POROMECHANICS OF POROUS AND FRACTURED RESERVOIRS Jishan Liu, Derek Elsworth KIGAM, Daejeon, Korea May 15-18, 2017 1. Poromechanics – Flow Properties (Jishan Liu) 1:1 Reservoir Pressure System – How to calculate overburden stress and reservoir pressure Day 11 1:2 Darcy’s Law – Permeability and its changes, reservoir classification 1:3 Mass Conservation Law – flow equations 1:4 Steady-State Behaviors – Solutions of simple flow problems 1:5 Hydraulic Diffusivity – Definition, physical meaning, and its application in reservoirs 1:6 Rock Properties – Their Dependence on Stress Conditions Day 1 ……………………………………………………………………………………………………………... 2. Poromechanics – Fluid Storage Properties (Jishan Liu) 2:1 Fluid Properties – How they change and affect flow Day 2 2:2 Mechanisms of Liquid Production or Injection 2:3 Estimation of Original Hydrocarbons in Place 2:4 Estimation of Ultimate Recovery or Injection of Hydrocarbons 2:5 Flow – Deformation Coupling in Coal 2:6 Flow – Deformation Coupling in Shale Day 2 ……………………………………………………………………………………………………………... 3. Poromechanics –Modeling Porous Medium Flows (Derek Elsworth) 3:1 Single porosity flows - Finite Element Methods [2:1] Lecture Day 3 3:2 2D Triangular Constant Gradient Elements [2:3] Lecture 3:3 Transient Behavior - Mass Matrices [2:6] Lecture 3:4 Transient Behavior - Integration in Time [2:7] Lecture 3:5 Dual-Porosity-Dual-Permeability Models [6:1] Lecture Day 3 ……………………………………………………………………………………………………………... 4. Poromechanics –Modeling Coupled Porous Medium Flow and Deformation (Derek Elsworth) 4:1 Mechanical properties – http://www.ems.psu.edu/~elsworth/courses/geoee500/GeoEE500_1.PDF Day 4 4:2 Biot consolidation – http://www.ems.psu.edu/~elsworth/courses/geoee500/GeoEE500_1.PDF 4:3 Dual-porosity poroelasticity 4:4 Mechanical deformation - 1D and 2D Elements [5:1][5:2] Lecture 4:5 Coupled Hydro-Mechanical Models [6:2] Lecture Day 4 ……………………………………………………………………………………………………………... 1 All sessions nominally1h:15m POROMECHANICS OF POROUS AND FRACTURED RESERVOIRS Jishan Liu, Derek Elsworth KIGAM, Daejeon, Korea May 15-18, 2017 1. Poromechanics – Flow Properties (Jishan Liu) 1:1 Reservoir Pressure System – How to calculate overburden stress and reservoir pressure Day 12 1:2 Darcy’s Law – Permeability and its changes, reservoir classification 1:3 Mass Conservation Law – flow equations 1:4 Steady-State Behaviors – Solutions of simple flow problems 1:5 Hydraulic Diffusivity – Definition, physical meaning, and its application in reservoirs 1:6 Rock Properties – Their Dependence on Stress Conditions Day 1 ……………………………………………………………………………………………………………... 2. Poromechanics – Fluid Storage Properties (Jishan Liu) 2:1 Fluid Properties – How they change and affect flow Day 2 2:2 Mechanisms of Liquid Production or Injection 2:3 Estimation of Original Hydrocarbons in Place 2:4 Estimation of Ultimate Recovery or Injection of Hydrocarbons 2:5 Flow – Deformation Coupling in Coal 2:6 Flow – Deformation Coupling in Shale Day 2 ……………………………………………………………………………………………………………... 3. Poromechanics –Modeling Porous Medium Flows (Derek Elsworth) 3:1 Single porosity flows - Finite Element Methods [2:1] Lecture Day 3 3:2 2D Triangular Constant Gradient Elements [2:3] Lecture 3:3 Transient Behavior - Mass Matrices [2:6] Lecture 3:4 Transient Behavior - Integration in Time [2:7] Lecture 3:5 Dual-Porosity-Dual-Permeability Models [6:1] Lecture Day 3 ……………………………………………………………………………………………………………... 4. Poromechanics –Modeling Coupled Porous Medium Flow and Deformation (Derek Elsworth) 4:1 Mechanical properties – http://www.ems.psu.edu/~elsworth/courses/geoee500/GeoEE500_1.PDF Day 4 4:2 Biot consolidation – http://www.ems.psu.edu/~elsworth/courses/geoee500/GeoEE500_1.PDF 4:3 Dual-porosity poroelasticity 4:4 Mechanical deformation - 1D and 2D Elements [5:1][5:2] Lecture 4:5 Coupled Hydro-Mechanical Models [6:2] Lecture Day 4 ……………………………………………………………………………………………………………... 2 All sessions nominally1h:15m Summary of Notation – Diffusion Equation ! $ !!! Tensor: %&$'"# $%&'" ()* !! ! + !"# # ! , , ! Matrix: %$ & $ ' $%&' " ()* # Indicial: $$$$!!! $$! $ %&"#!!!'./% & "! # './%$&$'./% ---( &*-01/(*$'" # +!!!)!* +!- + $$$$!!! Epanded: %&"#' +!!"!!! Advective-Diffusive Flows $ %&$'"# ! $ + Momentum Transfer - Fluid Mechanics – Navier-Stokes Equations (Incompressible) Tensor: ! !!!!! "#!!"2 !$%&' !! ! + !"# ! + Expanded: 003! , ! 0 !! !!!! 00"!-., 0 " 003 #"" "2- !!!.0" +!"# !"# 00## 3 , # 0# # 000 -.!#" + !"# 3:1 Single porosity flows - Finite Element Methods [2:1] https://youtu.be/46QiOhaC47c [2:1]!Fluid!Flow!and!Pressure!Diffusion! Recap!of!FEM! Comsol!Applied!to!Flow!! 1D!Element! ! ! 3:2 2D Triangular Constant Gradient Elements [2:3] http://youtu.be/a_8VZejdgTA [2:3]!Fluid!Flow!and!Pressure!Diffusion! Recap! 2D!Triangular!(Constant!Gradient)!Elements! ! Derivation! ! Example! ! EGEEfem! ! ! ! ! 3:3 Transient Behavior - Mass Matrices [2:6] https://youtu.be/fl5AVItg51E [2:6]!Fluid!Flow!and!Pressure!Diffusion! Recap! Kh + Sh! = q Transient!Behavior!!!!!! !! ! “Mass”!matrices! ! ! ! ! ! ! ! ! ! ! ! ! 3:4 Transient Behavior - Integration in Time [2:7] https://youtu.be/no5Y6dCXcyE [2:7]!Fluid!Flow!and!Pressure!Diffusion! Recap! Kh + Sh! = q Transient!Behavior!!!!!! !! ! Time!integration! ! EGEEfem! ! ! ! ! ! ! ! ! 3:5 Dual-Porosity-Dual-Permeability Models [6:1] Lecture https://youtu.be/key0TuOSDBU [6:1]!Linked!Mechanisms! Dual!Porosity/Dual!Permeability! ! Concept! ! Dual!permeability!! ! ! Heuristic!derivation! ! ! Comsol!implementation! ! ! ! POROMECHANICS OF POROUS AND FRACTURED RESERVOIRS Jishan Liu, Derek Elsworth KIGAM, Daejeon, Korea May 15-18, 2017 1. Poromechanics – Flow Properties (Jishan Liu) 1:1 Reservoir Pressure System – How to calculate overburden stress and reservoir pressure Day 13 1:2 Darcy’s Law – Permeability and its changes, reservoir classification 1:3 Mass Conservation Law – flow equations 1:4 Steady-State Behaviors – Solutions of simple flow problems 1:5 Hydraulic Diffusivity – Definition, physical meaning, and its application in reservoirs 1:6 Rock Properties – Their Dependence on Stress Conditions Day 1 ……………………………………………………………………………………………………………... 2. Poromechanics – Fluid Storage Properties (Jishan Liu) 2:1 Fluid Properties – How they change and affect flow Day 2 2:2 Mechanisms of Liquid Production or Injection 2:3 Estimation of Original Hydrocarbons in Place 2:4 Estimation of Ultimate Recovery or Injection of Hydrocarbons 2:5 Flow – Deformation Coupling in Coal 2:6 Flow – Deformation Coupling in Shale Day 2 ……………………………………………………………………………………………………………... 3. Poromechanics –Modeling Porous Medium Flows (Derek Elsworth) 3:1 Single porosity flows - Finite Element Methods [2:1] Lecture Day 3 3:2 2D Triangular Constant Gradient Elements [2:3] Lecture 3:3 Transient Behavior - Mass Matrices [2:6] Lecture 3:4 Transient Behavior - Integration in Time [2:7] Lecture 3:5 Dual-Porosity-Dual-Permeability Models [6:1] Lecture Day 3 ……………………………………………………………………………………………………………... 4. Poromechanics –Modeling Coupled Porous Medium Flow and Deformation (Derek Elsworth) 4:1 Mechanical properties – http://www.ems.psu.edu/~elsworth/courses/geoee500/GeoEE500_1.PDF Day 4 4:2 Biot consolidation – http://www.ems.psu.edu/~elsworth/courses/geoee500/GeoEE500_1.PDF 4:3 Dual-porosity poroelasticity 4:4 Mechanical deformation - 1D and 2D Elements [5:1][5:2] Lecture 4:5 Coupled Hydro-Mechanical Models [6:2] Lecture Day 4 ……………………………………………………………………………………………………………... 3 All sessions nominally1h:15m 4:1 Mechanical properties http://www.ems.psu.edu/~elsworth/courses/geoee500/GeoEE500_1.PDF >eaN ff'67'J s- W> U'X "( ,'- f-- Y- | 9'81 KN/-,3 0t,,,-,-r1c. SV'-$;, ]q*",1t" 2.+ r'6W-n 9, or .) U'^;t s(. qY- + grer*s tt 7r-"tr1 rL = vvl =L I Vs+V, |-r,1' \. 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