STOMP

Solution Control Card Options (CO2E)

For STOMP-CO2E, three classes of options are specified via the Solution Control Card:

  1. Execution Mode Options - used to specify the state of the simulation.
  2. Operational Mode Options - used to specify the solved equations and active processes.
  3. Interfacial Averaging Options - used to specify the model for computing state variables at the centroids of grid-cell surfaces.

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, 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. 

Execution Mode Options

Normal Mode

In the Normal mode, STOMP-CO2e executes from a declared start time, using an initial state declared through the Initial Conditions Card, until the declared stop time, the declared number of time steps, an execution error, or a sequence of convergence failures. The following keywords may also be used after specifying the "Normal" Execution Mode.

No Flow

This option results in the coupled flow and transport equations only being computed once, eliminating the flow calculations each time step for a reactive transport problem with a steady flow field. 

Info

No Flow Option

The No Flow option, when used in conjunction with the Normal or Restart execution modes, results in the coupled flow and transport equations only being computed once. This option can be used to eliminate the flow calculations each time step for a solute transport problem with a steady flow field. 

Restart Mode

In the Restart mode, STOMP-CO2e 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, the declared number of time steps, an execution error, or a sequence of convergence failures. The following keywords may be after specifying the "Restart" Execution Mode.

File

This option triggers STOMP-CO2e to read an additional character string, which is the name of the restart file.  

No Flow

This option results in the coupled flow and transport equations only being computed once, eliminating the flow calculations each time step for a reactive transport problem with a steady flow field. 

Info

No Flow Option

The No Flow option, when used in conjunction with the Normal or Restart execution modes, results in the coupled flow and transport equations only being computed once. This option can be used to eliminate the flow calculations each time step for a solute transport problem with a steady flow field. 

Info

Overwrite 

When the keyword "overwrite" is included in the initial or boundary conditions cards with any of the above options during a restart simulation, the specified values will overwrite those from the restart file.

Operational Mode Options

The Operational Mode is CO2E.  This identifier 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 and reactive species transport is specified via keyword modifiers to the operational mode.  Models for transporting reactive species are additionally controlled via keyword modifiers to the operational mode.

Operational Mode Options

STOMP-CO2E | Energy-Water-CO2-Salt | E-H2O-CO2-NaCl

Info

Accepted Keywords

One of the above keywords are required, and all are recognized for specifying the operational mode as STOMP-CO2E

Simplifications and additional options to the system can be specified via keyword modifiers in the Operational Mode.
Operational Mode Modifers...

Isothermal

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.

Operational Mode Modifiers for Reactive Transport

Reactive transport is specified by including the keyword ECKEChem in the Operational Mode field.  The reactive transport algorithms are controlled through the keyword options TVD and Roe Superbee. 

Warning
ECKEChemUsing this keyword requires the ECKEChem Module to be implemented in the simulator.

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 Solute Transport

If either TVD or Leonard keywords appear with the Eckechem keyword, then the Leonard-TVD transport scheme is implemented. This third-order scheme using a 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, avoiding 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

Courant-Number Limited Transport

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

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 in the unsaturated zone, or to some other user-specified value.

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 model 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 only called 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 are unchanged by precipitation and dissolution reactions. Mineral surface areas are always at the initial value.

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.

Interfacial Averaging Schemes

Harmonic
Geometric
Arithmetic
Upwind
Downstream
Moderated Upwind
Neiber Downstream

Interfacial Averaging Variables and Defaults

Field VariableDefault Interfacial Averaging Scheme
Aqueous Diffusion Harmonic
Gas Diffusion Harmonic
Aqueous Density Upwind
Gas Density Upwind
Aqueous Viscosity Harmonic
Gas Viscosity Harmonic
Aqueous Relative Permeability Upwind
Gas Relative Permeability Upwind
Aqueous Enthalpy Upwind
Gas Enthalpy Upwind
Effective Thermal Conductivity Harmonic
Intrinsic Permeability Harmonic
Porosity Harmonic

References: 

Datta-Gupta, A. L.W. Lake, G.A. Pope, K. Sepehnoori. 1991. High-resolution monotonic schemes for reservoir fluid flow simulation. In Situ, 15 (3) (1991), pp. 289–317.

Patankar, S. V. 1980. Numerical heat transfer and fluid flow. Hemisphere Publishing Corporation, Washington, D. C. 

 

 

   

 

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