WIPP_FLOW Mode Solution Controls¶

Within the OPTIONS block of the WIPP_FLOW Mode, several solution control parameters can be set. This page describes them all. An example of an input deck SIMULATION block that uses and sets some solution control parameters is shown below:

SIMULATION
SIMULATION_TYPE SUBSURFACE
PROCESS_MODELS
SUBSURFACE_FLOW FLOW
MODE WIPP_FLOW
OPTIONS
FIX_UPWIND_DIRECTION
GAS_COMPONENT_FORMULA_WEIGHT 2.01588D0 ! H2 kg/kmol
LIQUID_EQUATION_TOLERANCE    1.d-6
GAS_EQUATION_TOLERANCE       1.d-6
LIQUID_PRESSURE_TOLERANCE    1.d-5
GAS_SATURATION_TOLERANCE     1.d-4  ! (same functionality as EPS_SAT)
PRESSURE_REL_PERTURBATION    1.d-8
PRESSURE_MIN_PERTURBATION    1.d-2
SATURATION_REL_PERTURBATION  1.d-8
SATURATION_MIN_PERTURBATION  1.d-10
DTIMEMAX   1.25
SATLIMIT   1.d-3
DSATLIM    0.20
DSAT_MAX   1.0d-2
SATNORM    3.d-1
TSWITCH    1.d-2
EPS_PRES   1.d-2
EPS_SAT    4      ! (same functionality as GAS_SATURATION_TOLERANCE)
DPRELIM   -1.d8   ! Pa
DPRES_MAX  1.d7   ! Pa
PRESNORM   5.d5   ! Pa
LSCALE
DO_NOT_LSCALE
P_SCALE    1.d7
END
END
END
END


GAS_SATURATION_TOLERANCE (EPS_SAT)¶

The maximum relative change in gas saturation allowed in order for the solution to be accepted. For example, if GAS_SATURATION_TOLERANCE is $$1\times10^{-4}$$, then a change in gas saturation over a Newton iteration that is larger than $$1\times10^{-4}$$ will force another Newton iteration. The default value for GAS_SATURATION_TOLERANCE is $$1\times10^{-3}$$. Currently, the WIPP_FLOW card EPS_SAT implements the same functionality. If both are specified, the tighter tolerance of the two will be chosen and assigned.

SATLIMIT¶

Limit on gas saturation solution beyond which a solution will not be accepted. This limit is designed to ensure unphysical values for gas saturation are not accepted as solutions. If the gas saturation, $$S_g$$, at the end of a Newton iteration is $$1.0 + SATLIMIT < S_g$$ or $$S_g < -SATLIMIT$$, then another Newton iteration will be forced (i.e. the solution is not accepted). The default value for SATLIMIT is $$1\times10^{-3}$$. The value given must be smaller than DSATLIM.

DSATLIM¶

Limit allowed on gas saturation outside of the physically realistic range between 0.0 and 1.0, and intended to simply reject a solution that is beyond hope before any more computational effort is expended. If the gas saturation, $$S_g$$, at the end of a Newton iteration is $$1.0 + DSATLIM < S_g$$ or $$S_g < -DSATLIM$$, then the time step will be cut according to DELTFACTOR and the time step will be repeated. The default value for DSATLIM is $$0.20$$. The value given must be larger than SATLIMIT.

DPRELIM¶

Lower limit allowed for the liquid pressure (brine), and is intended to simply reject a solution that is beyond hope before any more computational effort is expended. If the liquid pressure, $$p_l$$, at the end of a Newton iteration is negative and $$p_l < DPRELIM$$, then the time step will be cut according to DELTFACTOR and the time step will be repeated. The default value for DPRELIM is $$-1\times10^{8}$$ Pa. The value given must be negative.

DSAT_MAX¶

The maximum absolute change in gas saturation allowed over a time step. If the solution has converged, but the absolute change in gas saturation was larger than DSAT_MAX, then the time step will be cut according to DELTFACTOR and the time step is repeated. The default value of DSAT_MAX is $$1.0$$.

DPRES_MAX¶

The maximum absolute change in liquid pressure (brine) allowed over a time step. If the solution has converged, but the absolute change in liquid pressure was larger than DPRES_MAX, then the time step will be cut according to DELTFACTOR and the time step is repeated. The default value of DPRES_MAX is $$1\times10^{7}$$ Pa.

EPS_SAT (GAS_SATURATION_TOLERANCE)¶

The digits of accuracy for the maximum relative change in gas saturation allowed in order for the solution to be accepted. For example, if EPS_SAT is 4, then a change in gas saturation over a Newton iteration that is larger than $$1\times10^{-4}$$ will force another Newton iteration. The default value for EPS_SAT is $$3$$. Currently, the WIPP_FLOW card GAS_SATURATION_TOLERANCE implements the same functionality. If both are specified, the tighter tolerance of the two will be chosen and assigned.

EPS_PRES¶

The maximum relative change in liquid pressure (brine) allowed over a time step. If the solution has converged, but the relative change in liquid pressure was larger than EPS_PRES, then an other Newton iteration will be forced. The default value of EPS_PRES is $$1\times10^{-3}$$.

SATNORM¶

The largest relative change in gas saturation that is allowed over a time step so that the next time step will be the same as the current time step. If the largest relative change in gas saturation happens to be larger than SATNORM, then the next time step will be reduced according to Section Algorithm That Determines Next Time Step Size. Similarly, if the largest relative change in gas saturation happens to be smaller than SATNORM, then the next time step will be increased, but this increase will be limited by the ramping factor given by DTIMEMAX. The default value for SATNORM is $$0.3$$.

PRESNORM¶

The largest relative change in liquid pressure that is allowed over a time step so that the next time step will be the same as the current time step. If the largest relative change in liquid pressure happens to be larger than PRESNORM, then the next time step will be reduced according to Section Algorithm That Determines Next Time Step Size. Similarly, if the largest relative change in liquid pressure happens to be smaller than PRESNORM, then the next time step will be increased, but this increase will be limited by the ramping factor given by DTIMEMAX. The default value for PRESNORM is $$5\times10^{5}$$ Pa.

TSWITCH¶

The value for gas saturation where SATNORM will switch between using the maximum relative change in gas saturation over a time step or the maximum absolute change in gas saturation over a time step to decide on the next time step size. If $$S_g > TSWITCH$$, then the maximum relative change in gas saturation will be used. If $$S_g < TSWITCH$$, then the maximum absolute change in the gas saturation will be used, so that division by a small number is avoided. Default value for TSWITCH is $$0.01$$.

DELTFACTOR (TIMESTEP_REDUCTION_FACTOR)¶

The time step reduction factor when non-convergence occurs and the time step is reduced and repeated. The equivalent functionality in PFLOTRAN is specified with the TIMESTEP_REDUCTION_FACTOR keyword in the TIMESTEPPER block. The default value for TIMESTEP_REDUCTION_FACTOR is $$0.5$$. An example of usage is below:

TIMESTEPPER FLOW
TIMESTEP_REDUCTION_FACTOR 0.5d0
MAX_TS_CUTS 8
END


DTIMEMAX¶

Maximum time step ramping factor for determining the value of the next time step. The default value for DTIMEMAX is $$1.25$$.

LSCALE¶

Toggles on scaling of Jacobian matrix and residual vector. The default value for LSCALE is TRUE.

DO_NOT_LSCALE¶

Toggles off scaling of Jacobian matrix and residual vector. The default value for LSCALE is FALSE.

P_SCALE¶

The scaling factor by which the Jacobian matrix and residual vector are scaled. For each row of the matrix, the scaling factor is multiplied by the row’s maximum absolute value. The row entries and corresponding entry in the residual vector are then divided by that value. The default value for P_SCALE is $$10^{7}$$.

MAXIT (ITMAX)¶

Maximum number of Newton iterations per time step. The default value for MAXIT is $$50$$ based on PETSc defaults. BRAGFLO recommends $$10$$.

NEWTON_SOLVER FLOW
MAXIT 10
END


MAX_TS_CUTS (IRESETMAX)¶

Maximum number of time step cuts before PFLOTRAN shuts down due to lack of convergence. The default value for MAX_TS_CUTS is $$16$$. BRAGFLO recomments $$40$$.

TIMESTEPPER FLOW
MAX_TS_CUTS 40
END


PRESSURE_REL_PERTURBATION (DHPRES_REL)¶

Relative change in liquid pressure for Jacobian derivative calculation. The default value for PRESSURE_REL_PERTURBATION is $$10^{-8}$$.

PRESSURE_MIN_PERTURBATION (DHPRES_MIN)¶

Minimum change in liquid pressure for Jacobian derivative calculation. The default value for PRESSURE_MIN_PERTURBATION is $$10^{-2}$$.

SATURATION_REL_PERTURBATION (DHSAT_REL)¶

Relative change in gas saturation Jacobian derivative calculation. The default value for SATURATION_REL_PERTURBATION is $$10^{-8}$$.

SATURATION_MIN_PERTURBATION (DHSAT_MIN)¶

Minimum change in gas saturation Jacobian derivative calculation. The default value for SATURATION_MIN_PERTURBATION is $$10^{-10}$$.

Algorithm That Determines Next Time Step Size¶

The time step ramping factor, DTIME, is automatically calculated in PFLOTRAN according to DTIME = (2.D0*DELTADEPNORM)/(DELTADEPNORM+DELTAMAX). The variable DELTADEPNORM is either SATNORM or PRESNORM. The variable DELTAMAX is the maximum absolute change in the primary dependent variables (gas saturation or liquid pressure), or it is the maximum relative change in the gas saturation is the current gas saturation value is larger than TSWITCH. The value for DTIME is chosen to be the minimum of the value calculated using the gas saturation change and the value using the liquid pressure change. The minimum of the calculated value of DTIME and solution control parameter DTIMEMAX is then chosen to multiply the current time step value to obtain the next time step value. A final check is made to ensure that the calculated value for the next time step is within the minimum and maximum time step sizes indicated in the input deck.