leak-off
  • Considerations for Model Optimization
  • Representation of a Discrete Fracture Network (DFN) for Fluid Flow Simulations
  • Geometrical and Topological Model of a Fractured Rock Mass
    • Introduction
    • 3DEC Geometrical Entities
      • Fluid Flow Data Structure
      • Accessing Flow Plane Data
      • Links between the Solid and Flow Models
      • Generation of Geometry of the Flow Model
  • Gas Flow
    • Implementation
    • Example
  • Fluid Discharge and Velocity
  • References
• Proppant
  • Introduction
  • Logic Overview
  • Basic Equations
    • Proppant Convection
    • Slurry Viscosity
  • Numerical Implementation
    • Transport with No Aperture Change
      • Transient Term
      • Advection Term
  • Mechanical Coupling
    • Aperture Change with No Transport
    • Load Carried by the Proppant Pack
    • Bridging
    • Proppant Convection
    • Condition at an Intersection Between Flow Planes
    • Timestep for Stability
    • Boundary and Initial Conditions
  • Examples
    • Planar Flow
    • Injection
    • Bridging
    • Proppant Settlement
• Fluid Flow Properties and Units