EQUILIBRATION

Defines a hydrostatic equilibration that computes the distribution for pressure and saturation versus depth, and it is used to initialise a study. See example below:

EQUILIBRATION initial_solution_1
  TYPE
    PRESSURE HYDROSTATIC
  /
  DATUM_D 1000.0 m
  PRESSURE 105.0 Bar
  RTEMP 50 C
  SALT_TABLE
    D_UNITS m
    CONCENTRATION_UNITS MOLAL
    SALTVD
     1000 0.95
     2500 3.0
    /
  END
/

The set of EQUILIBRATION instructions can optionally be associated with a name (‘initial_solution_1’ in the example above). The input sub-cards supported by the EQUILIBRATION are:

Additional considerations on how the study is initialised:

Examples:

DATUM_D

Depth of the reference datum. Require units. Defaults to 0.

PRESSURE

Reference pressure at datum. Must be entered or the code will return an error. Pressure units must be specified.

WGC_D

Defines the depth of the water-gas phase contact. Requires units. If not set defaults to 0. It is used only by the Multi-Gas-COMP-3 mode, and ignored by all other modelling options. Cannot be used in conjunction with OWC_D and OGC_D.

PCWG_OWC

Defines the capillary pressure between the water and the gas phases at the depth of the water-gas phase contact. It requires pressure units. If not set defaults to 0. It is used only by the Multi-Gas-COMP-3 mode, and ignored by all other modelling options.

OWC_D

Defines the depth of the oil-water phase contact. Requires units. If not set defaults to 0. It is ignored by the GAS_WATER and the Multi-Gas-COMP-3 modes, which do not model the oil phase. Cannot be used in conjunction with WGC_D.

PCOW_OWC

Defines the capillary pressure between the water and the oil phases at the depth of the oil-water phase contact. It requires pressure units. If not set defaults to 0. It is ignored by the GAS_WATER and the Multi-Gas-COMP-3 modes, which do not model the oil phase.

OGC_D

Defines the depth of the oil-gas phase contact. It requires units. If not set defaults to 0. It is ignored by the GAS_WATER, Multi-Gas-COMP-3 and TOIL_IMS modes. Cannot be used in conjunction with WGC_D.

PCOG_OGC

Capillary pressure between the oil and the gas phases at the depth of the oil-gas phase contact. Requires pressure units. If not set default to 0. It is ignored by the GAS_WATER, Multi-Gas-COMP-3 and TOIL_IMS modes.

BUBBLE_POINT_TABLE

The BUBBLE_POINT_TABLE defines the bubble point pressure (\(P_b\)) versus depth for all grid blocks associated with the hydrostatic equilibration. The table is used by the BLACK_OIL, Multi-gas (COMP 4) and SOLVENT_TL modes, and it is ignored by the other modelling options. See example below:

BUBBLE_POINT_TABLE
   D_UNITS m
   PRESSURE_UNITS Bar
   PBVD
     2430.0 333.0
     2470.0 335.0
  /
END

Units must be defined using D_UNITS and PRESSURE_UNITS. The data depth vs bubble point pressure are entered within the PBVD block.

The entries must be ordered for monotonically growing depths, and at least two entries are required for the internal interpolation to work. In the hydrostatic equilibration calculation, if for a given depth a bubble point pressure is found to be larger than the oil hydrostatic pressure, its value is reset to the hydrostatic oil pressure value to ensure \(P_b \leq P_o\).

To remove the PBVD table, the entire BUBBLE_POINT_TABLE block must be removed. If only the PBVD table is removed leaving the BUBBLE_POINT_TABLE block, the code returns an error as a PBVD is expected.

If the PBVD table is not defined, the datum and the oil-gas phase contact must have the same location ( DATUM_D = OGC_D), and the bubble point pressure below the OGC (i.e. undersaturated oil) is taken constant and equal to the pressure at datum. See example:

EQUILIBRATION initial_condition
  TYPE
   PRESSURE HYDROSTATIC
  /
  PRESSURE 327.0 Bar
  RTEMP 50 C
  DATUM_D 2430.0 m
  OGC_D     2430.0 m
  PCOG_OGC 0.5 Bar
  OWC_D 2470.0 m
  PCOW_OWC 0.5 Bar
/

RTEMP

Constant temperature value to assign to the reservoir. Note that currently only degrees Celsius are accepted, for any other temperature unit the software returns an error. RTEMP is an alternative to TEMPERATURE_TABLE, either one or the other can be supplied.

TEMPERATURE_TABLE

Define the temperature versus depth for all grid blocks associated with the hydrostatic equilibration. See example:

TEMPERATURE_TABLE
  D_UNITS m
  TEMPERATURE_UNITS C
  RTEMPVD
    2300.0 126.0
    2400.0 128.0
  /
END

Units must be defined using D_UNITS and TEMPERATURE_UNITS. The data depth vs temperature are entered within the RTEMPVD block. The entries must be ordered for monotonically growing depths, and at least two entries are required for the internal interpolation to work.

If the TEMPERATURE_TABLE is defined RTEMP cannot be supplied at the same time in the same equilibration, otherwise the code returns an error, as the temperature is ambiguously defined. To remove the RTEMPVD table, the entire TEMPERATURE_TABLE block must be removed. If only the RTEMPVD table is removed leaving the TEMPERATURE_TABLE block, the code returns an error as a RTEMPVD table is expected.

SALT_TABLE

Defines the brine salinity versus depth for all grid blocks associated with the hydrostatic equilibration. It is used by the Multi-Gas (COMP 3 and COMP 4), Multi-Component (COMP EOS) and GAS_WATER modes, while it is ignored by the other flow models. See example below:

SALT_TABLE
    D_UNITS m
    CONCENTRATION_UNITS MOLAL
    SALTVD
     1000 0.95
     2500 3.0
    /
END

Units must be defined using D_UNITS and CONCENTRATION_UNITS. CONCENTRATION_UNITS can take three different values, depending on which units the brine salinity values are entered:

  • MOLAL, for salt concentrations in molality (m).

  • MASS or MASS_FRACTION, for salt concentrations given as mass fractions (kg-salt/kg-brine).

  • MOLE or MOLE_FRACTION, for salt concentrations given as mole fractions, \(\frac{n_{NaCl}}{(n_{NaCl} + n_{H2O})}\)

In all three cases the values entered do not account for the dissolved CO2 in brine.

The data depth vs salinity are entered within the SALTVD block. The entries must be ordered for monotonically growing depths, and at least two entries are required for the internal interpolation to work.

If BRINE has already been used in the input deck to define a constant salinity, SALT_TABLE will overwrite it.

GAS_IN_LIQUID_MOLE_FRACTION

Defines the initial mole fraction of gas in water, dimensionless. If not set, defaults to 0. It is used only by the GAS_WATER mode. If the NOGASSOL option is active, i.e. dissolved gas is not modelled, this card cannot be entered or the simulator throws an error.

ZMFVD

Defines the reservoir non-aqueous phase composition versus depth for all grid blocks associated with the hydrostatic equilibration. It is used only by the Multi-Component mode (COMP EOS). See example below:

ZMFVD m frac
   1000.0 0.0315  0.6599 0.0869 0.0591 0.0967 0.0472 0.0153 0.0034
   3000.0 0.0315  0.6599 0.0869 0.0591 0.0967 0.0472 0.0153 0.0034
END

The ZMFVD keyword is followed by the length and composition units, (m, frac) in the example above. The first can take any of the length units accepted by the simulator, for the composition units two values are accepted [frac, percent]: frac requires the composition to be entered as mole fraction, percent requires the composition to be entered by percentage.

The non-aqueous phase composition can be defined by either ZMFVD in EQUILIBRATION or ZMF in EOS COMP, if the code finds both definitions in the input throws an error.

NUM_EQUIL_NODES

Defines the number of nodes used in the internal hydrostatic equilibration calculation. Below is an example:

EQUILIBRATION initial_sol
  TYPE
    PRESSURE HYDROSTATIC
  /
  DATUM_D 1000.0 m
  PRESSURE 105.0 Bar
  RTEMP 50 C
  GAS_IN_LIQUID_MOLE_FRACTION 1.D-4
  NUM_EQUIL_NODES 2001
/

The reservoir vertical extension is divided into (NUM_EQUIL_NODES – 1) equispaced depth intervals, and the one-dimensional grid obtained is used to carry out the hydrostatic equilibration calculation. If not entered, NUM_EQUIL_NODES defaults to 501. In some cases it might be beneficial to test higher resolutions than the default one to get a more accurate initial state.

Saturation Initialisation

Away from the transition zones, in the gas-saturated region, the gas maximum saturation is computed as \(S_{g,max}=1–S_{wco}\), where \(S_{wco}\) is the connate water, which is the smallest saturation value entered in the SWFN table, or explicitly entered when using analytical water saturation functions.

Away from the transition zones, in the water-saturated region, the maximum water saturation is computed as \(S_{w,max}=1–S_{gco}\), where \(S_{gco}\) is gas connate saturation, which is the smallest saturation value in the SGFN table or explicitly entered when using analytical gas saturation functions. Note that usually \(S_{gco}=0\).

The minimum and maximum values entered in SWFN and SGFN table or in the analytical saturation functions should be consistent, i.e \(S_{g,max} =1 – S_{w,min}\) and \(S_{w,max} =1 – S_{g,min}\). If these maximum values are not respected, they are reset automatically by software.

In the oil region, the oil saturation is computed as \(S_o=1–S_w–S_g\). In case of overlap the oil-water and oil-gas transition zones, a negative oil saturation may result calculation. In this region the software assumes no presence of oil, i.e. \(S_o=0\) and \(S_w=1−S_g\), and solves a non-linear pressure equilibration in Sw using the water and gas capillary pressure functions:

\[P_{cow}(S_w)+P_{cog}(S_g=1−S_w)=P_g–P_w.\]

The overall equilibration calculation assumes that the oil is lighter than the water, and the gas is lighter than the oil. If the user input do not reflects such assumption, an error will be thrown.

In the hydrostatic equilibration for the GAS_WATER module, the model must be fully saturated with water, as this mode does not support a gas-water contact.

EQUILIBRATION aliases and changes used before version OGS-1.6

The EQUILIBRATION keyword has two aliases: EQUIL and FLOW_CONDITION. Versions older than OGS-1.6 support only FLOW_CONDITION, which has to be used in combination with INITIAL_CONDITION and REGION. From OGS-1.6, EQUILIBRATION is the only keyword needed to initialise a study by hydrostatic equilibration.

Multiple Equilibration Regions

It is possible to define multiple equilibration regions, inserting a series of EQUILIBRATION cards, see example below:

EQUILIBRATION equil1
  TYPE
    PRESSURE HYDROSTATIC
  /
  PRESSURE 260.0 Bar
  DATUM_D 2600.0 m
  OWC_D 2500.0 m
  RTEMP 120 C
/

EQUILIBRATION equil2
  TYPE
    PRESSURE HYDROSTATIC
  /
  PRESSURE 260.0 Bar
  DATUM_D 2600.0 m
  OWC_D 2000.0 m
  RTEMP 120 C
/

For example this can be useful to define different phase contact depths, a situation that can be modelled by the simulator, as long as the two phase transition zones are not connected (e.g. two distinct oil traps). The equilibration data to be used by each grid block in the initialisation of the study is defined by the EQLNUM keyword found in the grdecl include file. EQLNUM associates each cell to an EQUILIBRATION data set, with the EQLNUM integer indices referring to the order in which EQUILIBRATION data sets are found in the input. That is, an EQLNUM value of 1 associates the cell with the first EQUILIBRATION block, 2 with the second and so on.

Gas-Water Equilibration example

The gas-water contact is not supported in the hydrostatic equilibration for the GAS_WATER module, therefore the model must be fully saturated with water. See example below:

EQUILIBRATION initial_sol
  TYPE
    PRESSURE HYDROSTATIC
  /
  DATUM_D 1000.0 m
  PRESSURE 105.0 Bar
  RTEMP 50 C
  GAS_IN_LIQUID_MOLE_FRACTION 1.D-4
  SALT_TABLE
    D_UNITS m
    CONCENTRATION_UNITS MOLAL
    SALTVD
     1000 0.95
     2500 3.0
    /
  END
/

Black Oil/Multi-Gas-COMP-4 Equilibration example

Below is an example of a hydrostatic equilibration for a black oil model, with variable \(P_b\) and temperature:

EQUILIBRATION initial_sol
  TYPE
    PRESSURE HYDROSTATIC
  /
  PRESSURE 330.0 Bar
  DATUM_D 2480.0 m
  OGC_D 2430.0 m
  PCOG_OGC 0.5 Bar
  OWC_D 2470.0 m
  PCOW_OWC 0.5 Bar
  BUBBLE_POINT_TABLE
    D_UNITS m
    PRESSURE_UNITS Bar
    PBVD
      2430.0 333.0
      2470.0 335.0
    /
  END
  TEMPERATURE_TABLE
    D_UNITS m
    TEMPERATURE_UNITS C
    RTEMPVD
      2300.0 126.0
      2400.0 128.0
    /
  END
/

Compositional Equilibration Example

Below is an example of a hydrostatic equilibration for a Multi-comnponent model (COMP EOS mode), with non-aqueous composition defined with ZMFVD:

EQUILIBRATION equil_1

  TYPE
    PRESSURE hydrostatic
  /

  OIL_PRESSURE 3550 psi
  DATUM_D  7500 ft
  OGC_D    7499.0 ft
  OWC_D    7500.0 ft
  PCOG_OGC 0.0    Bar
  PCOW_OWC 0.0    Bar

  ZMFVD m frac
     1000.0 0.0315  0.6599 0.0869 0.0591 0.0967 0.0472 0.0153 0.0034
     3000.0 0.0315  0.6599 0.0869 0.0591 0.0967 0.0472 0.0153 0.0034
  END

  RTEMP 93.4 C
/

Multi-Gas-COMP-3 Equilibration Example

Below is an example of a hydrostatic equilibration for a Multi-Gas-COMP-3 model, which uses a gas-water phase contact to define the gas cap location:

EQUILIBRATION

  TYPE
    PRESSURE hydrostatic
   /

  PRESSURE 330.94 Bar
  DATUM_D  2550.0 m
  WGC_D    2550.0 m
  PCWG_WGC 0.0    Bar

  RTEMP 75.0 C
/