AQNUM_DATA
This data block sets up a numerical aquifer - an aquifer explicitly modelled by a cell in the simulation. The format of this block is typically:
AQNUM_DATA A1
RPV 200000000 m^3
RPI 2.13175 m^3/d/bar
CONN_D 10 10 1 1 1 1 X+
VISC 2 cp
REP_CELL_D 12 1 1
END
The aquifer will be modelled by a single representative cell, selected by REP_CELL_D. This cell should be placed away from the main reservoir in an inactive region of the grid.
The deliverability is defined by the aquifer \(PI\), or productivity index, which is the reservoir volume delivery rate per unit pressure drawdown into the reservoir. This has the advantage of being easy to estimate, but of course the flow per unit drawdown depends on the viscosity of the fluid. A very viscous fluid would show a low \(PI\), a very mobile fluid would show a large \(PI\). So it is useful to specify the viscosity, \(\mu\), at which the \(PI\) is defined, and then construct a total aquifer-reservoir transmissibility, \(T\), as:
Once the aquifer is set up in the model, it is isolated from the rest of the model, other than through aquifer-reservoir connections defined by connection boxes set using CONN_D or CONN_Z.
The initial solution and the effective rock compressibility are taken from the values for the representative cell. The initial solution in the aquifer is obtained from the usual hydrostatic equilibration for the aquifer depth and the equilibration region for that cell.
The options supported by AQNUM_DATA are:
RPV
This specifies the aquifer pore volume at reference conditions. See example above.
The actual reservoir volume of the aquifer will include the rock compressibilty.
The aquifer pore volume can alternatively be specified by using the LENGTH, AREA and POROSITY keywords as follows.
If LENGTH, AREA and POROSITY keywords are provided, but not RPV, then it will be obtained as:
See the example input in the LENGTH section.
RPI
This specifies the aquifer productivity index of the numerical aquifer. See example above.
Units are required and may be specified as:
m^3/d/bar : rm3 per day per Bar drawdown
or:
bbl/d/psi : rb per day per psi drawdown
or:
m^3/s/Pa : rm3 per second per Pascal drawdown
Only these three unit options are allowed. Note that these productivities are in terms of reservoir volumes. The surface volume PI would be \(SPI\), given by:
Where \(B_w\) is the water phase formation volume factor.
If the LENGTH, AREA, PERM and VISC keywords are available, but not RPI, then it will be obtained as:
This is based on the usual expression for transmissibility, \(T=K.A/d\), then \(RPI = T/\mbox{visc}\), where \(d=\mbox{length}/2\) is the distance from the end of the numerical aquifer cell to the centre.
In anything other than pure SI values, a unit conversion constant is required, so that:
If the area is in m^2, perm in mD, length in m, visc in cp, then \(C=0.00852702\), and the units of RPI will be in bbl/d/psi.
If area is in ft^2, perm in mD, length in ft, visc in cp, then \(C=0.00112712\), and RPI will be in bbl/d/psi.
Examples of input of numerical aquifers using RPV/RPI or geometrical input in field and metric units, together with a comparison with the case of using an extra grid cell as the aquifer, and using no aquifer at all, may be found in the Cirrus repository regression tests:
[repo]/regression_tests/towg/gw/
as the examples:
aqcomptest_geo_aqnumad.in
aqcomptest_geo_aqnumadf.in
aqcomptest_geo_aqnumpv.in
aqcomptest_geo_aqnumpvf.in
aqcomptest_geo_cells.in
aqcomptest_geo_none.in
Note the first 5 cases all give the samve pressure rise, but this is different from the last case.
LENGTH
Part of an alternative way of defining the Reservoir Pore Volume (RPV), along with AREA and POROSITY. Has units of length, e.g. m.
Also part of an alternative way of defining the Reservoir Productivity Index (RPI), along with AREA, PERM and VISC.
See example below:
AQNUM_DATA SOUTH
AREA 40E5 m^2
LENGTH 1E5 m
POROSITY 0.1
RPI 127 m^3/d/Bar
CONN_D 5 10 1 1 1 10 Y-
VISC 0.5 cp
REP_CELL_D 12 3 1
END
AREA
Part of an alternative way of defining the Reservoir Pore Volume (RPV), along with LENGTH and POROSITY. Has units of area, e.g. m^2.
Also part of an alternative way of defining the Reservoir Productivity Index (RPI), along with LENGTH, PERM and VISC.
See example above.
POROSITY
Part of an alternative way of defining the Reservoir Pore Volume (RPV), along with LENGTH and AREA. Defined as a fraction, between 0 and 1.
See example above.
PERM
Part of an alternative way of defining the Reservoir Productivity Index (RPI), along with LENGTH, AREA, and VISC. Has units of millidarcy, mD.
VISC
Part of an alternative way of defining the Reservoir Productivity Index (RPI), along with LENGTH, AREA, and PERM. Has units of centipoise, cP.
CONN_D/CONN_Z
Specifies blocks of connections to attach aquifer to reservoir cell faces. See also the corresponding entries for AQUIFER_DATA: CONN_D and CONN_Z.
More than one connection box may be entered. CONN_D uses the Eclipse cell k-index convention, counting down from the top of the reservoir, and CONN_Z counts up from the bottom of the reservoir.
DEPTH
Defines the depth of the aquifer, in units of length, e.g. m. See example below:
AQNUM_DATA SOUTH
RPV 40E9 m^3
DEPTH 2005 m
RPI 127 m^3/d/Bar
CONN_D 5 10 1 1 1 10 Y-
VISC 0.5 cp
REP_CELL_D 12 3 1
END
The depth of the numerical aquifer cell defaults to the depth of the representative cell, but this may be overwritten with DEPTH.
ZAQUIFER
An alternative to DEPTH expressed as an elevation, so that:
REP_CELL_D/REP_CELL_Z
Ways of defining the location of the representative cell. See example above.
To be followed by three values, the I,J,K indices of the representative cell.
REP_CELL_D uses the Eclipse cell k-index convention, counting down from the top of the reservoir, and REP_CELL_Z uses the traditional Pflotran one of counting up from the bottom of the reservoir.
Note: the rock and water compressibility will be taken from the values for the representative cell. These cannot currently be set to custom values for the aquifer.
If the representative cell is initially not active, it will be made active.
AQCON_AREA/AQCON_AREA_PERM
These are options for controlling the manner in which the total aquifer-reservoir flow is divided between all the cells connected to the aquifer. See example below:
AQNUM_DATA SOUTH
RPV 40E9 m^3
AQCON_AREA_PERM
RPI 127 m^3/d/Bar
CONN_D 5 10 1 1 1 10 Y-
VISC 0.5 cp
REP_CELL_D 12 3 1
END
If AQCON_AREA is used the flow is divided on the basis of the area of the cell face connected to the aquifer.
If AQCON_AREA_PERM is used the flow is divided on the basis of the product of the area of the cell face and the permeability of the the cell in the direction of the face.
The default is AQCON_AREA.
These keywords have no arguments.
Note that these two keywords can be used in both the AQUIFER_DATA and AQNUM_DATA blocks.