public  subroutine HelmRKPR(nco, NDE, NTD, rn, V, T, Ar, ArV, ArTV, ArV2, Arn, ArVn, ArTn, Arn2)  
    
    Calculate the reduced residual Helmholtz Energy and it’s derivatives with the RKPR EOS
    Arguments
        
    
      
        | Type | Intent | Optional | Attributes |  | Name |  | 
    
        
            | integer, | intent(in) |  |  | :: | nco |  | 
        
            | integer, | intent(in) |  |  | :: | NDE |  | 
        
            | integer, | intent(in) |  |  | :: | NTD |  | 
        
            | real(kind=pr), | intent(in) |  |  | :: | rn(nco) |  | 
        
            | real(kind=pr), | intent(in) |  |  | :: | V |  | 
        
            | real(kind=pr), | intent(in) |  |  | :: | T |  | 
        
            | real(kind=pr), | intent(out) |  |  | :: | Ar |  | 
        
            | real(kind=pr), | intent(out) |  |  | :: | ArV |  | 
        
            | real(kind=pr), | intent(out) |  |  | :: | ArTV |  | 
        
            | real(kind=pr), | intent(out) |  |  | :: | ArV2 |  | 
        
            | real(kind=pr), | intent(out) |  |  | :: | Arn(nco) |  | 
        
            | real(kind=pr), | intent(out) |  |  | :: | ArVn(nco) |  | 
        
            | real(kind=pr), | intent(out) |  |  | :: | ArTn(nco) |  | 
        
            | real(kind=pr), | intent(out) |  |  | :: | Arn2(nco,nco) |  | 
    
  
    
        
      Variables
      
    
      
        | Type | Visibility | Attributes |  | Name |  | Initial |  | 
    
        
            | real(kind=pr), | public |  | :: | AUX |  |  |  | 
        
            | real(kind=pr), | public |  | :: | ArT |  |  |  | 
        
            | real(kind=pr), | public |  | :: | ArTT |  |  |  | 
        
            | real(kind=pr), | public |  | :: | Bmix |  |  |  | 
        
            | real(kind=pr), | public |  | :: | D |  |  |  | 
        
            | real(kind=pr), | public |  | :: | D1 |  |  |  | 
        
            | real(kind=pr), | public |  | :: | D2 |  |  |  | 
        
            | real(kind=pr), | public |  | :: | FFB |  |  |  | 
        
            | real(kind=pr), | public |  | :: | FFBB |  |  |  | 
        
            | real(kind=pr), | public |  | :: | FFBV |  |  |  | 
        
            | real(kind=pr), | public |  | :: | auxD2 |  |  |  | 
        
            | real(kind=pr), | public |  | :: | dBi(nco) |  |  |  | 
        
            | real(kind=pr), | public |  | :: | dBij(nco,nco) |  |  |  | 
        
            | real(kind=pr), | public |  | :: | dD1i(nco) |  |  |  | 
        
            | real(kind=pr), | public |  | :: | dD1ij(nco,nco) |  |  |  | 
        
            | real(kind=pr), | public |  | :: | dDdT |  |  |  | 
        
            | real(kind=pr), | public |  | :: | dDdT2 |  |  |  | 
        
            | real(kind=pr), | public |  | :: | dDi(nco) |  |  |  | 
        
            | real(kind=pr), | public |  | :: | dDiT(nco) |  |  |  | 
        
            | real(kind=pr), | public |  | :: | dDij(nco,nco) |  |  |  | 
        
            | real(kind=pr), | public |  | :: | f |  |  |  | 
        
            | real(kind=pr), | public |  | :: | fB |  |  |  | 
        
            | real(kind=pr), | public |  | :: | fBD1 |  |  |  | 
        
            | real(kind=pr), | public |  | :: | fD1 |  |  |  | 
        
            | real(kind=pr), | public |  | :: | fD1D1 |  |  |  | 
        
            | real(kind=pr), | public |  | :: | fVD1 |  |  |  | 
        
            | real(kind=pr), | public |  | :: | fv |  |  |  | 
        
            | real(kind=pr), | public |  | :: | fv2 |  |  |  | 
        
            | real(kind=pr), | public |  | :: | g |  |  |  | 
        
            | real(kind=pr), | public |  | :: | gv |  |  |  | 
        
            | real(kind=pr), | public |  | :: | gv2 |  |  |  | 
        
            | integer, | public |  | :: | i |  |  |  | 
        
            | integer, | public |  | :: | j |  |  |  | 
        
            | real(kind=pr), | public |  | :: | totn |  |  |  |