APMonitor

! APMonitor Modeling Language
! https://www.apmonitor.com

! Ethanol Production Model
Model ferm

  Parameters
    v.in     = 100     ! Flow in [gpm]
    v.out    = 100     ! Flow out [gpm]

    ! feed concentrations
    cS[4].in  = 25.7     ! starch      [wt%]
    cS[3].in = 0.5       ! maltotriose [wt%]
    cS[2].in = 0.5       ! maltose     [wt%]
    cG.in  = 2.0         ! glucose     [wt%]
    cP.in = 0.5          ! ethanol     [wt%]
    cX.in = 0.1          ! yeast       [wt%]

    ! gluco-amylase catalyzed reactions
    ! starch => glucose
    kS = 1000.0    ! [1/h]
    ! glucose => ethanol
    kP = 10.0   ! [1/h]

    ! concentration based on amount of GA added to F. Reactor
    ! 90ml/min over 50 hours of feed prep for 550,000 gal container = 0.0122 wt%
    ! 276 L added over 7 hours of fill + 1/2 gal GA in yeast/urea prep
    ! = 73.5 gal / 550000 gal * 100% = 0.01427
    cGA = 1.25e-2   ! [wt%]
  End Parameters

  Variables
    V6    = 0.5,    > 0.5    ! volume [M-gal]
    cS[4] = 25.0,   >-0.1    ! starch      [wt%]
    cS[3] = 1.85,   >-0.1    ! maltotriose [wt%]
    cS[2] = 5.69,   >-0.1    ! maltose     [wt%]
    cG    = 7.31,   >-0.1    ! glucose     [wt%]
    cP    = 12.05,  >-0.1    ! ethanol     [wt%]
    !Level = 10.0,   > 1e-6      ! level  [ft]
  End Variables

  Intermediates
    ! yeast concentration
    cX = cX.in

    ! 1 ft3  =  7.481  gal 
    !pi        = 3.1415
    !Vmax      = 550000 / 7.481  ! gal * (ft3/gal)
    !h_d_ratio = 2.5             ! height to diameter ratio
    !diameter  = (4 * Vmax / (pi*2.5))^(1/3)
    !hmax      = h_d_ratio * diameter

    rho = 4             ! density [kg/gal]
    m6  = V6 * rho      ! mass   [kg]
    d_m6 = $V6 * rho     ! mass derivative [kg/hr]
    m.in   = v.in  * rho * 60 ! mass flow in  [kg/hr]
    m.out  = v.out * rho * 60 ! mass flow out [kg/hr]

    ! pathways
    !   C6H12O6 + 6 O2 => 6 CO2      + 6 H2O
    !   C6H12O6        => 2 CH3CH2OH + 2 CO2
    !   180 gm            2*46 gm    + 2*44 gm
    Rsx    = 0.607      ! gm yeast / gm glucose for reaction
    Rsp    = 0.466      ! gm ethanol / gm glucose (theoretical is 51%, with energy for yeast activity ~47%)
    Rpc    = 44/46      ! gm CO2 / gm ethanol (44 gm/mol / 46 gm/mol)

    ! Kinetic constants

    ! S(i) => (gluco-amylase) => S(i-1) + G
    ! rates of consumption (wt%/kg/hr)
    rS[4] = kS*cS[4]*cGA
    rS[3] = kS*cS[3]*cGA - 3/4 * kS*cS[4]*cGA  ! 3/4 of S[4] becomes S[3]
    rS[2] = kS*cS[2]*cGA - 2/3 * kS*cS[3]*cGA  ! 2/3 of S[3] becomes S[2]

    ! rate of generation of glucose
    rG = kS*cS[2]*cGA + 1/3 * kS*cS[3]*cGA + 1/4 * kS*cS[4]*cGA

    ! rate of generation of ethanol
    rP = kP*cX*cG

    ! rate of generation of yeast
    rX = 0
  End Intermediates

  Equations
    ! level
    !Level = 4 * V6 * 1e6 / (pi*diameter^2)

    ! mass balance
    d_m6 = (m.in - m.out - Rpc*rP*m6) * 1e-6       + m6 - 4 ! M-kg/hr

    ! mass balances
    (m6*$cS[4] + d_m6*cS[4]) = -m6 * rS[4] + (m.in*cS[4].in - m.out*cS[4]) * 1e-6
    (m6*$cS[3] + d_m6*cS[3]) = -m6 * rS[3] + (m.in*cS[3].in - m.out*cS[3]) * 1e-6
    (m6*$cS[2] + d_m6*cS[2]) = -m6 * rS[2] + (m.in*cS[2].in - m.out*cS[2]) * 1e-6

    ! species balance for glucose -- Mkg/hr
    (m6*$cG + d_m6*cG) = m6 * (rG - rX/Rsx - rP/Rsp) + (m.in*cG.in - m.out*cG) * 1e-6

    ! species balance for ethanol -- Mkg/hr
    (m6*$cP + d_m6*cP) = m6 * rP            + (m.in*cP.in - m.out*cP) * 1e-6                                   
  End Equations

End Model