Fuel Ethanol
Apps.FuelEthanol History
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! 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
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! 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
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!! Fuel Ethanol Production Plant
* %list list-page% [[Attach:ethanol.apm |Fuel Ethanol]]
* %list list-page% [[Attach:ethanol.apm |Fuel Ethanol]]