The RealGasH2O and RealGasBrine Options Of The Tough+ Code For The Simulation Of Coupled Fluid And Heat Flow In Tight/Shale Gas Systems George J. Moridis Lawrence Berkeley National Laboratory RPSEA F3G Project College Station, TX, March 24, 2014
OUTLINE Background Code Description Fundamental equations Capabilities TOUGH+ Inputs Validation Examples Applications Examples
SIMULATION CODE TOUGH+ Core Code with Options Member of the TOUGH+ family of codes [Moridis et al., 2008] FORTRAN 95/2003 Object-Oriented Programming Structure Modular structure, ease of expansion, maximum traceability
SIMULATION CODE T+RGW Code (serial and parallel) TOUGH+RealGas (T+RG), TOUGH+RealGasH2O (T+RGW): Conventional and tight/shale gas simulations (dry and wet systems, respectively) H2O and up to 11 gas components, non-isothermal (up to 13 eqs) T+RGB Code (serial and parallel) TOUGH+RealGasH2O + salt 1 extra component (salt) and 1 extra phase (halite) Effect of salt on thermophysical properties & porosity, permeability
CODE DESCRIPTION Fundamental Equations Mass/heat balance Mass accumulation M A,G S X + S (1 ) R i, =w,g i (i 1,...,N G )
CODE DESCRIPTION Fundamental Equations Gas Sorption Langmuir isotherm Equilibrium and Kinetic i p dgm L for ELaS p dg p L d i p k dg m L L i for KLaS dt p dg p L Multi component Additionally: Linear and Freundlich
Fundamental equations Heat accumulation M (1 ) R T C R (T) dt S A,G T 0 N U (1 ) G R u i Y i i 1 Flow terms
Fundamental equations Gas Flow: Inertial, slippage, diffusion effects F G 1 b G v G X G J G, =w,o,g i (i 1) P G J G S G 1 7 3 S 3 D G G G X G S G G DIFFUSIVE FLOW D G G X G, =w,o,g i (i 1) b (1 K n ) 1 4K n 1 P G 1 K n 1 RT K n 2 G P G M r pore 2.81708 k Knudsen diffusion Klinkenberg parameter 128 15 tan 1 0.4 4 K 2 n
Fundamental equations Dusty gas model (multi component diffusion) Non Darcy Flow Options: Forchheimer equation Additional Non Darcy Option: Barree and Conway model (2007)
Fundamental equations Heat Flow Sources and Sinks ˆ q A,G X q, =w,g i (i 1,...,N G ); q ˆ H2O Properties: Steam tables (IFC, 1967; NIST, 2000) A,G q h Real gas mixture properties: Cubic equations of state (RK, SRK, PR), 11 component library (Moridis et al., 2008; WebGasEOS); to be enhanced with nano PVT data
Fundamental equations Porosity and permeability relationships Additional physics/thermodynamics Gas dissolution into liquid phases Effects of dissolved gases on oil viscosity and density Wide range of multi phase relative permeability and capillary pressure options
Fracture treatment: Discrete and MINC The Multiple Interactive Continua (MINC) Model Double model (Ns = 1) MINC: Ns shells in the matrix; Nf in fractures Dual k model (Ns = 1)
TOUGH+ Inputs and Features (v2.0) Namelist-based (maximum flexibility, built-in keyword recognition) Dynamic memory allocation Backward compatibility: ROCKS, ELEME, CONNE, INCON On-the-fly changes Built-in initialization (option-specific) Initialization flexibility, time-variable boundary conditions
TOUGH+ Inputs and features (v2.0) >>>IO_FILES: Begin of the data block &IO_File_Names IO_file_nomenclature = USER-NAMED,! Options: 'STANDARD-T',! 'INPUT-FILE-NAME-BASED' OR! 'USER-SPECIFIED' MESH_file_name = 'AAA-MESH', INCON_file_name = 'AAA-INCON SAVE_file_name = 'AAA-SAVE', SinkSource_file_name = 'AAA-SINK&SOURCE / <<<End of the <IO_FILES> data block For 'INPUT-FILE-NAME-BASED, with Test_AAA as input file name: Test_AAA.INCON Test_AAA.SAVE Test_AAA.MESH Test_AAA.SINK&SOURCE
TOUGH+ Inputs and features (v2.0) >>>MEMORY: Begin &Basic_EOS_Parameter_Definitions EOS_Name = 'HYDRATE-EQUILIBRIUM', number_of_components = 2, number_of_equations = 3 / &System_Size_Specifications coordinate_system = 'Cylindrical', num_characters_in_element_name = 5, Max_number_of_elements = 48000, Max_number_of_connections = 110000, Max_number_of_sources_and_sinks = 200, Max_number_of_geologic_media = 12 / &Simulation_Specifications porosity_perm_dependence_f =.FALSE.,! DEFAULT value:.false. scaled_capillary_pressure_f =.FALSE.,! DEFAULT value:.false. reversible_porosity_change_f =.TRUE., accounting_for_diffusion_f =.FALSE.,! Default value:.false. active_connections_only_f =.FALSE., boundaries_in_matrix_f =.FALSE., equilibration_run_f =.FALSE. / &Coupled_Processes coupled_geochemistry_f =.FALSE.,! DEFAULT value:.false.! geochem_property_update = 'C',! Options: 'C,'I,'T,'N (=DEFAULT) coupled_geomechanics_f =.FALSE.,! DEFAULT value:.false.! geomechanical_code_name = ' ',! DEFAULT value:.false.! geomech_property_update = 'C',! Options: 'C,'I,'T,'N (=DEFAULT)! number_of_geomech_param = 0 / <<<END of the MEMORY data block
TOUGH+ Inputs and features (v2.0) >>>TIME_DISCRETIZATION DATA &Time_Discretization_Data Max_number_of_timesteps = 30, time_at_simulation_beginning = 0.0d0, time_at_simulation_end = 6.5535e5,! (sec) initial_timestep = 1.0e-1,! (sec) maximum_timestep = 4.23E+4,! (sec) Dt_reduction_factor = 2.0d0, Dt_increase_factor = 2.0d0, units_of_time = 'sec',! = <min>,<hrs>,<days> num_of_user_defined_timesteps = 0 / <<<END of TIME_DISCRETIZATION DATA block >>>NR_ITERATION DATA &NR_Iteration_Data Max_number_of_NR_iterations = 10, criterion_for_dt_increase = 5, relative_convergence_criterion = 2.5d-5, absolute_convergence_criterion = 1.0d0, NR_solution_weighing_factor = 1.0d0 / <<<END of NR_ITERATION DATA block
TOUGH+ Inputs and features (v2.0) >>>EQUILIBRATION &Equilibration_Reference_Data elevation_at_high_reference_t = -1.050015E+02, elevation_at_low_reference_t = -5.0e-4, high_reference_t = 7.4500000000000d+00, low_reference_t = 3.9000000000000d+00, geothermal_gradient = 0.0d0, geothermal_gradient_units = "C/m", pressure_units = 'Pa', temperature_units = 'C' length_units = 'm / &Upper_Boundary_Conditions upper_boundary_medium_name = "TopBB", upper_boundary_elevation = -1.0d-3, upper_boundary_state = "Aqu", upper_boundary_pv = 7.0312000000000E+06, 4.8503580464383E-05, 3.9000000000000E+00, upper_boundary_pv_names = 'P, X_m_A, T', UB_P_variable_num = 1, UB_T_variable_num = 4 / &Lower_Boundary_Conditions Lower_boundary_medium_name = "BotBB", Lower_boundary_state = "Aqu", Lower_boundary_PV = 6.7986989401800E+06, 4.8503580464383E-05, 7.4500000000000E+00, Lower_boundary_PV_names = 'P, X_m_A, T', LB_P_variable_num = 1, LB_T_variable_num = 4 / <<<END of EQUILIBRATION
VALIDATION EXAMPLES Problem V1: Real gas flow in a cylindrical reservoir SPECIFICS Analytical solution of Fraim & Wattenbarger (1986) using pseudo pressure concept
VALIDATION EXAMPLES Problem V1: Real gas flow in a cylindrical reservoir Analytical solution of Fraim & Wattenbarger (1986)
VALIDATION EXAMPLES Problem V2: Water flow in a cylindrical reservoir SPECIFICS Analytical solution of Blasingame (1993) pseudo steady state
VALIDATION EXAMPLES Problem V2: Water flow in a cylindrical reservoir
VALIDATION EXAMPLES Problem V3: Gas flow in a tight gas reservoir with vertical well intersecting a vertical fracture plane SPECIFICS Analytical solutions of Cinco Ley et al. (1978) and Cossio (2012)
VALIDATION EXAMPLES Problem V3: Gas flow in a tight gas reservoir with vertical well intersecting a vertical fracture plane Point cloud of pressure distribution
VALIDATION EXAMPLES Problem V3: Gas flow in a tight gas reservoir with vertical well intersecting a vertical fracture plane Contour plot of pressure distribution
VALIDATION EXAMPLES Problem V3: Gas flow in a tight gas reservoir with vertical well intersecting a vertical fracture plane F CD = 10 F CD = 10 4 Analytical solutions of Cinco Ley et al. (1978)
VALIDATION EXAMPLES Problem V4: The Warren and Root (1963) Problem
VALIDATION EXAMPLES Problem V5: Klinkenberg Flow Analytical solutions of Wu et al. (1988)
APPLICATION EXAMPLES Problem A1: Gas production from a shale gas reservoir using a horizontal well System Subdomains S 1: The original (undisturbed) rock system Matrix Possibly naturally fractured: Native fractures (NF)
APPLICATION EXAMPLES: Problem A1 Well system, full schematic Symmetry argument Computational element: Symmetry and repeatability (Freeman et al., 2009) Repeatability
APPLICATION EXAMPLES: Problem A1 Important parameters d sr : thickness of stress release fractured zone around wellbore d f : primary fracture spacing b: primary fracture aperture y f : y reach of the primary fractures L y : reservoir width h: reservoir thickness Similarly for vertical wells Type I: Reference
APPLICATION EXAMPLES: Problem A1 Numerical simulation results: 800,000 elements (Freeman, 2010; Moridis et al., 2010)
APPLICATION EXAMPLES: Problem A1 Numerical simulation results: 800,000 elements (Freeman, 2010; Moridis et al., 2010)
APPLICATION EXAMPLES: Problem A1 Sensitivity analyses (Freeman et al., 2011)
APPLICATION EXAMPLES Problem A2: Gas production from a shale gas reservoir with a complex fracture system using a horizontal well System Subdomains S 1: The original (undisturbed) rock system Matrix Possibly naturally fractured: Native fractures (NF) S 2: Fractures induced during stimulation: Primary fractures (PF) Dominant pathways of flow to well May intercept the NF system S 3: Stress release fractures related to PF: Secondary fractures (SF) Usually perpendicular to PF Penetrate S 1, connected to PF, may intercept NF S 4: Stress release fractures related to well drilling: Radial/tertiary fractures (RF/TF) Usually cylindrical shape centered around the well axis Connected to S 1 and PF, may intercept NF and SF
APPLICATION EXAMPLES: Problem A1 Type II: Stress release planar fractures (secondary) Similarly for vertical wells Important parameters d sf : x reach of the secondary fractures y sf : y reach of the secondary fractures
APPLICATION EXAMPLES: Problem A2 Type III: Native & primary fractures Similarly for vertical wells Native fractures Difficult to describe individually
APPLICATION EXAMPLES: Problem A2 Type IV: All types of fractures Similarly for vertical wells
APPLICATION EXAMPLES: Problem A2 Numerical simulation results: up to 1,200,000 elements (Freeman, 2010; Moridis et al., 2010)
APPLICATION EXAMPLES Problem A3: Flowing gas composition changes in shale gas wells System Specifics: Type I Type I Gas Composition CH4 : 80% C 2 H 6 : 7% C 3 H 8 : 5% C 4 H 10 : 5% C 5 H 12 : 2% C 6 H 16 : 1%
APPLICATION EXAMPLES: Problem A3 Numerical simulation results: 800,000 elements (Freeman et al., 2012)
APPLICATION EXAMPLES Problem A4: Evaluation of potential environmental impact of hydraulic fracturing on shallow groundwater Core parametric envelope: Shale permeability: k = 10-18, 10-19, 10-21 m 2 (1 μd, 0.1 μd, 1.0 nd) Aquifer permeability: k = 3 10-13, 3 10-12 m 2 (0.3 D, 3.0 D) Connecting fracture/fault permeability: k = 3 10-9, 3 10-11, 3 10-12 m 2 ( 3000 D, 30 D, 3.0 D) Penetrating offset well casing permeability: k = 3 10-9, 3 10-12, 3 10-15, 3 10-18 m 2 ( 3000 D, 3.0 D, 3.0 md, 3.0 μd) Overburden separation (shale to aquifer): z = 200 m, 800 m, 2000 m Production strategies: 1. Water well (Q w = 0.1 kg/s) and shale gas well (P c = ½ P res ) producing 2. Shale gas well producing 3. Water well producing 4. No production from either formation
Mesh Generation Process
Simulation Results: High k Breakthrough k f = 3000 D k f = 3.0 D k shale = 0.1 μd, k aquif = 0.3 D, z = 200m
Simulation Results: Penetrating Offset Well k shale = 0.1 μd, k wellc = 3.0 D, k aquif = 3.0 D k shale = 0.1 μd, k aquif = 3.0 D