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MPHASE¶
The MPHASE keyword defines options for the MPHASE supercritical CO\(_2\)subsurface flow mode. For more details and governing equations see the Theory Guide.
SIMULATION Options¶
(under SUBSURFACE_FLOW in SIMULATION PROCESS_MODELS block)
TIMESTEPPER Options¶
Basic Settings
- CFL_GOVERNOR
Specifies a maximum CFL (Courant–Friedrichs–Lewy) number that governs time step size. Subsequent time steps are calculated as a function of the maximum flow velocity and grid discretization such that the CFL is not exceeded.
- CONCENTRATION_CHANGE_GOVERNOR
Specifies a maximum absolute change in concentration [mole fraction] that governs time step size. Subsequent time steps are calculated such that the governing concentration change is not exceeded.
- PRESSURE_CHANGE_GOVERNOR
Specifies a maximum absolute change in pressure [Pa] that governs time step size. Subsequent time steps are calculated such that the governing pressure change is not exceeded.
- SATURATION_CHANGE_GOVERNOR
Specifies a maximum absolute change in saturation [-] that governs time step size. Subsequent time steps are calculated such that the governing saturation change is not exceeded.
- TEMPERATURE_CHANGE_GOVERNOR
Specifies a maximum absolute change in temperature [C] that governs time step size. Subsequent time steps are calculated such that the governing temperature change is not exceeded.
NEWTON_SOLVER Options¶
Basic Settings
- ANALYTICAL_JACOBIAN
Calculate derivatives in Jacobian analytically.
- ATOL <float>
Declare convergence when the 2-norm of residual is less than ATOL \(\left(\|f(x_n)\|<\text{ATOL}\right)\). (default: \(10^{-50}\)).
- CONVERGENCE_INFO
Opens a block for toggling ON/OFF convergence information in screen output (default: YES to all). See example below.
2R, FNORM, 2NORMR - 2-norm of residual
2X, XNORM, 2NORMX - 2-norm of solution
2U, UNORM, 2NORMU - 2-norm of update
IR, INORMR - inifinity norm of residual
IU, INORMU - inifinity norm of update
- DTOL <float>
Declare divergence (cut the time step) when the 2-norm of the residual is greater than DTOL times the 2-norm of the initial residual \(\left(\frac{\|f(x_n)\|}{\|f(x_0)\|}>\text{DTOL}\right)\). (default: \(10^{4}\)).
- ITOL <float>
Declare convergence when the infinity norm of residual is less than ITOL \(\left(\|f(x_n)\|_{inf}<\text{ITOL}\right)\). (default: not used).
- MAXIMUM_NUMBER_OF_ITERATIONS <int>
Maximum number of Newton iterations before reporting failed convergence.
- NO_PRINT_CONVERGENCE
Toggle off printing of convergence information.
- NTRDC_OPTIONS or NTR_OPTIONS
Opens a block for trust-region options and parameters (SNES_TYPE NTRDC or SNES_TYPE NTR required)
TR_TOL - trust-region tolerance (default: \(1.0^{-12}\))
ETA1 - trust-region parameter \(0.0 \le \eta_1 \le \eta_2\), \(\rho \ge \eta_1\) breaks out of the inner iteration (default: \(\eta_1=0.001\))
ETA2 - trust-region parameter \(0.0 \le \eta_1 \le \eta_2\), \(\rho \ge \eta_2\) shrinks the trust-region (default: \(\eta_2=0.25\))
ETA3 - trust-region parameter \(\eta_3 > \eta_2\), \(\rho \ge \eta_3\) expands the trust-region (default: \(\eta_3=0.75\))
T1 - trust-region parameter, shrinking factor of trust-region (default: 0.25)
T2 - trust-region parameter, initial size of trust-region, \(\Delta_0*\|x\|_2\) (default: 0.1)
DELTA_M - trust-region parameter, max size of trust-region, \(\Delta_M*\|x\|_2\) (default: 0.5)
DELTA_0 - trust-region parameter, initial size of trust-region, \(\Delta_0*\|x\|_2\) (default: 0.1)
AUTO_SCALE - TRUE enables solution update scaling meaning all types of unknowns are equally treated when evaluating solution update (recommended for WIPP-FLOW, TH); FALSE disables solution update scaling meaning that solution update evaluation will focus more on pressure than other unknowns (recommended for GENERAL, HYDRATE).
AUTO_SCALE_MAX - used with AUTO_SCALE, caps the maximum auto-scaling factor
- NUMERICAL_JACOBIAN
Calculate derivatives in Jacobian numerically.
- PRINT_LINEAR_ITERATIONS
Prints the number of linear iterations for each Newton iteration to the screen.
- RTOL <float>
Declare convergence when the 2-norm of the residual is less than RTOL times the 2-norm of the initial residual \(\left(\frac{\|f(x_n)\|}{\|f(x_0)\|}<\text{RTOL}\right)\). (default: \(10^{-8}\)).
- SNES_TYPE <string>
The default is LINE_SEARCH (Basic, see PETSc documenetation) from PETSc which is Newton-Raphson nonlinear solver. NTRDC is the Newton Trust-Region Dogleg-Cauchy nonlinear solver, and NTR is the Newton Trust-Region nonlinear solver. The difference between NTRDC and NTR is that NTRDC adds steepest-descent solution update to the Newton solution iff it optimizes better than Newton solution alone within the trust-region. NTR only applies Newton solution update and it is truncated by the trust-region. NTRDC MAY perform better with LESS phase state change simulations for GENERAL MODE.
- STOL <float>
Declare convergence when the 2-norm of the update divided by the 2-norm of the solution is less than STOL \(\left(\frac{\|x_n-x_{n-1}\|}{\|x_{n-1}\|}<\text{STOL}\right)\). (default: \(10^{-8}\)).
- VERBOSE_LOGGING
Prints additional convergence information to screen.
Expert Settings
- MATRIX_TYPE <string>
Format of main solver matrix. PETSc Mat (i.e. AIJ, BAIJ, or HYPRESTRUCT).
- MAXF <int>
Maximum number of function evaluations before reporting failed convergence.
- MAX_NORM <float>
Declare divergence (cut the time step) when the infinity norm of the residual is greater than MAX_NORM \(\left( \| f(x_n) \|_{inf} > \text{MAX_NORM} \right)\). (default: \(10^{20}\)).
- MINIMUM_NUMBER_OF_ITERATIONS <int>
Newton solver convergence requires at least MINIMUM_NUMBER_OF_ITERATIONS.
- NO_FORCE_ITERATION
Toggle off the forcing of at least 1 linear iteration. The default is to force at least 1 linear iteration. In a quasi-stationary state, the initial residual may be sufficiently small for convergence, but often it is better to force at least one iteration.
- NO_INFINITY_NORM
Toggle off calculation of infinity norm on residual and update vectors. The default is to calculate the infinity norm.
- PRECONDITIONER_MATRIX_TYPE <string >
Format of preconditioning matrix. PETSc Mat (i.e. AIJ, BAIJ, or HYPRESTRUCT). Default is same as solver.
- PRINT_DETAILED_CONVERGENCE
Toggle on printing of detailed convergence information.
Examples¶
SIMULATION
SIMULATION_TYPE SUBSURFACE
PROCESS_MODELS
SUBSURFACE_FLOW flow
MODE MPHASE
/
/
END
...
SUBSURFACE
NUMERICAL_METHODS FLOW
TIMESTEPPER
TS_ACCELERATION 8
PRESSURE_CHANGE_GOVERNOR 5.e4
TEMPERATURE_CHANGE_GOVERNOR 5.d0
CONCENTRATION_CHANGE_GOVERNOR 1.e-2
SATURATION_CHANGE_GOVERNOR 0.025
/
NEWTON_SOLVER
ATOL 1.d-12
RTOL 1.d-12
STOL 1.d-30
DTOL 1.d15
ITOL 1.d-8
MAXIMUM_NUMBER_OF_ITERATIONS 25
MAXF 100
/
/
...
