Lecture 8. Mole balance: calculations of microreactors, membrane reactors and unsteady state in tank reactors

Size: px

Start display at page:

Download "Lecture 8. Mole balance: calculations of microreactors, membrane reactors and unsteady state in tank reactors"

Martina Fleming
5 years ago
Views:

1 Lecture 8 Mole balance: calculations of microreactors, membrane reactors and unsteady state in tank reactors

2 Mole alance in terms of oncentration and Molar low Rates Working in terms of number of moles (N, N,..) or molar flow rates (, etc) rather than conversion could be more convenient at some instances The difference in calculation: we will write mole balance for each and every species in the reactor

3 Isothermal reaction design algorithm

4 Mole balance: Liquid phase or liquid phase with no volume change, concentration is the preferred variable a + b c + dd b c d + + D a a a

5 Mole balance: Gas phase or e.g. PR, for every species d j j dv = r Generic power rate law oncentration in terms of flow rates r = = k α β j 0 j T0 T T P 0 T for isothermal operation P y dy The pressure drop equation W 2y 0 = α T T The total flow rate T N = j= 1 j

Microreactors characterized by high surface area to volume ratios thus, heat and mass transfer resistances are reduced or eliminated surface catalyzed reactions can be facilitated hot spots in highly

6 Microreactors characterized by high surface area to volume ratios thus, heat and mass transfer resistances are reduced or eliminated surface catalyzed reactions can be facilitated hot spots in highly exothermic reactions can be eliminated highly exothermic reactions can be carried out isothermically leak or microexplosion in a single unit causes a minimal damage to the system shorter residence times and narrower residence time distribution microreactor with a heat exchanger microplant with reactor, valves and mixers

7 Microreactor: example 2NOl 2NO + l 2 Gas reaction carried out at 425º and 1641kPa. Pure NOL is fed and the reaction follows elementary rate law. It s desired to produce 20 t/year in a bank of 10 microreactors in parallel. Each microreactor has 100 channels, each 0.2mm sq and 250mm long. Plot the molar flow rate as a function of volume down the length of the reactor. The rate constant k=0.29 dm 3 /mol s at 500K, E=24 kcal/mol To produce 20 t per year at 85% conversion requires 2.26x10-5 mol/s per channel

8 Example 2NOl 2NO + l Mole balance d dv = r d dv = r d dv = r 2 Rate law r = k Stoichiometry r = 2r = r = ; = ; = T0 T0 T0 T T T T = + +

9 Example

10 Membrane reactors used to increase conversion when the reaction is thermodynamically limited (e.g. with small K) or to increase selectivity in when multiple reactions are occurring H 3H + H inert membrane reactor with catalyst pellet on the feed side (IMR) catalyst membrane reactor (MR)

Membrane reactors H 3H + H 6 12 2 6 6 3+ d Mole balances: dv = r d dv = r + = 0 V V+

11 Membrane reactors H 3H + H d Mole balances: dv = r d dv = r + = 0 V V+ V generation R V r V IN by flow OUT by diffusion d dv = r R OUT by flow no accumulation

12 Membrane reactors d dv = r R R = W a= k a( ) c S Diffusion flux area per volume concentration in the sweep gas channel mass transfer coefficient a π DL = = 2 π LD /4 4 D ssuming S =0 and introducing k c R = k = kca c

13 Example: Dehydrogenation reaction Typical reactions: dehydrogenation of ethylbenzene to styrene; dehydrogenation of butane to butene dehydrogenation of propane to propene Problem: for a reaction of type + where an equilibrium constant Kc=0.05 mol/dm 3 ; temperature 227º, pure enters chamber at 8.2 atm and 227º at a rate of 10 mol/min write differential mole balance for,, Plot the molar flow rate as a function of space and time calculate conversion at V=400 dm 3. ssume that the membrane is permeable for only, catalyst density is rb=1.5 g/cm 3, tube inside diameter 2cm, reaction rate k=0.7 and transport coefficient k c =0.2 min -1.

14 Mole balance: d dv = r Example d r R dv = d dv = r Rate law r = k Transport out of the reactor R Stoichiometry = k c K = T0 = T0 T0 T T P 0 = T0 = = RT0 r = r = r 0.2 mol/dm 3 = T

15 POLYMTH solution Example

16 Use of Membrane reactors to enhance selectivity is fed uniformly through the membrane d r dv = + R

17 Unsteady state operation of stirred reactors reactor start-up semibatch w. cooling reactive distillation during the start up of a reactor: slow addition of component to a large quantity of e.g. when reaction is highly exothermic or unwanted side reaction can occur at high concentration of one of the products is vaporized and withdrawn continuously.

18 Startup of STR onversion doesn t have any meaning in startup so we have to use concentrations dn 0 + rv = dt d V0 or liquid phase with 0 + rτ = τ, τ = constant overflow dt v0 or the 1 st order reactions e.g. to reach 99% steady state concentration d 1+ τ k r = k + = dt τ τ 0, 0 t = 1 exp ( 1+ τ k) 1+ τ k τ S 0 τ =, ts = τ k 1+ τ k ts ts = 4.6τ = 4.6 k

19 Semibatch reactors semibatch reactors could be used e.g. to improve selectivity k + D D k + U U r r = k 2 D = k 2 U S selectivity: / DU r k = = r k D D U U

20 Semibatch equations or component : rv 0 ( ) dn d V Vd dv = = = + dt dt dt dt V = V0 + v0t v + rv= Vd dt d dt v = r V 0 or component : rv = = rv+ 0 Vd dt dn dt dv dt rv + = + v 0 0 d dt v = r + V ( ) 0 0

Problems P4-19: microreactor is used to produce a phosgene in a gas phase. The microreactor is 20mm long, 500 µm in diameter and packed with catalyst particles 35 µm in diameter.

21 Problems P4-19: microreactor is used to produce a phosgene in a gas phase. The microreactor is 20mm long, 500 µm in diameter and packed with catalyst particles 35 µm in diameter. The entering pressure is 830 kpa and the entering flow to each reactor is equimolar. Molar flow rate for O 2 is 2x10-5 mol/s, the volumetric flow 2.83x10-7 m 3 /s, the weight of catalyst in one microreactor W=3.5x10-6 kg. the reactor is kept isothermal at 120º. The rate law: r = k

22 Problems P4-26: large component in the processing train for fuel cell technology is the water gas shift membrane reactor, where H 2 can diffuse out the sides of the membrane while the other gases cannot. O + H O O + H ased on the following information plot the concentration and molar flow rates of each of the reacting species down the length of the membrane reactor. ssume: the volumetric feed is 10dm 3 /min at 10atm; equil molar feed of O and water vapour with T0 =0.4mol/dm 3, equilibrium constant K e =1.44, reaction rate k=1.37 dm 6 /mol kg cat min, mass transfer coefficient for H 2 kc=0.1dm 3 /mol kg cat min.ompare with PR.

Lecture 8. Mole balance: calculations of microreactors, membrane reactors and unsteady state in tank reactors

Lecture 8. Mole balance: calculations of microreactors, membrane reactors and unsteady state in tank reactors Lecture 8 Mole balance: calculations of microreactors, membrane reactors and unsteady state in tank reactors Mole alance in terms of Concentration and Molar Flow Rates Working in terms of number of moles