rlpm

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

    Group 1 - KEYWORD “group”, GROUP_NUMBER

    • The Group 1 KEYWORD “group”, which starts each model sequence.

    Group 2 - KEYWORD “rlp” PHASE, MODEL_TYPE, RLP_PARAM(i), i = 1, NUMP

    • At minimum, one entry is made for relative permeability of the wetting phase in the model. If an entry for a non-wetting phase is not present, Rnw will be calculated using the same model and parameters as Rw.

    Group 3 (optional) - KEYWORD “cap”, COUPLE, MODEL_TYPE, CAP_PARAM(i), i = 1, NUMP

    • One entry is made for each phase-couple in the model. If absent, Cp=0

    NUMP is the number of parameters needed for the selected model type (see parameter table).

    Alternatively, to enter relative permeability and capillary pressure values in a table.

    Group 2 - KEYWORD “table”, COUPLE

    Note

    For backwards compatability with earlier versions of FEHM Group 2 can be: KEYWORD “table” Table# PHASE1 PHASE2 COUPLE. Table#,PHASE1,& PHASE2 will be ignored.

    Group 3 - SATURATION, PHASE1 RELPERM, PHASE2 RELPERM, CAPILLARY PRESSURE

    Group 3 is entered multiple times to cover the full range of wetting phase saturation (0. - 1.0).

    Table input is terminated with KEYWORD ‘end’ or a blank line. Note input saturation is the saturation of the wetting phase, and PHASE1 is the wetting phase.

    -or-

    Group 3 - KEYWORD “file”

    TABLE_FILE

    Table data will be read from the specified file.

    Model input is terminated with KEYWORD ‘end’ or a blank line.

    Group 4 - JA, JB, JC, GROUP_NUMBER

    Input Variable Format Description
    KEYWORD character group rlp cap
    GROUP_NUMBER integer Identifier for the current model.
    PHASE character Fluid state: water air co2_liquid co2_sc co2_gas vapor methane_hydrate oil gas
    MODEL_TYPE character See Tables 1-3
    RLP_PARAM real Input parameters for the specified relative permeability model. See Tables 1-2
    NUMP integer Number of parameters specified for the model (see Tables 1 and 3).
    COUPLING character Phase couple air/water water/co2_liquid water/co2_gas co2_liquid/co2_gas water/vapor air/vapor
    CAP_PARAM real Input parameters for the specified capillary pressure model. See Table 3
    TBLNUM integer Table identifier.
    PHASE1 character Fluid state of the wetting phase (see PHASE for phase ID)
    PHASE2 character Fluid state of the non-wetting phase (see PHASE for phase ID)

    Optional parameters are shown in bold. Table 1. Relative permeability options

    Model type Input Parameter      
      1 2 3 4
    Linear Sr Smax    
    Exponential Sr Smax λ C
    Corey Sr Smax    
    Brooks-Corey Sr Smax λ D
    Van Genuchten (5 model type options, Table 2) Sr Smax m  

    Table 2. Van Genuchten Relative permeability options

    Keyword Independent variable \(R_{nw}\)
    \(Vg_1\) S \(1.-R_{w}\)
    \(Vg\) S VG formula
    \(Vg_{1_{cap}}\) Cp \(1.-R_w\)
    \(Vg_{cap}\) Cp Roseangela
    \(Vg_{corey}\) S Corey formula

    For dual porosity problems with Van Genuchten models, an optional line can follow the ‘rlp’ line with the following format:

    KEYWORD "fracture" Sr Smax m Fracture_k Matrix_k Vf FMIT

    Note: for backwards compatability with earlier versions of FEHM:

    1. the following input style is accepted for all the Van Genuchten model. \(α_G\) will be ignored.
    Van Genuchten Sr Smax \(α_G\) n 
    KEYWORD "fracture" Sr Smax m α_G Fracture_k Matrix_k Vf FMIT

    1. the keyword ‘rlp’ can be omitted.

      Table 3. Capillary Pressure options

    Model type   Input Parameter        
      1 2 3 4 5 6
    Linear Sr Smax        
    Linear_for Cpo Sco        
    Exponential Sr Smax C      
    Brooks-Corey Sr Smax λ \(C_{pe}\) S1 S2
    Van Genuchten Sr Smax \(α_G\) n S1 S2

    For dual porosity problems with Van Genuchten models, an optional line can follow the ‘cap’ line with the following format:

    KEYWORD "fracture" Sr Smax m

    Table 4

    Parameter Format Description
    Sr real Residual (or minimum) wetting-phase saturation.
    Smax real Maximum wetting-phase saturation.
    λ real Exponent in exponential & Brooks-Corey models
    α real Inverse of air entry head, \(α_G\) (1/m)
    n real Parameter n from van Genuchten (1980).
    C real Optional constant in exponential model, =1 if omitted
    k real Optional constant in Brooks-Corey model, (Miller et al., 1998, pg.88) =2 if omitted
    Cpo real Capillary pressure at zero saturation (MPa)
    So real Saturation when Capillary pressure is zero (-)
    \(C_{pe}\) real Capillary entry pressure (MPa)
    Fracture_k real Fracture permeability (m2)
    Matrix_k real Matrix permeability (m2)
    Vf real Fracture volume fraction
    FMIT real Fracture-matrix interaction term.
    S1 real VG fitting parameter
    S2 real VG cutoff saturation

    Both Brooks-Corey and Van Genuchten models can be unstable at low saturations. Parameters S1 and S2 can be used to provide approximations to the curves at low saturations, avoiding numerical instability.

    The approximation will replace the B-C or V-G model for saturations less than S2.

    If S < S2, then:

    • If S1=0 (Van Genuchten model only), the curve will be forced to have zero slope at S=0
    • If S1>0, Cp will vary linearly from Cp(S=S2) to Cp(S=0)=S1*Cp(S=S2) where Cp(S=S2) is capillary pressure at S=S2 calculated according to the B-C or V-G model
    • If S1<0, Cp will vary linearly from Cp(S=S2) to Cp(S=0) at the slope of the Cp curve at S2 calculated according to the B-C or V-G model

    Examples

    Example 1. Water Rw according to corey, non-wetting phase will be 1-Rw. Cp=0

    rlpm        
    group 1      
    rlp water corey 0.3 0.1
    end        
    1 140 1 1  
             

    Example 2. Air/Water problem. Both water and air will have linear rlp models. Capillary pressure of air/water will be according to the linear forsyth model.

    rlpm          
    group 1        
    rlp water linear 0.3 1.0  
    rlp air linear 0.1 .7  
    cap air/water linear_for 93.6
    		 
    end          
    1 0 0 1    
               

    Example 3. Air/Water problem. Water (and air, by default) will both have vg rel perm model (see Table 2 for details). Air/water capillary pressure will be vg.

    rlpm                  
    group 10                
    rlp water vg_1 0.0001 1.0 3.0        
    cap air/water vg 0.0001 1.0 3.0 3.0
    		0.05  
    end                  
    1 0 0 10            
                       

    Example 5. Dual porosity air/water problem. Water (and air, by default) will both have vg rel perm model, calculated using capillary pressure as the independent variable (see Table 2 for details). Air/water capillary pressure will be vg. Fracture rel perm and capillary pressure models are specified, as well.

    rlpm                  
    group 1                
    rlp water vg_cap 0.0212 1.0 1.62        
    fracture 0.03 1.0 3.00 4.06e-09 2.04e-18 2.93e-04
    		   
    cap air/water vg 0.0212 1.0 0.00715 1.62
    		0.0312  
    fracture 0.03 1.0 12.05 3.00 20.0 0.0001      
    group 2                
    rlp water vg_cap 0.154 1.0 0.371 2.37      
    fracture 0.03 1.0 13.72 3.00 7.14e-09 2.51e-18 9.27e-05
    		 
    cap air/water vg_cap 0.154 1.0 0.371 2.37
    		0.164  
    fracture 0.03 1.0 13.72 3.00 20.0 0.0001      
    end                  
    -1 0 0 1            
    -2 0 0 2            
                       

    Example 6. Water/vapor problem. Group 1 applies a corey relative permeability function (also applied to vapor, by default). cp=0. Group 2 applies interpolated values from a table, read from an external file “doe_rlpm.table”. (note: this file can be generated by FEHM by using the keyword ‘rel’ in the hist macro)

    rlpm          
    group 1        
    rlp water corey 0.3 0.1  
    group 2        
    table water/vapor        
    file          
    input/doe_rlpm.table          
    end          
    1 140 1 2    
               

    For example, the file doe_rlpm.table would contain an arbitrary number header rows (each header row must contain a character in the first column) followed by an arbitrary number of lines each containing the following information: saturation, relative permeability (wetting phase), relative permeability (non-wetting phase),and capillary pressure (MPa).

    FEHM V3.00pgi64 10-10-20 QA:NA 10/20/2010 14:23:18      
    * DOE Code Comparison Project, Problem 5, Case A *      
    Relative permeability and Capillary pressure      
    “Saturation” “Liquid” “Vapor” “Capillary pressure”      
    0.00000000 0.00000000 1.00000000 0.00000000
    0.500000000E-01 0.00000000 1.00000000 0.00000000
    0.100000000 0.00000000 1.00000000 0.00000000
    0.150000000 0.00000000 1.00000000 0.00000000
    0.200000000 0.00000000 1.00000000 0.00000000
    0.250000000 0.00000000 1.00000000 0.00000000
    0.300000000 0.732682696E-64 1.00000000 0.00000000
    0.350000000 0.482253086E-04 0.834442515 0.00000000
    0.400000000 0.771604938E-03 0.675154321 0.00000000
    0.450000000 0.390625000E-02 0.527343750 0.00000000
    0.500000000 0.123456790E-01 0.395061728 0.00000000
    0.550000000 0.301408179E-01 0.281201775 0.00000000
    0.600000000 0.625000000E-01 0.187500000 0.00000000
    0.650000000 0.115788966 0.114535108 0.00000000
    0.700000000 0.197530864 0.617283951E-01 0.00000000
    0.750000000 0.316406250 0.273437500E-01 0.00000000
    0.800000000 0.482253086 0.848765432E-02 0.00000000
    0.850000000 0.706066744 0.110918210E-02 0.00000000
    0.900000000 1.00000000 0.00000000 0.00000000
    0.950000000 1.00000000 0.00000000 0.00000000
    1.00000000 1.00000000 0.00000000 0.00000000

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