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Derivatives.f90
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Derivatives.f90
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!^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^!^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
!^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^!^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
!! 3D oil reservoir Simulator project
!! by Mehrdad Gharib Shirangi From Spring 2010 until Fall 2010
!! mehrdad.ghsh@gmail.com
!! Copy Right by Mehrdad Gharib Shirangi
!^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^!^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
!^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^!^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Module Derivative
! contains transmissibility functions
use globalvar
use Trans
implicit none
!real :: Press
contains
real*8 function DTrxa_DP(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 :: delx_avg , Press
real*8 :: denomenator, press_term, Dip_cor
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'a' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind + 1
delx_avg = (Deltax(i+1) + Deltax(i)) / 2.0
denomenator = 1 / 2.0 * ( Deltax(i+1) / ( kx(ind+1) * Deltay(j) * Deltaz(ind+1) ) + Deltax(i)/( kx(ind)*Deltay(j)*Deltaz(ind) ) )
Dip_cor = delx_avg ** 2 / ((Zblock(ind)-Zblock(N_ind)) ** 2 + delx_avg ** 2)
if ( D_Poten( ind , N_ind , m ) > 0 ) then !( Potential(ind,m) > Potential(N_ind,m) ) then ! upstream block
if (wrt=='a') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw(ind) / ( mu_w (ind) * B_w(ind ) ) * ( B_der(ind ,'w') / B_w(ind ) + mu_der(ind ,'w') / mu_w(ind) )
Else
press_term = - k_ro(ind) / ( mu_o (ind) * B_o(ind ) ) * ( B_der(ind ,'o') / B_o(ind ) + mu_der(ind , 'o') / mu_o(ind) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw( N_ind ) / ( mu_w (N_ind) * B_w(N_ind ) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) + mu_der(N_ind ,'w') / mu_w(N_ind) )
Else
press_term = - k_ro( N_ind) / ( mu_o ( N_ind) * B_o( N_ind ) ) * ( B_der( N_ind ,'o') / B_o( N_ind ) + mu_der( N_ind , 'o') / mu_o( N_ind) )
EndIf
Endif
EndIf
DTrxa_DP = betac * Dip_cor * press_term /denomenator
Endfunction DTrxa_DP
!*******************************************************************************************
real*8 function DTrxb_DP(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 :: delx_avg , Press
real*8 :: denomenator, press_term, Dip_cor
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'b' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind - 1
delx_avg = (Deltax(i-1) + Deltax(i))/2.0
denomenator = 1 / 2.0 * ( Deltax(i-1) / ( kx(ind-1) * Deltay(j) * Deltaz(ind-1) ) + Deltax(i)/( kx(ind)*Deltay(j)*Deltaz(ind) ) )
Dip_cor = delx_avg ** 2 / ((Zblock(ind)-Zblock(N_ind)) ** 2 + delx_avg ** 2)
if ( D_Poten( ind , N_ind , m ) > 0 ) then ! upstream block
if (wrt=='b') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw(ind) / ( mu_w (ind) * B_w(ind ) ) * ( B_der(ind ,'w') / B_w(ind ) )
Else
press_term = - k_ro(ind) / ( mu_o (ind) * B_o(ind ) ) * ( B_der(ind ,'o') / B_o(ind ) + mu_der(ind , 'o') / mu_o(ind) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw( N_ind ) / ( mu_w (N_ind) * B_w(N_ind ) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) )
Else
press_term = - k_ro( N_ind) / ( mu_o ( N_ind) * B_o( N_ind ) ) * ( B_der( N_ind ,'o') / B_o( N_ind ) + mu_der( N_ind , 'o') / mu_o( N_ind) )
EndIf
Endif
EndIf
DTrxb_DP = betac * Dip_cor * press_term /denomenator
Endfunction DTrxb_DP
!*******************************************************************************************
real*8 function DTryb_DP(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 :: dely_avg , Press
real*8 :: denomenator, press_term, Dip_cor
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'b' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind - Nx
dely_avg = (Deltay(j-1) + Deltay(j))/2.0
denomenator = 1 / 2.0 * ( Deltay(j-1) / ( ky(N_ind) * Deltax(i) * Deltaz(N_ind) ) + Deltay(j)/( ky(ind) * Deltax(i) * Deltaz(ind) ) )
Dip_cor = dely_avg ** 2 / ((Zblock(ind)-Zblock(N_ind)) ** 2 + dely_avg ** 2)
if ( D_Poten( ind , N_ind , m ) > 0 ) then ! upstream block
if (wrt=='b') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw(ind) / ( mu_w (ind) * B_w(ind ) ) * ( B_der(ind ,'w') / B_w(ind ) )
Else
press_term = - k_ro(ind) / ( mu_o (ind) * B_o(ind ) ) * ( B_der(ind ,'o') / B_o(ind ) + mu_der(ind , 'o') / mu_o(ind) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw( N_ind ) / ( mu_w (N_ind) * B_w(N_ind ) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) )
Else
press_term = - k_ro( N_ind) / ( mu_o ( N_ind) * B_o( N_ind ) ) * ( B_der( N_ind ,'o') / B_o( N_ind ) + mu_der( N_ind , 'o') / mu_o( N_ind) )
EndIf
Endif
EndIf
DTryb_DP = betac * Dip_cor * press_term /denomenator
Endfunction DTryb_DP
!*******************************************************************************************
real*8 function DTrya_DP(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 :: dely_avg, Press
real*8 :: denomenator, press_term, Dip_cor
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'a' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind + Nx
dely_avg = (Deltay(j+1) + Deltay(j))/2.0
denomenator = 1 / 2.0 * ( Deltay(j+1) / ( ky(N_ind) * Deltax(i) * Deltaz(N_ind) ) + Deltay(j)/( ky(ind) * Deltax(i) * Deltaz(ind) ) )
Dip_cor = dely_avg ** 2 / ((Zblock(ind)-Zblock(N_ind)) ** 2 + dely_avg ** 2)
if ( D_Poten( ind , N_ind , m ) > 0.0 ) then ! upstream block
if (wrt=='a') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw(ind) / ( mu_w (ind) * B_w(ind ) ) * ( B_der(ind ,'w') / B_w(ind ) )
Else
press_term = - k_ro(ind) / ( mu_o (ind) * B_o(ind ) ) * ( B_der(ind ,'o') / B_o(ind ) + mu_der(ind , 'o') / mu_o(ind) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw( N_ind ) / ( mu_w (N_ind) * B_w(N_ind ) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) )
Else
press_term = - k_ro( N_ind) / ( mu_o ( N_ind) * B_o( N_ind ) ) * ( B_der( N_ind ,'o') / B_o( N_ind ) + mu_der( N_ind , 'o') / mu_o( N_ind) )
EndIf
Endif
EndIf
DTrya_DP = betac * Dip_cor * press_term /denomenator
Endfunction DTrya_DP
!*******************************************************************************************
real*8 function DTrzb_DP(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 :: denomenator, press_term , Press
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'a' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind - Nx * Ny
denomenator = 1 / 2.0 * ( Deltaz(N_ind) / ( kz(N_ind) * Deltax(i) * Deltay(j) ) + Deltaz(ind)/( kz(ind) * Deltax(i) * Deltay(j) ) )
if ( D_Poten( ind , N_ind , m ) > 0 ) then ! upstream block
if (wrt=='b') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw(ind) / ( mu_w (ind) * B_w(ind ) ) * ( B_der(ind ,'w') / B_w(ind ) )
Else
press_term = - k_ro(ind) / ( mu_o (ind) * B_o(ind ) ) * ( B_der(ind ,'o') / B_o(ind ) + mu_der(ind , 'o') / mu_o(ind) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw( N_ind ) / ( mu_w (N_ind) * B_w(N_ind ) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) )
Else
press_term = - k_ro( N_ind) / ( mu_o ( N_ind) * B_o( N_ind ) ) * ( B_der( N_ind ,'o') / B_o( N_ind ) + mu_der( N_ind , 'o') / mu_o( N_ind) )
EndIf
Endif
EndIf
DTrzb_DP = betac * press_term /denomenator
Endfunction DTrzb_DP
!*******************************************************************************************
real*8 function DTrza_DP(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 ::delz_avg , Press
real*8 :: denomenator, press_term
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'a' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind + Nx * Ny
denomenator = 1 / 2.0 * ( Deltaz(N_ind) / ( kz(N_ind) * Deltax(i) * Deltay(j) ) + Deltaz(ind)/( kz(ind) * Deltax(i) * Deltay(j) ) )
if ( D_Poten( ind , N_ind , m ) > 0 ) then ! upstream block
if (wrt=='a') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw(ind) / ( mu_w (ind) * B_w(ind ) ) * ( B_der(ind ,'w') / B_w(ind ) )
Else
press_term = - k_ro(ind) / ( mu_o (ind) * B_o(ind ) ) * ( B_der(ind ,'o') / B_o(ind ) + mu_der(ind , 'o') / mu_o(ind) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0.0
Else
if ( m == 'w') then
press_term = - k_rw( N_ind ) / ( mu_w (N_ind) * B_w(N_ind ) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) )
Else
press_term = - k_ro( N_ind) / ( mu_o ( N_ind) * B_o( N_ind ) ) * ( B_der( N_ind ,'o') / B_o( N_ind ) + mu_der( N_ind , 'o') / mu_o( N_ind) )
EndIf
Endif
EndIf
DTrza_DP = betac * press_term /denomenator
Endfunction DTrza_DP
!*******************************************************************************************
real*8 function DTrxa_DS(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 :: delx_avg , Press
real*8 :: denomenator, press_term, Dip_cor
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'a' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind + 1
delx_avg = (Deltax(i+1) + Deltax(i))/2.0
denomenator = 1 / 2.0 * ( Deltax(i+1) / ( kx(ind+1) * Deltay(j) * Deltaz(ind+1) ) + Deltax(i)/( kx(ind)*Deltay(j)*Deltaz(ind) ) )
Dip_cor = delx_avg ** 2 / ((Zblock(ind)-Zblock(N_ind)) ** 2 + delx_avg ** 2)
if ( D_Poten( ind , N_ind , m ) > 0 ) then ! upstream block
if (wrt=='a') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( ind ) / ( mu_w ( ind ) * B_w( ind ) ) + k_rw(ind) / ( mu_w ( ind) * B_w(ind) ) * ( B_der(ind ,'w') / B_w(ind ) + mu_der(ind ,'w') / mu_w(ind) ) * PCO_der(ind)
Else
press_term = DkrodS( ind ) / ( mu_o ( ind ) * B_o( ind ) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( N_ind ) / ( mu_w ( N_ind ) * B_w( N_ind ) ) + k_rw(N_ind) / ( mu_w ( N_ind) * B_w(N_ind) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) + mu_der(N_ind ,'w') / mu_w(N_ind) ) * PCO_der(N_ind)
Else
press_term = DkrodS( N_ind ) / ( mu_o ( N_ind ) * B_o( N_ind ) )
EndIf
Endif
EndIf
DTrxa_DS = betac * Dip_cor * press_term /denomenator
Endfunction DTrxa_DS
!*******************************************************************************************
real*8 function DTrxb_DS(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 :: delx_avg , Press
real*8 :: denomenator, press_term, Dip_cor
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'b' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind - 1
delx_avg = (Deltax(i-1) + Deltax(i))/2.0
denomenator = 1 / 2.0 * ( Deltax(i-1) / ( kx(N_ind) * Deltay(j) * Deltaz(N_ind) ) + Deltax(i)/( kx(ind)*Deltay(j)*Deltaz(ind) ) )
Dip_cor = delx_avg ** 2 / ((Zblock(ind)-Zblock(N_ind)) ** 2 + delx_avg ** 2)
if ( D_Poten( ind , N_ind , m ) > 0 ) then ! upstream block
if (wrt=='b') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( ind ) / ( mu_w ( ind ) * B_w( ind ) ) + k_rw(ind) / ( mu_w ( ind) * B_w(ind) ) * ( B_der(ind ,'w') / B_w(ind ) ) * PCO_der(ind)
Else
press_term = DkrodS( ind ) / ( mu_o ( ind ) * B_o( ind ) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( N_ind ) / ( mu_w ( N_ind ) * B_w( N_ind ) ) + k_rw(N_ind) / ( mu_w ( N_ind) * B_w(N_ind) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) ) * PCO_der(N_ind)
Else
press_term = DkrodS( N_ind ) / ( mu_o ( N_ind ) * B_o( N_ind ) )
EndIf
Endif
EndIf
DTrxb_DS = betac * Dip_cor * press_term /denomenator
Endfunction DTrxb_DS
!*******************************************************************************************
real*8 function DTryb_DS(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 ::dely_avg , Press
real*8 :: denomenator, press_term, Dip_cor
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'b' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind - Nx
dely_avg = (Deltay(j-1) + Deltay(j))/2.0
denomenator = 1 / 2.0 * ( Deltay(j-1) / ( ky(N_ind) * Deltax(i) * Deltaz(N_ind) ) + Deltay(j)/( ky(ind) * Deltax(i) * Deltaz(ind) ) )
Dip_cor = dely_avg ** 2 / ((Zblock(ind)-Zblock(N_ind)) ** 2 + dely_avg ** 2)
if ( D_Poten( ind , N_ind , m ) > 0 ) then ! upstream block
if (wrt=='b') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( ind ) / ( mu_w ( ind ) * B_w( ind ) )+ k_rw(ind) / ( mu_w ( ind) * B_w(ind) ) * ( B_der(ind ,'w') / B_w(ind ) ) * PCO_der(ind)
Else
press_term = DkrodS( ind ) / ( mu_o ( ind ) * B_o( ind ) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( N_ind ) / ( mu_w ( N_ind ) * B_w( N_ind ) ) + k_rw(N_ind) / ( mu_w ( N_ind) * B_w(N_ind) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) ) * PCO_der(N_ind)
Else
press_term = DkrodS( N_ind ) / ( mu_o ( N_ind ) * B_o( N_ind ) )
EndIf
Endif
EndIf
DTryb_DS = betac * Dip_cor * press_term /denomenator
Endfunction DTryb_DS
!*******************************************************************************************
real*8 function DTrya_DS(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 :: dely_avg , Press
real*8 :: denomenator, press_term, Dip_cor
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'a' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind + Nx
dely_avg = (Deltay(j+1) + Deltay(j) )/2.0
denomenator = 1 / 2.0 * ( Deltay(j+1) / ( ky(N_ind) * Deltax(i) * Deltaz(N_ind) ) + Deltay(j)/( ky(ind) * Deltax(i) * Deltaz(ind) ) )
Dip_cor = dely_avg ** 2 / ((Zblock(ind)-Zblock(N_ind)) ** 2 + dely_avg ** 2)
if ( D_Poten( ind , N_ind , m ) > 0 ) then ! upstream block
if (wrt=='a') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( ind ) / ( mu_w ( ind ) * B_w( ind ) ) + k_rw(ind) / ( mu_w ( ind) * B_w(ind) ) * ( B_der(ind ,'w') / B_w(ind ) ) * PCO_der(ind)
Else
press_term = DkrodS( ind ) / ( mu_o ( ind ) * B_o( ind ) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( N_ind ) / ( mu_w ( N_ind ) * B_w( N_ind ) ) + k_rw(N_ind) / ( mu_w ( N_ind) * B_w(N_ind) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) ) * PCO_der(N_ind)
Else
press_term = DkrodS( N_ind ) / ( mu_o ( N_ind ) * B_o( N_ind ) )
EndIf
Endif
EndIf
DTrya_DS = betac * Dip_cor * press_term /denomenator
Endfunction DTrya_DS
!*******************************************************************************************
real*8 function DTrzb_DS(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 :: denomenator, press_term , Press
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'b' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind - Nx * Ny
denomenator = 1 / 2.0 * ( Deltaz(N_ind) / ( kz(N_ind) * Deltax(i) * Deltay(j) ) + Deltaz(ind)/( kz(ind) * Deltax(i) * Deltay(j) ) )
if ( D_Poten( ind , N_ind , m ) > 0 ) then ! upstream block
if (wrt=='b') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( ind ) / ( mu_w ( ind ) * B_w( ind ) ) + k_rw(ind) / ( mu_w ( ind) * B_w(ind) ) * ( B_der(ind ,'w') / B_w(ind ) ) * PCO_der(ind)
Else
press_term = DkrodS( ind ) / ( mu_o ( ind ) * B_o( ind ) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( N_ind ) / ( mu_w ( N_ind ) * B_w( N_ind ) ) + k_rw(N_ind) / ( mu_w ( N_ind) * B_w(N_ind) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) ) * PCO_der(N_ind)
Else
press_term = DkrodS( N_ind ) / ( mu_o ( N_ind ) * B_o( N_ind ) )
EndIf
Endif
EndIf
DTrzb_DS = betac * press_term /denomenator
Endfunction DTrzb_DS
!*******************************************************************************************
real*8 function DTrza_DS(i,j,k,m,wrt) ! the value of the derivative of x transmissibility between a gridblock and a next grid
integer :: ind , N_ind ! Neighbor grid index
integer :: i,j,k
real*8 :: denomenator, press_term , Press
Character*1 :: m ! 'o' or 'w' : oil or water
Character*1 :: wrt ! 'a' , 'c' ! wrt to after , or before or itself
ind = (k-1) * Nx * Ny + (j-1) * Nx + i
N_ind = ind + Nx * Ny
denomenator = 1 / 2.0 * ( Deltaz(N_ind) / ( kz(N_ind) * Deltax(i) * Deltay(j) ) + Deltaz(ind)/( kz(ind) * Deltax(i) * Deltay(j) ) )
if ( D_Poten( ind , N_ind , m ) > 0 ) then ! upstream block
if (wrt=='a') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( ind ) / ( mu_w ( ind ) * B_w( ind ) ) + k_rw(ind) / ( mu_w ( ind) * B_w(ind) ) * ( B_der(ind ,'w') / B_w(ind ) ) * PCO_der(ind)
Else
press_term = DkrodS( ind ) / ( mu_o ( ind ) * B_o( ind ) )
EndIf
EndIf
else
if (wrt=='c') then
press_term = 0
Else
if ( m == 'w') then
press_term = DkrwdS( N_ind ) / ( mu_w ( N_ind ) * B_w( N_ind ) ) + k_rw(N_ind) / ( mu_w ( N_ind) * B_w(N_ind) ) * ( B_der(N_ind ,'w') / B_w(N_ind ) ) * PCO_der(N_ind)
Else
press_term = DkrodS( N_ind ) / ( mu_o ( N_ind ) * B_o( N_ind ) )
EndIf
Endif
EndIf
DTrza_DS = betac * press_term /denomenator
Endfunction DTrza_DS
!*******************************************************************************************
!*******************************************************************************************
real*8 function B_der(ind , m )
integer :: ind , n2 , m2 , i4 ! Neighbor grid index
Character*1 :: m ! 'o' or 'w' : oil or water
real*8 :: p2 , X
if (m=='o') then
p2 = pressure(ind)
n2 = N_Bo
m2 = 1
do while (abs(n2-m2) .NE. 1)
i4 = FLOOR(m2 + (n2-m2+1)/2.0)
if (p2 < Bo_p(i4,1) ) then
n2 = FLOOR(m2+(n2-m2+1)/2.0);
else
m2 = FLOOR(m2+(n2-m2+1)/2.0);
end if
end do
B_der = (Bo_p(n2,2)-Bo_p(m2,2))/(Bo_p(n2,1)-Bo_p(m2,1))
! B_der = -5.0d-5
Else
p2 = W_press(ind)
!B_der = - PVTW(2) / ( ( 1 + PVTW(3) * (p2 - PVTW(1) ) )**2 ) * PVTW(3)
X = PVTW(3) * (p2 - PVTW(1) )
B_der = - PVTW(2) / ( ( 1 + X + ( X ** 2 )/2.0 )**2 ) * ( PVTW(3) + ( PVTW(3) ** 2 ) * (p2 - PVTW(1) ) )
EndIf
Endfunction B_der
!*******************************************************************************************
real*8 function mu_der(ind , m )
integer :: ind ! Neighbor grid index
Character*1 :: m ! 'o' or 'w' : oil or water
real*8 :: p1
Integer :: m1,n1 , i5
p1 = pressure(ind)
if (m=='w') then
mu_der = 0.0
else
n1 = N_mup
m1 = 1
do while (abs(n1-m1) .NE. 1)
i5 = floor(m1 + (n1-m1+1)/2.0)
if (p1 < mu_p(i5,1) ) then
n1 = floor(m1+(n1-m1+1)/2.0);
else
m1 = floor(m1+(n1-m1+1)/2.0);
end if
end do
mu_der = (mu_p(n1,2)-mu_p(m1,2))/(mu_p(n1,1)-mu_p(m1,1))
Endif
Endfunction mu_der
!*******************************************************************************************
real*8 function gama_der(ind , m)
integer :: ind ! Ind is the block number which we want to have the derivative wrt the pressure of that block
Character*1 :: m ! 'o' or 'w' : oil or water
!Character*1 :: wrt ! 'a' , 'c' ! wrt to after , or before or itself
If ( m == 'o' ) then
gama_der = - den_o / ( 144.0 * 2.0 * ( B_o(ind) ) **2 ) * B_der(ind , 'o' )
Else !( m == 'w' )
gama_der = - den_w / ( 144.0 * 2.0 * ( B_w(ind) ) **2 ) * B_der(ind , 'w' )
EndIf
Endfunction gama_der
!*******************************************************************************************
real*8 function Dkr_dS(index , m1) ! this function calculates the Derivative of Kr wrt the saturation of the block
Implicit None
!
integer :: index ! Ind is the block number which we want to have the derivative wrt the saturation of that block
Character*1 :: m1 ! 'o' or 'w' : oil or water
real*8 :: swater
Integer :: m ,n
swater = sw(index)
n = n_Kr
m = 1
do while (abs(n-m) .NE. 1)
if ( swater < Sw_mat(floor(m+(n-m+1)/2.0))) then
n = floor(m+(n-m+1)/2.0);
else
m = floor(m+(n-m+1)/2.0);
end if
end do
if ( m1 == 'o' ) then
if ((swater > Sw_mat(n_Kr - 1) ) .OR. (swater .LT. Sw_mat(1) ) ) then
Dkr_dS = 0.0
Else
Dkr_dS = (kro(n)-kro(m))/(Sw_mat(n)-Sw_mat(m))
EndIf
else
if ( (swater > 1.0 ) .OR. (swater .LT. Sw_mat(1) ) ) then
Dkr_dS = 0.0
Else
Dkr_dS = (krw(n)-krw(m))/(Sw_mat(n)-Sw_mat(m))
EndIf
EndIf
Endfunction Dkr_dS
!*******************************************************************************************
real*8 function PCO_der(ind)
integer :: ind
real*8 :: Swater
Integer :: m,n
Swater = sw(ind)
if ( Swater .LE. Sw_mat(1) ) then
n = 2
m = 1
elseif ( Swater .GE. 1.0 ) then
n = n_Kr
m = n_Kr - 1
else
n = n_Kr
m=1
do while (abs(n-m) .NE. 1)
if (Swater < Sw_mat( floor(m+(n-m+1)/2.0) ) ) then
n = floor(m+(n-m+1)/2.0);
else
m = floor(m+(n-m+1)/2.0);
end if
end do
EndIf
PCO_der = (Pcow(n) - Pcow(m))/(Sw_mat(n) - Sw_mat(m))
! PCO_der = - 3 * 34.98 * Swater ** 2 + 2 * 83.96 * Swater - 67.17
Endfunction PCO_der
!*******************************************************************************************
!*******************************************************************************************
real*8 function B_der_P(p , m )
integer :: ind , n2 , m2 , i4 ! Neighbor grid index
Character*1 :: m ! 'o' or 'w' : oil or water
real*8 :: p , p2 , X
p2 = p
if (m=='o') then
n2 = N_Bo
m2 = 1
do while (abs(n2-m2) .NE. 1)
i4 = FLOOR(m2 + (n2-m2+1)/2.0)
if (p2 < Bo_p(i4,1) ) then
n2 = FLOOR(m2+(n2-m2+1)/2.0);
else
m2 = FLOOR(m2+(n2-m2+1)/2.0);
end if
end do
B_der_P = (Bo_p(n2,2)-Bo_p(m2,2))/(Bo_p(n2,1)-Bo_p(m2,1))
! B_der = -5.0d-5
Else
!B_der = - PVTW(2) / ( ( 1 + PVTW(3) * (p2 - PVTW(1) ) )**2 ) * PVTW(3)
X = PVTW(3) * (p2 - PVTW(1) )
B_der_P = - PVTW(2) / ( ( 1 + X + ( X ** 2 )/2.0 )**2 ) * ( PVTW(3) + ( PVTW(3) ** 2 ) * (p2 - PVTW(1) ) )
EndIf
Endfunction B_der_P
!*******************************************************************************************
!*******************************************************************************************
real*8 function PCO_der_Sw(Swater)
integer :: ind
real*8 :: Swater
Integer :: m,n
if ( Swater .LE. Sw_mat(1) ) then
n = 2
m = 1
elseif ( Swater .GE. 1.0 ) then
n = n_Kr
m = n_Kr - 1
else
n = n_Kr
m=1
do while (abs(n-m) .NE. 1)
if (Swater < Sw_mat( floor(m+(n-m+1)/2.0) ) ) then
n = floor(m+(n-m+1)/2.0);
else
m = floor(m+(n-m+1)/2.0);
end if
end do
EndIf
PCO_der_Sw = (Pcow(n) - Pcow(m))/(Sw_mat(n) - Sw_mat(m))
! PCO_der = - 3 * 34.98 * Swater ** 2 + 2 * 83.96 * Swater - 67.17
Endfunction PCO_der_Sw
!*******************************************************************************************
EndModule Derivative