Execution Mode Options

Two Execution Modes are recognized: Normal, and Restart. In the Normal mode, initial state conditions are declared through the Initial Conditions Card. In the Restart mode, initial state conditions are assigned via a restart file from a previous execution or declared through the Initial Conditions Card, with the option of using the special overwrite option for selected parameters. Unless specified through the Output Control Card, restart files (i.e., restart.n) are generated at each plot.n write event, and have name extensions that correspond to the generating time step (e.g., the file restart.0028 would have been generated at the conclusion of time step 28). Restart files are text files that contain simulation time and control information, and a collection of field variables needed to redefine the simulation state for the operational mode.

Restart Mode

In the Restart mode, STOMP executes from either a declared start time or the start time specified in the restart file, using an initial state defined by a previous execution, until the declared stop time or the declared number of time steps is reached, or an execution error or a sequence of convergence failures occur.

The additional keyword "file" triggers STOMP to read an additional character string, which is the name of the restart file.

Info

When the keyword "overwrite" is included in the Initial Conditions Card or the Boundary Conditions Card with any of the above options during a restart simulation, the specified values will overwrite those from the restart file.

Operational Model Options

The Operational Mode is STOMP-CO2 (or STOMP-CO2E for the non-isothermal version). This required keyword is used to make certain that the operational mode of the STOMP executable matches the operational mode declared in the input file. The solved coupled equations, activation of solute transport, and reactive species transport is specified via keyword modifiers to the operational mode. Models for transporting passive solutes and reactive species are controlled via additional keyword modifiers to the operational mode. For example, solute transport is solved using the Patankar method, unless the keywords TVD or Roe Superbee also appear.

Additional options can be specified via keyword modifiers specified after the operational mode keyword:

Isothermal (only for STOMP-CO2E)

This modifier deactivates the energy conservation equation from the set of solved coupled equations. Temperature will not change with time during the simulation. Using this modifier is the equivalent of running STOMP-CO2E as STOMP-CO2.

Isobrine

This modifier deactivates the salt-mass conservation equation from the set of solved coupled equations. Salt concentrations will be set to zero during the simulation.

Invariant Fluid Density and Viscosity

This modifier holds density and viscosity constant in the aqueous and gas phases.

Fractional CO2 Solubility

This modifier reduces CO₂ solubility in the aqueous phase.

ECKEChem

This modifier activates reactive species transport. The reactive transport algorithms use the same transport schemes as the solute transport model, and therefore are controlled through the keyword options TVD and Roe Superbee.

Additional sub modifiers for reactive species transport are:

Patankar

This is the default method and can be optionally specified.

First-Order Upwind

The simplest upwind scheme possible is the first-order upwind scheme, which uses a finite difference stencil to simulate the direction of flow.

Leonard-TVD Scheme

This third-order scheme using a total variation diminishing (TVD) technique (Datta Gupta et al. 1991) is most appropriate for advection-dominated flow (high Peclet numbers). Conventional techniques, like the one discussed by Patankar (1980), suffer from artificial diffusion that smears otherwise sharp fronts. The smearing is a result of the first-order approximation of the advective term in the transport equation. Datta Gupta et al. (1991) proposed and successfully tested a third-order differencing scheme with an appropriate flux limiting function which significantly minimizes numerical diffusion, while, at the same time, avoids oscillations that commonly affect classical higher-order schemes.

Roe Superbee

All first order schemes suffer from artificial diffusion and all second order schemes suffer from dispersion, which creates oscillations around any discontinuities. Flux-limiter methods switch between a second order approximation when the region is smooth and a first order approximation when near a discontinuity. The Superbee limiter applies the minimum limiting and maximum steepening possible to remain TVD.

Courant

This keyword specifies courant-number limited transport. The user specifies a dimensionless number that is used to characterize the relative extent of numerical oscillations in the numerical solution. The Courant Number is associated with the time discretization, and is calculated by multiplying cell velocity by the time step, and dividing that quantity by the distance. Given a certain spatial discretization, the time step must be selected such that the Courant number remains less than or equal to 1, or to some other user-specified value.

Vadose Courant

This keyword specifies vadose zone courant-number limited transport. This option limits the application of the Courant number to the unsaturated cells in the domain. For a given a certain spatial discretization, the time step calculation will be determined such that the Courant number remains less than or equal to 1 or some other user-specified value, in the unsaturated zone.

Equilibrium Reduced

With this option, the equilibrium aqueous speciation reactions are decoupled from the kinetic reactions. This can improve convergence and decrease run times.

Minimum Concentration

This option is a numerical control that allows for the specification of the minimum aqueous concentration for all species in the simulation.

Log

Since concentrations of species are positive and because mass action laws in chemistry involve products and powers, logarithms of concentrations can be used to solve the geochemical reaction equations.

Guess

This option can be used to establish the initial concentrations within the simulation domain. This routine is called once during the initialization routine.

Porosity Alteration with Precipitation

As minerals precipitate and dissolve, the new mineral volumes are used to calculate changes in porosity for the porous medium.

Effective Reaction Area

This option will scale the mineral reaction area based on the water saturation of the cell.

Constant Surface Area

Mineral surface areas remain unchanged by precipitation and dissolution reactions. Mineral surface areas are always maintained at the initial value.

Warning

Using the keyword "ECKEChem" requires the ECKEChem Module to be implemented in the simulator. When using Operational Mode Modifiers for Reactive Transport, include the keyword "transport" only when solutes are also being simulated. For example, for geochemical reactive species only, "Eckechem w/ TVD" might be specified. If non-geochemical species are simulated, then "Eckechem w/ Transport w/ TVD would be specified.

References

Datta-Gupta, A, LW Lake, GA Pope, and K Sepehnoori. 1991. High-Resolution Monotonic Schemes for Reservoir Fluid Flow Simulation. In Situ, 15(3):289-317.

Patankar, SV. 1980. Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, Washington, D. C.

Interfacial Averaging Options

State variables at the centroids of grid-cell surfaces are required to compute fluxes between grid-cell centroids. Models for computing the state variables on grid-cell surfaces are referred to as interfacial averaging schemes and use the state variables at adjacent grid-cells to compute the surface variables. Default interfacial averaging schemes or various variable types have been selected for STOMP. Schemes other than the defaults can be specified.

Interfacial Averaging Schemes

Field variables, which include physical, thermodynamic, and hydrologic properties, are defined in the finite-difference formulation at the node centers. Conversely, flux variables are defined at node interfaces. Computation of flux variables requires knowledge of field variables at node interfaces. Values of flux variables at node interfaces are evaluated by averaging the field values for the two nodes adjoining an interfacial surface. Interfacial averaging schemes may be declared individually for each field variable through the Interfacial Averaging Variables input.

The default interfacial averaging schemes for the simulator are shown in the Table below. For simulations of physical systems involving heat transfer, it should be noted that convergence problems might arise if the density properties are not averaged with upwind weighting. Likewise, infiltration problems typically demonstrate strong dependencies on the relative permeability of the infiltrating fluid.

List of Interfacial Averaging Schemes

• Harmonic
• Geometric
• Arithmetic
• Upwind
• Downstream
• Moderated Upwind
• Neiber Downstream

Default Interfacial Averaging Schemes