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
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