!
!  Subroutine: USR_PROP_Kg                                             !
!  Purpose: User hook for calculating the gas phase conductivity.      !
!                                                                      !
!                                                                      !
!^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^!
      SUBROUTINE USR_PROP_Kg(IJK)

      use error_manager
      use fldvar, only: t_g, x_g, p_g, ro_g
      use param1, only: undefined_i, zero, one, half
      use physprop, only: k_g, mw_g, mw_avg, nmax
      use run, only: units

      implicit none

! Dummy arguments
!---------------------------------------------------------------------//
! index
      INTEGER, INTENT(IN) :: IJK

! Local Variables:
!---------------------------------------------------------------------//
! error flag
      INTEGER :: IER = undefined_i
      CHARACTER(LEN=40) :: err_prop
!......................................................................!
! if using this quantity then remove definition of ier
      ier = 1

real :: K_g, K_go, ep_g

  ! Define the given constants
  ep_g = 0.48 ! Replace with your desired value
  K_go = 0.0257   ! Replace with your desired value
  
  ! Calculate k_g
  K_g(IJK) = ((1.0 - sqrt(1.0 - ep_g(IJK))) * k_go) / ep_g(IJK)

! Assign the fluid conductivity
      K_g(IJK) = ZERO

      IF (IER /= UNDEFINED_I) THEN
         write(err_prop, '("gas conductivity")')
         WRITE(ERR_MSG,9999) trim(err_prop)
         CALL LOG_ERROR()
 9999 FORMAT('ERROR 9999: The user-defined properties routine was ',&
         'invoked for',/,A,' but this generic error',/,'message exi',&
         'sts. Either choose a different model or correct',/,'mfix/,'&
         'model/usr_properties.f')
      ENDIF
      RETURN
      END SUBROUTINE USR_PROP_Kg