`rlp`¶

Relative permeability and capillary pressure model. Several models are available.

Group 1 - IRLP(i), RP1, RP2, RP3, RP4, RP5, RP6, RP7, RP8, RP9, RP10, RP11, RP12, RP13, RP14, RP15, RP16 (number of parameters entered depends on model selected)
Group 2 - JA, JB, JC, I

Only those parameters defined for a given model need to be input. Group 1 is ended when a blank line is encountered. The parameter i is incremented each time a Group 1 line is read. Group 2 lines will refer to this parameter. For model numbers 4, 6, and 7 (the combined van Genuchten model), the permeability is isotropic and overwrites the input from macro perm. Macro fper can be used with models 4, 6, and 7 to introduce anisotropy.

Input Variable	Format	Description
IRLP(i)	integer	Relative permeability model type.
Model -1: IRLP(i) = -1, constant relative permeability, linear capillary pressure (4 parameters required).
RP1	real	Liquid relative permeability (\(m^2\)).
RP2	real	Vapor relative permeability (\(m^2\)).
RP3	real	Capillary pressure at zero saturation (\(MPa\)).
RP4	real	Saturation at which capillary pressure goes to zero.
Model 1: IRLP(i) = 1, linear relative permeability, linear capillary pressure (6 parameters required).
RP1	real	Residual liquid saturation.
RP2	real	Residual vapor saturation.
RP3	real	Maximum liquid saturation.
RP4	real	Maximum vapor saturation.
RP5	real	Capillary pressure at zero saturation (MPa).
RP6	real	Saturation at which capillary pressure goes to zero.
Model 2: IRLP(i) = 2, Corey relative permeability, linear capillary pressure (4 parameters required).
RP1	real	Residual liquid saturation.
RP2	real	Residual vapor saturation.
RP3	real	Capillary pressure at zero saturation (MPa).
RP4	real	Saturation at which capillary pressure goes to zero.
Model 3: IRLP(i) = 3, van Genuchten relative permeability, van Genuchten capillary pressure (6 parameters required). In this model permeabilities are represented as a function of capillary pressure [rlp(h)].
RP1	real	Residual liquid saturation.
RP2	real	Maximum liquid saturation.
RP3	real	Inverse of air entry head, \(\alpha_G\) (1/m) [note some data is given in (1/Pa) convert using pressure = ρgΔh].
RP4	real	Power n in van Genuchten formula.
RP5	real	Low saturation fitting parameter, multiple of cutoff capillary pressure assigned as maximum capillary pressure. If RP5 < 0 then a linear fit from the cutoff saturation (RP6) is used. The slope of the cutoff saturation is used to extend the function to saturation = 0. If RP5 = 0, a cubic fit is used. The slope at the cutoff saturation is matched and the conditions \(\frac{\partial}{\partial S}Pcap = 0\) and \(\frac{\partial^2}{\partial S}Pcap = 0\) are forced at \(S = 0\). If RP5 > 0, a multiple of the value of the capillary pressure at the cutoff saturation, \(RP5\cdot Pcap(S_{cutoff}\) is forced at \(S = 0\).
RP6	real	Cutoff saturation used in fits described for RP5, must be greater than RP1.
Model 4: IRLP(i) = 4, van Genuchten relative permeability, van Genuchten capillary pressure, effective continuum (15 parameters required). In this model permeabilities are represented as a function of capillary pressure [rlp(h)].
RP1	real	Residual liquid saturation, matrix rock material.
RP2	real	Maximum liquid saturation, matrix rock material.
RP3	real	Inverse of air entry head, \(\alpha_G\) (1/m) [note some data is given in (1/Pa) convert using pressure = \(\rho g \Delta h\)], matrix rock material.
RP4	real	Power n in van Genuchten formula, matrix rock material.
RP5	real	Low saturation fitting parameter, matrix rock material, multiple of cutoff capillary pressure assigned as maximum capillary pressure. If RP5 < 0 then a linear fit from the cutoff saturation (RP6) is used. The slope of the cutoff saturation is used to extend the function to saturation = 0.
		If RP5 = 0, a cubic fit is used. The slope at the cutoff saturation is matched and the conditions \(\frac{\partial}{\partial S}Pcap = 0\) and \(\frac{\partial^2}{\partial S}Pcap = 0\) are forced at \(S = 0\). If RP5 > 0, a multiple of the value of the capillary pressure at the cutoff saturation, \(RP5\cdot Pcap(S_{cutoff})\) is forced at \(S = 0\).
RP6	real	Cutoff saturation used in fits described for RP5, must be greater than RP1.
RP7	real	Residual liquid saturation, fracture material.
RP8	real	Maximum liquid saturation, fracture material.
RP9	real	Inverse of air entry pressure, \(\alpha_G\) (1/m) [note some data is given in(1/Pa) convert using pressure = \(\rho g \Delta h\)], fracture material.
RP10	real	Power n in van Genuchten formula, fracture material.
RP11	real	Low saturation fitting parameter, fracture material, multiple of cutoff capillary pressure assigned as maximum capillary pressure. If RP11 < 0 then a linear fit from the cutoff saturation (RP12) is used. The slope of the cutoff saturation is used to extend the function to saturation = 0.If RP11 = 0, a cubic fit is used. The slope at the cutoff saturation is matched and the conditions \(\frac{\partial}{\partial S}Pcap = 0\) and \(\frac{\partial^2}{\partial S}Pcap = 0\) are forced at \(S = 0\). If RP11 > 0, a multiple of the value of the capillary pressure at the cutoff saturation, \(RP11\cdot Pcap(S_{cutoff})\) is forced at \(S = 0\).
RP12	real	Cutoff saturation used in fits described for RP11, must be greater than RP7.
RP13	real	Fracture permeability (\(m^2\)). This is the permeability of the individual fractures. The bulk permeability of the fracture continuum is \(RP13\times RP15\). Can be made anisotropic with macro FPER.
RP14	real	Matrix rock saturated permeability (\(m^2\)). Can be made anisotropic with macro FPER.
RP15	real	Fracture volume fraction. Is equal to the fracture aperture divided by the fracture spacing (with same units). Sometimes called fracture porosity.
Model 5: IRLP(i) = 5, van Genuchten relative permeability, van Genuchten capillary pressure (6 parameters required). This model and its input are the same as for Model 3 except that permeabilities are represented as a function of saturation [rlp(S)] rather than capillary pressure.
Model 6: IRLP(i) = 6, van Genuchten relative permeability, van Genuchten capillary pressure, effective continuum (15 parameters required). This model and its input are the same as for Model 4 except that permeabilities are represented as a function of saturation [rlp(S)] rather than capillary pressure.
Model 7: IRLP(i) = 7, van Genuchten relative permeability, van Genuchten capillary pressure, effective continuum with special fracture interaction term (16 parameters required). This model and its input are the same as for Model 6 except that the an additional term is included which represents the fracture-matrix interaction.
RP16	real	Fracture-matrix interaction term. If RP16 ≤ 0, then an additional multiplying term equal to the relative permeability is applied to the fracture-matrix interaction term for dual permeability problems. If RP16 > 0, then an additional multiplying term equal to \(slRP16\) and \((1.-sl)RP16\) is applied to the fracture-matrix interaction terms for the liquid and vapor phases, respectively, for dual permeability problems. Here, \(sl\) is the value of saturation at the given node.
Model 10: IRLP(i) = 10, linear relative permeability with minimum relative permeability values, linear capillary pressure (8 parameters required).
RP1	real	Residual liquid saturation.
RP2	real	Residual vapor saturation.
RP3	real	Maximum liquid saturation.
RP4	real	Maximum vapor saturation.
RP5	real	Minimum liquid permeability (\(m^2\)).
RP6	real	Minimum vapor permeability (\(m^2\)).
RP7	real	Capillary pressure at zero saturation (\(MPa\)).
RP8	real	Saturation at which capillary pressure goes to zero.

The following is an example of rlp. In this example, Corey type relative permeability is specified, with residual liquid saturation of 0.3, residual vapor saturation of 0.1, a base capillary pressure of 2 MPa, and capillary pressure goes to zero at a saturation of 1. This model is assigned to nodes numbered 1 through 140.

rlp
2	0.3	0.1	2.0

1	140	1	1

rlp¶

`rlp`¶