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63 Cards in this Set
- Front
- Back
What is the general mole balance equation
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Fjo - Fj + Gj = DNj/dt
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What is the rate of generation in a chemical reaction?
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G = r*integral(V)
r = rate of reaction V = volume |
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What is the equation for a batch reactor?
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dN/dt = r*V
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What is the equation for a continous flow process?
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Fj = Fjo + rV = 0
V = (Fj - Fjo)/r |
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What is the equation for a tubular reactor?
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dFj/dV= r
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What is the equation of a PFR?
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dFa/dW = r'a
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What are some assumptions of the CSTR?
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-steady state
-perfectly mixed |
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What are some assumptions of a batch reactor?
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-no inflow nor outflow
-perfectly mixed |
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What are some assumptions of a tubular flow reactor?
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continously consumed as it goes down the reactor
-no radial variation in reacton rate -turbulent flow |
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Equation relation Flow rate and concentration
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Fj = Cj*v
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What are the assumptions of a plug flow reactor?
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-no readial gradients in concentration temperature or reactionr ate
-steady state |
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What is conversion?
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moles of A reacted/moles of A fed
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What is the relation between conversion and moles?
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Na = Nao(1-X)
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What is the batch reactor equation in terms of conversion?
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Nao(dX/dt) = -RaV
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What is the design equation for a CSTR in terms of conversion?
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V = FaoX/(-rA)
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What is the design equation for a tubular flow reactor (PFR) in terms of conversion?
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V = Fao(integral(dX/-Ra)
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What is the design equation for a PBR in terms of conversion?
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W = Fao(integral(dX/-Ra)
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What happens when a bunch of CSTRS in in series?
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It behaves as if it is FR
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How do PFRs behave in series?
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It does not matter if you have two PFRs or one continous PFR, since the equation is the same.
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What is space time?
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tau = V/vo, reactor volume/(volumetric flow rate). it is in seconds.
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What is space velocity?
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inverse of space time.
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How are the reaction rates related?
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aA + bB -> cC + dD
-ra/a = -rb/b = rc/c = rd/d |
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How are reaction per unit weight and rate per unit volume related?
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-ra = (bulk density)(-r'a)
bulk density is a function of volumetric flow rate |
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How does one substutite partial pressures with concentration in ideal gas reaction?
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Pi = CiRT
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How is concentration and moles related in a batch reactor?
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Ca = Na/V
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How is concentration of A(limiting reactant) related to concentration i (other reactant)?
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Ci = Cao (omega(i) -i/aX)
omega = Cio/Cao = Nio/Nao = uop/yao omega = 1 if equimolar omega = i/a if stoichoimtric |
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What is the total change in moles in batch reactor ?
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Nt = Nto + delta*Nao*X
delta = d/a + c/a - b/a -1 |
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In a gas reactor, what is v (volumetric flow rate)
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v = vo(Ft/Fto)(Po/P)(P/To):
v = vo(1+ epilson*X)(Po/P)(P/To) derived from: Ct = Ft/v = P/(ZRT) Cto = Fto/vo = Po/(ZoRTo) |
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How can Ft/Fto be reduced?
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Ft/Fto = 1 + epislon*X
epislon = yao*(delta) |
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What is the Damkohler number?
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Da = -raoV/Fao
for a first order reactor Da = time-space*k1 for a second order reaction Da = time-space*k2*Cao X = Da/(1+Da) in first order reaction |
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For a series reactor how is time-space, and the damkohler number related for CSTR?
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X = 1 - 1/(1+Da)^n - 1-1/)(1+theta*k)^n
assuming the CSTR are same size and operating at same temeperatue and first order |
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Estimatation of Da and X relation for firreversible reaction
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Da<0.1 then X <0.1
Da > 10 then X> .9 |
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In a pressure drop raction, dX/dW, it is a function of what two variables
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function of X and P
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dP/dz equation (complex)
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-G/(pgD)(1-porosity)/porosity^3[150(1-porosoity)*viscosity)/D + 1.75G]
G = density*velocity = superificial mass velocity p = gass density z = length down packed bed D = diameter of particle in bed |
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equation for density
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density = (initial density)* vo/v
= initial density *(P/Po)(To/T)(Fto/Ft) |
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dP/dz equation (simplified)
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dP/dz = -Bo(Po/P)(T/To)(Ft/Fto)
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from dP/dz to dP/dw
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W = (1-porosity)Acz*density of solid catalyst
Ac = cross sectional aread dW = (1-porosity)Ac*density of solid catalyst dP/dW = dP/dz*dz/dW = -BoPoTFt/(Ac(1-porosity)pc*P*To*Fto) |
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dP/dW simplified
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y = P/Po
dy/dW = -alpha/2u(T/to)*(1+epislon*X) dP/dW = alpha/2u(T/to)*(1+epislon*X)(Po/(P/Po)) |
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What is the energy balance equation
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Q - Ws +sum(FioHio) - sum(FiHi) = dEsys/dt
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What is the Energy balance of a CSTR with heat exchanger?
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Xeb = [(UA/Fao(T-Ta) + sum(Ni0/Na0*Cpi(T-To)]/-DeltaHrxo)
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PFR with heat exchanger:
dT/dV |
r*deltaHrx(T)-Ua(T-Ta)/[Fao(sum(Ni/Na)*Cpi + DeltaCpX)]
U = heat transfer coefficient a = heat exchange area per volume of reactor(m^2/m^3) |
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PBR in terms of conversion w/ heat exchanger
dT/dW |
r'*deltaHrx(T)-Ua](bulk density)(T-Ta)/[Fao(sum(Ni/Na)*Cpi + DeltaCpX)]\
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PBR heat exchanger in terms of molar flow rates
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r*deltaHrx(T)-Ua(T-Ta)/sum[FiCpi]
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PBR heat exchanger in terms of molar flow rates
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r'*deltaHrx(T)-Ua](bulk density)(T-Ta)/[Fao(sum(Ni/Na)*Cpi + DeltaCpX)]\
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batch with heat exhcanger: dT/dt
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(rV)(deltaHrx)-UA(T-Ta)/sum(NCp)
Ta= temperature of coolant/heater U = heat exchange coefficient A = area of heat exchange |
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semibatch or unsteady CSTR:
dT/dt |
[Q-Ws-sum(Fio(Cpi(T-Tio)+[(-deltaHrx(T)(-rV)]/sum(NiCpi)
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multiple reactions in a PFR
dT/dV |
[sum(rDelaH) -Ua(T-Ta)]/[sum(FjCpj]
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variable heat exchange fluid temperature,Ta
co-current |
dTa/dV = Ua(T-Ta)/(mCp)
V= 0, Ta = Tao |
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variable heat exchange fluid temperature,Ta
counter-current |
dTa/dV = Ua(Ta-T)/(mCp)
V = Vfina Ta = Tao |
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deltaCp
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d/aCpd +c/aCpc - b/aCpb - Cpa
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Adiabatic and no shaft energy balance for conversion
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X = sum(Ni/Na*Cpi(T-To)/-[Hrx(Tr) + deltaCp(T0Tr)]
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Adiabatic and no shaft energy balance for temperature
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T = X[-deltaH(Tr) + sum(Ni/Na)CpiTo + XdeltaCpTr]/[sum(Ni/NaCpi) + X*deltaCp]
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instantaneous selectivity
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Rd/Ru = [rate of formation of D]/[rate of formation of U]
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overall selectivity
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Fd/Fu = [exit molar flow rate of desired product]/[exit flow rate of undesired product]
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instanous yield
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rd/-ra
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overall yield
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Nd/(Fao - Fa)
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maximumizing the desired product of one reactant in cased of only one reactant and unknown activation energy
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if alpha1 (desired) greater than alpha2(undesired) then keep concentration of A as high as possible. USe a PFR or batch
if alpha1(desired) less than alpha 2 (undesired used dilutes) |
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maximization of desired product in tersm of activation energy
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If Ed > Eu, then run at higher temperature. If Ed < Eu then run at a lower temperature.
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maximization of desired product of two reactants
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alpha 1 > alpha 2, beta 1 < beta 2
-semibatch reactor with B moving in slowly -tubular reactor with side stream of B -series of small CSTR with only small amounts of B |
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what is the integration factor
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dy/dt + f(t)y = g(t)
y = e^(-int(fdt))*int(g(t)e^int(fdt)_K1e^(-int(fdt) dy/dt + k2y = k1e^(-k1t) y = k1/(k2-k1)[e^(-k1t)-e^(-k2t)] |
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semi-batch reactor mass balance
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raV = dN/adt
Fbo = dNb/dt |
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semi-batch reaction, equation for b
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d(VCb)/dt = dV/dtCb + VdCb/dt = rbV + Fbo = rbV + voCbo
dV/dt = vo dCb/dt = rb + vo(Cbo-Cb)/V V = Vo + vot |
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membrane reactor
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dFb/dV = rb - Rb
Rb = rate of diffustion out. Rb = kcCb=kc''(Cb-Cbs) A = AREA/volume = 4/D |