Rock and fluid properties

Define permeability, porosity, thermal properties, dispersion, and saturation functions for the seven facies. Facies 1 through 6 are permeable sands; facies 7 represents the sealing unit.

Rock properties

rock

Type: matrix with seven rows and two columns

Each row defines one facies as [permeability, porosity]. Permeability is in mD and porosity is dimensionless. Rows correspond to facies 1 through 7.

# Columns: 1) permeability [mD], 2) porosity [-]
rock = [
    [0.10132, 0.10], # Facies 1
    [101.324, 0.20], # Facies 2
    [202.650, 0.20], # Facies 3
    [506.625, 0.20], # Facies 4
    [1013.25, 0.25], # Facies 5
    [2026.50, 0.35], # Facies 6
    [1e-5,    1e-6], # Facies 7
]

kzMult

Type: non-negative number

Sets the multiplier applied to permeability in the z direction.

kzMult = 0.1

rockExtra

Type: array of two positive numbers

Applies to: SPE11B and SPE11C

Sets rock specific heat capacity in kJ/(kg K) and rock density in kg/m3.

# 1) specific heat capacity [kJ/(kg K)], 2) density [kg/m3]
rockExtra = [0.85, 2500.0]

rockCond

Type: array with seven non-negative numbers

Units: W/(m K)

Sets thermal conductivity for facies 1 through 7.

rockCond = [1.9, 1.25, 1.25, 1.25, 0.92, 0.26, 2.0]

dispersion

Type: array with seven non-negative numbers

Units: m

Sets dispersivity for facies 1 through 7.

dispersion = [10, 10, 10, 10, 10, 10, 0]

Saturation functions

The function variables contain validated Python expressions. They are evaluated using s_w and the facies properties in safu.

krw

Defines wetting-phase relative permeability.

krw = "(max(0, (s_w - swi) / (1 - swi))) ** 1.5"

krn

Defines non-wetting-phase relative permeability.

krn = "(max(0, (1 - s_w - sni) / (1 - sni))) ** 1.5"

pcap

Defines capillary pressure in Pa.

pcap = "penmax * math.erf(pen * ((s_w-swi) / (1.-swi)) ** (-(1.0 / 1.5)) * math.pi**0.5 / (penmax * 2))"

s_w

Defines the wetting-saturation points used to tabulate the functions.

s_w = "(np.exp(np.flip(np.linspace(0, 5.0, npoints))) - 1) / (np.exp(5.0) - 1)"

safu

Type: matrix with seven rows and five columns

Each row defines one facies:

1. swi: irreducible wetting saturation, dimensionless.

2. sni: residual non-wetting saturation, dimensionless.

3. pen: capillary entry pressure, Pa.

4. penmax: maximum capillary pressure, Pa.

5. npoints: number of tabulated points.

# Columns: 1) swi [-], 2) sni [-], 3) pen [Pa],
#          4) penmax [Pa], 5) npoints [-]
safu = [
    [0.32, 0.1, 193531.39, 3e7, 1000], # Facies 1
    [0.14, 0.1,   8654.99, 3e7, 1000], # Facies 2
    [0.12, 0.1,   6120.00, 3e7, 1000], # Facies 3
    [0.12, 0.1,   3870.63, 3e7, 1000], # Facies 4
    [0.12, 0.1,   3060.00, 3e7, 1000], # Facies 5
    [0.10, 0.1,   2560.18, 3e7, 1000], # Facies 6
    [0,      0,         0, 3e7,    2], # Facies 7
]

Visualize the saturation functions

The following figures compare the relative-permeability and capillary-pressure functions for all six permeable facies. Facies 7 is omitted because it represents the sealing unit.

Wetting- and non-wetting-phase relative permeability for facies 1 through 6.

Capillary pressure for facies 1 through 6.

Generate the figures with plopm

Run the commands from a directory containing the generated SPE11C OPM Flow input files. The same color identifies each facies in both figures.

Relative permeability

Plot the non-wetting and wetting curves for facies 1 through 6.

plopm -i SPE11C -x '[0,1]' -lw 5 -fz 18 -fs 8,6 -yl 'Capillary pressure, $p_c$ [bar]' -xl 'Liquid saturation, $s_w$ [-]' -xnt 6 -v pcwg1,pcwg2,pcwg3,pcwg4,pcwg5,pcwg6 -y '[0,300]' -llb 'Facies 1  Facies 2  Facies 3  Facies 4  Facies 5  Facies 6' -c b,#ff7f0e,#2ca02c,#d62728,#9467bd,#8c564b -ls '--,(0, (1, 1)),-.,(0, (1, 10)),(0, (1, 1)),(5, (10, 3)),(0, (5, 10))'

Capillary pressure

Plot the gas-water capillary-pressure curves for facies 1 through 6:

plopm -i SPE11C -x '[0,1]' -lw 5 -fz 18 -fs 8,6 -yl 'Capillary pressure, $p_c$ [bar]' -xl 'Liquid saturation, $s_w$ [-]' -xnt 6 -v pcwg1,pcwg2,pcwg3,pcwg4,pcwg5,pcwg6 -y '[0,300]' -llb 'Facies 1  Facies 2  Facies 3  Facies 4  Facies 5  Facies 6' -c b,#ff7f0e,#2ca02c,#d62728,#9467bd,#8c564b -ls '--,(0, (1, 1)),-.,(0, (1, 10)),(0, (1, 1)),(5, (10, 3)),(0, (5, 10))'

See the plopm documentation for the complete saturation-function and styling options.