ANDRA Benchmark Workshop (Paris-Orly, April 27) Javeri (GRS, Köln, Germany): 2-Dim. Case 1B Code TOUGH2/EOS7 developed by Pruess et al, Lawrence Berkeley National Laboratories, California, USA (199), Since 199 Five TOUGH-Workshops at Berkeley
Main Features of TOUGH2/EOS7 - Three Dimensional Transport of Water, Brine, Air and Heat in an Anisotropic Porous Medium - Mass Conservation Equations for each Mass Component (here: 3) including Advection and Diffusion in both Phases and considering Gas Solubility (Henry) - Darcy Equations for Liquid and Gas Phase including Relative Permeabilities and Capillary Pressure depending upon Liquid Saturation - Liquid Phase: Water, Brine (Tracer) and Dissolved Gas - Gas Phase: Vapour and Gas - Water Properties using Complete Water Steam Table - Heat Conservation Equation including Conduction and Convection - Space Discretization employing Volume Elements - Fully Implicit First Order Time Discretization - Newton/Raphson Iteration for Non-Linearities - Integral Finite Difference Method - Bi-Conjugate Gradient Solver - Scalar Quantities (Pressure, Temperature, Mass Fraction, etc) at the Centre of the Volume Element - Vector Quantities (Velocity, Mass Flux, etc) at the Interface between the Elements - Primary Variables: Gas Pressure, Gas saturation, Liquid Mass fraction, Temperature - Passive Volume Elements with Zero Volume are placed just outside the Main Domain to simulate the Boundary Conditions of the First Kind (Prescribed Scalar Quantities like Pressure, Temperature, Mass Fraction). The Distance between the Passive Elements and the actual Domain should be nearly Zero. Conservation Equations are not solved for the Passive Volume Elements.
Major Own Code Modifications - Hydrogen instead of Air - Space dependant Heterogeneity, Porosity and Permeability highly space dependant - Porosity and Permeability depending upon Pressure and Temperature (Convergence of Rock Salt) - Anisotropic Diffusion and Dispersion in both Phases - Time dependant Boundary Condition of the Third Kind - Decay of a Tracer - Coupling with the three dimensional Geomechanical Code FLAC3D to study coupled THM Processes (currently under Development) Applications Since 1992 several Brine, Gas, Heat and Nuclide Transport Analyses in one to three dimensional Configurations, more than 25 GRS Reports on TOUGH2 Applications employing different Equation of State Modules - EOS5: Water and Hydrogen - EOS7: Water, Brine and Air - EOS7R: Water, Brine, Air, Mother Nuclide, Daughter Nuclide - EOS9NT: Water, Passive Gas Phase, Many Nuclide Chains
Major Model Features (Case 1B) - Substantially same Physical Model as in Original Code Version (very close to ANDRA Proposal) - Full Consideration of geometrical Dimension and Material Parameters as specified by ANDRA - Refinement of Calculation of Capillary Pressure (V-G- Relation) specially for Gas Saturation less than.1. The capillary pressure is linearized between gas saturation.1 and. - Number of Volume Elem. for the Right Half of the Model: Base Case: 324 Elem. (Variation: 468 Elements) - Time steps between 1E3 and 8E1 sec - Number of Time steps: 1657 - Duration of Simulation: till (numerical) steady state reached - CPU-Time: 66 h (IBM Work station, 1.4 GHz) Case 1A Not analyzed, since the Case 1A is a Simplification of Case 1B (Also Lack of Manpower and Funding)
Javeri (GRS, Köln, Germany) Results Andra-Benchmark 2-Dim. Case 1B Code: modified version of TOUGH2/EOS7 Number of Volume Elem. for the Right Half of the Model: Base Case: 324 Elem. (Variation: 468 Elements) Horizontal x-direction: 45 Elem. with a length between.5 and 5 m Horizontal y-direction: 1 Elem. with a width of 1 m Vertical z-direction: 72 Elem. with a height between.1 and 5 m Hydrogen Sources in the Primary Packages Chapter 1.7.1 At t = 795 years gas phase disappears At t = 2.35E5 years Total Hydrogen mass in both phases is less than 1 kg 12 ANDRA-Benchmark Case 1B: Two Dimensional Gas Transport 15 Total Gas Phase Vol. in m³ 8 4 Model: Only Right Half Volume of Gas Phase Mass of Hydrogen 1 5 Total Hydrogen Mass in Gas and Liquid Phase in kg 1 1 1 1 1 1 1 Time in Years
Chapter 1.7.2 No gas phase flow through the upper and lower limits Chapter 1.7.3: Primary Package 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas-Transport (x_andra = 11 m, z_andra = 62 m) 1 Pressure in MPa 6 4 2 ab6819- bc15-pgas ab6819- bc15-pcap ab6819- bc15-liq-sat,75,5,25 Liquid Saturation 1 1 1 1 1 1 1 Time in Years
Chapter 1.7.3: Concrete of Packages 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas-Transport (x_andra = 11 m, z_andra = 64.9 m) ab6819-b415-pgas 1 ab6819-b415-pcap Pressure in MPa 6 4 2 ab6819-b415-liq-sat,75,5,25 Liquid Saturation 1 1 1 1 1 1 1 Time in Years
Chapter 1.7.3: Clearances 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas-Transport (x_andra = 11 m, z_andra = 69.2 m) ab6819-aq15-gas 1 ab6819-aq15-pcap Pressure in MPa 6 4 2 ab6819-aq15-liq-sat,75,5,25 Liquid Saturation 1 1 1 1 1 1 1 Time in Years
Chapter1.7.3: Filler concret 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas-Transport (x_andra = 11 m, z_andra = 7 m) 1 6,75 Pressure in MPa 4 2 ab6819-an15-gas ab6819-an15-pcap ab6819-an15-liq-sat,5,25 Liquid Saturation 1 1 1 1 1 1 1 Time in Years
Chapter1.7.3: Fractured zone 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas-Transport (x_andra = 11 m, z_andra = 71.3 m) 1 6,75 Pressure in MPa 4 2 ab6819-aj15-gas ab6819-aj15-pcap ab6819-aj15-liq-sat,5,25 Liquid Saturation 1 1 1 1 1 1 1 Time in Years
Chapter 1.7.3: Disturbed Zone 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas-Transport (x_andra = 11 m, z _andra = 73 m) 1 Pressure in MPa 6 4 2 ab6819-af15-gasp ab6819-af15-pcap ab6819-af15-liq-sat,75,5,25 Liquid Saturation 1 1 1 1 1 1 1 Time in Years
Chapter 1.7.3: Callovo Oxfordian (COX) 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas-Transport (x_andra = 11 m, z_andra = 77 m) 1 ab6819-ac15-gas Pressure in Mpa 6 4 2 ab6819-ac15-pcap ab6819-ac15-liq-sat,75,5,25 Liquid Saturation 1 1 1 1 1 1 1 Time in Years
Chapter 1.7.3-A: Variation of Mesh size: Base Case: 324 Elements for the right half of the Model (El. size between.5 and 5 m) Variation: 468 Elements for the right half of the Model (El. size between.5 and 15 m) 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas-Transport (Primary Package: x_andra = 11 m, z_andra = 62 m) Gas Pressure in MPa 6 4 2 ab6819: 324 Elements in right half of the Model ab6869: 468 Elements in right half of the Model 1 1 1 1 1 1 1 Time in Years
Chapter 1.7.4 Horizontal Position of Gas Saturation Front in Meter 8 6 4 2 ANDRA-Benchmark Case 1B: Two Dimensional Gas Transport Horizontal Position of Gas Saturation Front From Vertical Axis at z = 65 m 1 1 1 1 1 1 1 Time in Years
Chapter 1.7.5 t = x = 13 m 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas Transport 1 Pressure in MPa 6 4 2 ab6819-t- x3-gas ab6819-t- x3-pcap ab6819-t- x3-gas-sat,75,5,25 Gas Saturation 1 2 3 4 5 6 7 8 9 1 11 12 13 Vertical Axis in Meter
Chapter 1.7.5 t = 1 Years x = 13 m 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas Transport 1 Pressure in MPa 6 4 2 ab6819- t1-x3- Gas ab6819- t1-x3- pcap ab6819- t1-x3- Gas-Sat 1 2 3 4 5 6 7 8 9 1 11 12 13 Vertical Axis in Meter,75,5,25 Gas Saturation
Chapter 1.7.5 t = 1 years x = 13 m 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas Transport 1 Pressure in MPa 6 4 2 ab6819- t1-x3- Gas ab6819- t1-x3- pcap ab6819- t1-x3- Gas-Sat 1 2 3 4 5 6 7 8 9 1 11 12 13 Vertical Axis in Meter,75,5,25 Gas Saturation
Chapter 1.7.5 t = 4 years x = 13 m 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas Transport 1 Pressure in MPa 6 4 2 ab6819- t4221-x3- Gas ab6819- t4221-x3- pcap ab6819- t4221-x3- Gas-Sat 1 2 3 4 5 6 7 8 9 1 11 12 13 Vertical Axis in Meter,75,5,25 Gas Saturation
Chapter 1.7.5 t = 8 years x = 13 m no gas phase 8 ANDRA-Benchmark Case 1B: Two Dimensional Gas Transport 1 Pressure in MPa 6 4 2 ab6819- t7976-x3- Gas ab6819- t7976-x3- Gas-Sat ab6819- t7976-x3- pcap 1 2 3 4 5 6 7 8 9 1 11 12 13 Vertical Axis in Meter,75,5,25 Gas Saturation
Chapter 1.7.6 Attention: The isovalue maps are not very accurate, as the mesh size is very irregular between.5 and 5 m. 13 12 11 Vertical Axis in Meter 1 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 Horizontal Axis in Meter Figure nn-nn: Gas saturation at t = in case 1B.8.5.2.1.1.1.1
Chapter 1.7.6 13 12 11 Vertical Axis in Meter 1 9 8 7 6 5 4 3 2 1 2 4 6 8 1 Horizontal Axis in Meter Figure nn-nn: Gas saturation at t = 5 years in case 1B.7.5.2.1.1.1.1
Chapter 1.7.6 13 12 11 Vertical Axis in Meter 1 9 8 7 6 5 4 3 2 1 2 4 6 8 1 Horizontal Axis in Meter Figure nn-nn: Gas saturation at t = 1 years in case 1B.7.5.2.1.1.1.1
Chapter 1.7.6 13 12 11 Vertical Axis in Meter 1 9 8 7 6 5 4 3 2 1 2 4 6 8 1 Horizontal Axis in Meter Figure nn-nn: Gas saturation at t = 1 years in case 1B.7.5.2.1.1.1.1
Chapter 1.7.6 13 12 11 Vertical Axis in Meter 1 9 8 7 6 5 4 3 2 1 2 4 6 8 1 Horizontal Axis in Meter.7.5.2.1.1.1.1 Figure nn-nn: Gas saturation at t = 2 years in case 1B
Chapter 1.7.6 13 12 11 Vertical Axis in Meter 1 9 8 7 6 5 4 3 2 1 2 4 6 8 1 Horizontal Axis in Meter.6.5.2.1.1.1.1 Figure nn-nn: Gas saturation at t = 4 years in case 1B
Chapter 1.7.6 13 12 11 1 Vertical Axis in Meter 9 8 7 6 5 4 3 2 1.1 2 4 6 8 1 Horizontal Axis in Meter Figure nn-nn: Gas pressure in MPa at t = in case 1B
Chapter1.7.6 13 12 11 1 Vertical Axis in Meter 9 8 7 6 5 4 3 2 1 2 4 6 8 1 Horizontal Axis in Meter Figure nn-nn: Gas pressure in MPa at t = 1 years in case 1B
Chapter 1.7.6 13 12 < 4.4 11 1 Vertical Axis in Meter 9 8 7 6 5 4 3 2 1 2 4 6 8 1 Horizontal Axis in Meter Figure nn-nn: Gas pressure in MPa at t = 1 years in case 1B
Chapter 1.7.7 Hydrogen (gas phase) flow through the interface between filler concrete and fractured zone,1 ANDRA-Benchmark Case 1B: Two Dimensional Gas-Transport Hydrogen: 1 mol =.2 kg ab6819-gas-fil-frz 1 Right Half: Gas Out-Flow in kg/year,1,1 ab6819-gas-fil-frz 1 1 Total Model: Gas Out-Flow in mol/year,1 1 1 1 1 1 1 1 Time in Years,1