1. Story Behind HW2 Powerball, LLC.
Make H2 from Na inside Ping pong balls
Cut open under water
Na +H2O  NaOH + ½ H2 ↑
Fuel tank for bus in LA, Sailboats, Autos
DOE funding required Fuel Cycle to be Evaluated
NaOH back to Na using CH4

2. Introduce HW 3 Objective
Maximize Yield and Selectivity for a Series-Parallel Reaction
Gain Experience with Aspen-Kinetic Reactors
Heuristic 7
For competing reactions, both in series and parallel adjust T and P and catalyst to obtain high yields of the desired products. Check that there are no kinetic limits to this assumption.
Gain Experience with Aspen-Optimizer
& Ratio of Reactants

3. Maximize Desired Product
Series Reactions
AB(desired)CD
Plug Flow Reactor
Optimum Time in Reactor

4. Rate Selectivity Parallel Reactions Rate Selectivity
A+BR (desired)
A+BS
Rate Selectivity
(αD- αU) >1 make CA as large as possible
(βD –βU)>1 make CB as large as possible
(kD/kU)= (koD/koU)exp[-(EA-D-EA-U)/(RT)]
EA-D > EA-U T
EA-D < EA-U T

5. Attainable Region
S,S&L Chapt. 8

6. Attainable Region
Graphical method that is used to determine the entire space feasible concentrations
Useful for identifying reactor configurations that will yield the optimal products

7. Procedure
Step 1: Construct a trajectory for a PFR from the feed point, continuing to complete conversion or chemical equilibrium
Step 2: When the PFR bounds a convex region, this constitutes a candidate AR. The procedure terminates if the rate vectors outside the candidate AR do not point back into it.
Step 3: The PFR trajectory is expanded by linear arcs, representing mixing between the PFR effluent and the feed stream, extending the candidate AR.
Step 4: Construct a CSTR trajectory to see if the AR can be extended. Place linear arcs, which represent mixing, on the CSTR trajectory to ensure the trajectory remains convex.
Step 5: A PFR trajectory is drawn from the position where the mixing line meets the CSTR trajectory. If the PFR trajectory is convex, it extends the previous AR to form a expanded AR. Then return to step 2. Otherwise, repeat the procedure from Step 3.

8. Example
Reactions
Rate Equations

9. Step 1
Begin by constructing a trajectory for a PFR from the feed point, continuing to the complete conversion of A or chemical equilibrium
Solve the PFR design equations numerically
Use the feed conditions as initial conditions to the o.d.e.
Adjust integration range, t (residence time), until complete conversion or to equilibrium

10. PFR Design Equations

11. Solve Numerically Runge-Kutta

12. Solve Numerically

13. Step 2
Plot the PFR trajectory from the previous results. Check to see if rate vectors outside AR point back into it (e.g. Look for non-convex regions on the curve. Tangent line passing (1,0))
AR=Attainable Rection
Desired

14. Step 3
Expand the AR as much as possible with straight arcs that represent mixing of reactor effluent and feed stream
(1-a)
PFR a

15. Interpreting points on mixing line
Larger Attainable Region
(1-a)
(1-a)
PFR
PFR
CA=
CB=
CA=0.72
CB=
a = 0.64
CA=1
CB=0
CA=1
CB=0

16. Mixing of Streams Reactant Bypass
Vector Equation, i component is CA, j component is CB
α =fraction of mixture of stream 1in the mixed stream
Feed mixing fraction: a = 0. 64

17. Step 4
If a mixing arc extends the attainable region on a PFR trajectory, check to see if a CSTR trajectory can extend the attainable region
For CSTR trajectories that extend the attainable region, add mixing arcs to concave regions to ensure the attainable region remains convex
Solve CSTR multiple NLE numerically
Vary t until all feed is consumed or equilibrium is reached

18. CSTR Design Equations

19. Solve numerically at various t until complete conversion or equilibrium is achieved

20. CSTR Extends Attainable Region

21. Plot extends attainable region
i.c. for step 5
Plot extends attainable region
Enlarges
Attainable
Region
(1-a)
CSTR a
CA=1
CB=0

22. Possible Configuration at this point
PFR
1-α
CA=1
CB=0
CSTR a
CA=1
CB=0
0.38

23. But you can do better than even this!
Add PFR after mix point

24. Step 5
A PFR trajectory is drawn from the position where the mixing line meets the CSTR trajectory. If this PFR trajectory is convex, it extends the previous AR to form an expanded candidate AR. Then return to Step 2. Otherwise repeat Step 3

25. Solve PFR equations with modified initial conditions
Vary integration range
New feed point

26. Max. Attainable Region
(1-a)
PRF
CSTR a
0.38

27. Keep track of feed points
Initial feed point occurs at far right on AR
Mixing lines connect two points
Connect reactors and mixers with feed points to get network

28. Reactor configuration for highest selectivity
CA=1
CB=0
CSTR
PFR
CA=0.185
CB=
CA=0.38
CB=0.0001

29. Go back to calculations for optimal reactor sizing

30. Other factors to consider
Annualized, operating, and capital costs might favor designs that don’t give the highest selectivity
If objective function (e.g. $ = f{CA} + f{CB}) can be expressed in terms of the axis variable, a family of objective contours can be plotted on top of the AR
The point where a contour becomes tangent to the AR is the optimum
Temperature effects
Changing temperature will change the AR
Need energy balance for non-isothermal reactions
Make sure to keep track of temperature

31. Profit ($) = 15000*CB-15*CA2 Optimal point not at highest selectivity
PFR
CSTR

32. Conclusions Need to know feed conditions
AR graphical method is 2-D and limited to 2 independent species
Systems with rate expressions involving more than 2 species need to be reduced
Atom balances are used to reduce independent species
Independent species = #molecular species - #atomic species
If independent species < 2, AR can be used by Principle of Reaction Invariants