Kinetics

Front 1

What is the general mole balance equation

Back 1

Fjo - Fj + Gj = DNj/dt

Front 2

What is the rate of generation in a chemical reaction?

Back 2

G = r*integral(V)
r = rate of reaction
V = volume

Front 3

What is the equation for a batch reactor?

Back 3

dN/dt = r*V

Front 4

What is the equation for a continous flow process?

Back 4

Fj = Fjo + rV = 0

V = (Fj - Fjo)/r

Front 5

What is the equation for a tubular reactor?

Back 5

dFj/dV= r

Front 6

What is the equation of a PFR?

Back 6

dFa/dW = r'a

Front 7

What are some assumptions of the CSTR?

Back 7

-steady state
-perfectly mixed

Front 8

What are some assumptions of a batch reactor?

Back 8

-no inflow nor outflow
-perfectly mixed

Front 9

What are some assumptions of a tubular flow reactor?

Back 9

continously consumed as it goes down the reactor
-no radial variation in reacton rate
-turbulent flow

Front 10

Equation relation Flow rate and concentration

Back 10

Fj = Cj*v

Front 11

What are the assumptions of a plug flow reactor?

Back 11

-no readial gradients in concentration temperature or reactionr ate
-steady state

Front 12

What is conversion?

Back 12

moles of A reacted/moles of A fed

Front 13

What is the relation between conversion and moles?

Back 13

Na = Nao(1-X)

Front 14

What is the batch reactor equation in terms of conversion?

Back 14

Nao(dX/dt) = -RaV

Front 15

What is the design equation for a CSTR in terms of conversion?

Back 15

V = FaoX/(-rA)

Front 16

What is the design equation for a tubular flow reactor (PFR) in terms of conversion?

Back 16

V = Fao(integral(dX/-Ra)

Front 17

What is the design equation for a PBR in terms of conversion?

Back 17

W = Fao(integral(dX/-Ra)

Front 18

What happens when a bunch of CSTRS in in series?

Back 18

It behaves as if it is FR

Front 19

How do PFRs behave in series?

Back 19

It does not matter if you have two PFRs or one continous PFR, since the equation is the same.

Front 20

What is space time?

Back 20

tau = V/vo, reactor volume/(volumetric flow rate). it is in seconds.

Front 21

What is space velocity?

Back 21

inverse of space time.

Front 22

How are the reaction rates related?

Back 22

aA + bB -> cC + dD
-ra/a = -rb/b = rc/c = rd/d

Front 23

How are reaction per unit weight and rate per unit volume related?

Back 23

-ra = (bulk density)(-r'a)

bulk density is a function of volumetric flow rate

Front 24

How does one substutite partial pressures with concentration in ideal gas reaction?

Back 24

Pi = CiRT

Front 25

How is concentration and moles related in a batch reactor?

Back 25

Ca = Na/V

Front 26

How is concentration of A(limiting reactant) related to concentration i (other reactant)?

Back 26

Ci = Cao (omega(i) -i/aX)
omega = Cio/Cao = Nio/Nao = uop/yao
omega = 1 if equimolar
omega = i/a if stoichoimtric

Front 27

What is the total change in moles in batch reactor ?

Back 27

Nt = Nto + delta*Nao*X
delta = d/a + c/a - b/a -1

Front 28

In a gas reactor, what is v (volumetric flow rate)

Back 28

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)

Front 29

How can Ft/Fto be reduced?

Back 29

Ft/Fto = 1 + epislon*X
epislon = yao*(delta)

Front 30

What is the Damkohler number?

Back 30

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

Front 31

For a series reactor how is time-space, and the damkohler number related for CSTR?

Back 31

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

Front 32

Estimatation of Da and X relation for firreversible reaction

Back 32

Da<0.1 then X <0.1
Da > 10 then X> .9

Front 33

In a pressure drop raction, dX/dW, it is a function of what two variables

Back 33

function of X and P

Front 34

dP/dz equation (complex)

Back 34

-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

Front 35

equation for density

Back 35

density = (initial density)* vo/v
= initial density *(P/Po)(To/T)(Fto/Ft)

Front 36

dP/dz equation (simplified)

Back 36

dP/dz = -Bo(Po/P)(T/To)(Ft/Fto)

Front 37

from dP/dz to dP/dw

Back 37

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)

Front 38

dP/dW simplified

Back 38

y = P/Po
dy/dW = -alpha/2u(T/to)*(1+epislon*X)
dP/dW = alpha/2u(T/to)*(1+epislon*X)(Po/(P/Po))

Front 39

What is the energy balance equation

Back 39

Q - Ws +sum(FioHio) - sum(FiHi) = dEsys/dt

Front 40

What is the Energy balance of a CSTR with heat exchanger?

Back 40

Xeb = [(UA/Fao(T-Ta) + sum(Ni0/Na0*Cpi(T-To)]/-DeltaHrxo)

Front 41

PFR with heat exchanger:
dT/dV

Back 41

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)

Front 42

PBR in terms of conversion w/ heat exchanger
dT/dW

Back 42

r'*deltaHrx(T)-Ua](bulk density)(T-Ta)/[Fao(sum(Ni/Na)*Cpi + DeltaCpX)]\

Front 43

PBR heat exchanger in terms of molar flow rates

Back 43

r*deltaHrx(T)-Ua(T-Ta)/sum[FiCpi]

Front 44

PBR heat exchanger in terms of molar flow rates

Back 44

r'*deltaHrx(T)-Ua](bulk density)(T-Ta)/[Fao(sum(Ni/Na)*Cpi + DeltaCpX)]\

Front 45

batch with heat exhcanger: dT/dt

Back 45

(rV)(deltaHrx)-UA(T-Ta)/sum(NCp)
Ta= temperature of coolant/heater
U = heat exchange coefficient
A = area of heat exchange

Front 46

semibatch or unsteady CSTR:
dT/dt

Back 46

[Q-Ws-sum(Fio(Cpi(T-Tio)+[(-deltaHrx(T)(-rV)]/sum(NiCpi)

Front 47

multiple reactions in a PFR
dT/dV

Back 47

[sum(rDelaH) -Ua(T-Ta)]/[sum(FjCpj]

Front 48

variable heat exchange fluid temperature,Ta
co-current

Back 48

dTa/dV = Ua(T-Ta)/(mCp)

V= 0, Ta = Tao

Front 49

variable heat exchange fluid temperature,Ta
counter-current

Back 49

dTa/dV = Ua(Ta-T)/(mCp)
V = Vfina Ta = Tao

Front 50

deltaCp

Back 50

d/aCpd +c/aCpc - b/aCpb - Cpa

Front 51

Adiabatic and no shaft energy balance for conversion

Back 51

X = sum(Ni/Na*Cpi(T-To)/-[Hrx(Tr) + deltaCp(T0Tr)]

Front 52

Adiabatic and no shaft energy balance for temperature

Back 52

T = X[-deltaH(Tr) + sum(Ni/Na)CpiTo + XdeltaCpTr]/[sum(Ni/NaCpi) + X*deltaCp]

Front 53

instantaneous selectivity

Back 53

Rd/Ru = [rate of formation of D]/[rate of formation of U]

Front 54

overall selectivity

Back 54

Fd/Fu = [exit molar flow rate of desired product]/[exit flow rate of undesired product]

Front 55

instanous yield

Back 55

rd/-ra

Front 56

overall yield

Back 56

Nd/(Fao - Fa)

Front 57

maximumizing the desired product of one reactant in cased of only one reactant and unknown activation energy

Back 57

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)

Front 58

maximization of desired product in tersm of activation energy

Back 58

If Ed > Eu, then run at higher temperature. If Ed < Eu then run at a lower temperature.

Front 59

maximization of desired product of two reactants

Back 59

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

Front 60

what is the integration factor

Back 60

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)]

Front 61

semi-batch reactor mass balance

Back 61

raV = dN/adt
Fbo = dNb/dt

Front 62

semi-batch reaction, equation for b

Back 62

d(VCb)/dt = dV/dtCb + VdCb/dt = rbV + Fbo = rbV + voCbo
dV/dt = vo
dCb/dt = rb + vo(Cbo-Cb)/V
V = Vo + vot

Front 63

membrane reactor

Back 63

dFb/dV = rb - Rb
Rb = rate of diffustion out.
Rb = kcCb=kc''(Cb-Cbs)
A = AREA/volume = 4/D