Steady-state Nonisothermal reactor Design Part I CSTRs with Heat Exchange. PFRs with Heat Exchange.

Non Isothermal Process Most reactions are not carried out isothermally Focus is then on heat effects in chemical reactors Basic design equation such as rate laws, stoichiometric relationships used for isothermal reactor design are valid for non-isothermal reactors The major difference is method of evaluating the temperature effect e.g. length of PFR, or heat is removed from a CSTR

Non Isothermal Process So what additional information is needed to design non-isothermal reactors ? Example: For the following reaction A → B Calculate the reactor volume necessary for 70% conversion Note: The reaction is exothermic, reactor is operated adiabatically. So temperature increases with conversion down the length of reactor

Non Isothermal Process Solution: Mole Balance (design equation) Rate Law (Arrhenius equation) k = f(T)

Non Isothermal Process Stoichiometry (liquid phase), v = vo Combining and cancelling the entering concentration CA0=0

Non Isothermal Process The final equation We require a relationship which relates X and T, T and V to solve the above equation The energy balance will provide the relationship

Non Isothermal Process Energy Balance we need appropriate energy balance to relate temperature and conversion or reaction rate For adiabatic reaction we have So we have all equations needed to solve the conversion and temperature profile

The Energy Balances We know that for a closed system, the energy balance is For open (continuous) flow system where mass crosses the system boundaries

The Energy Balances The energy balance of the case of only one species entering and leaving becomes

The Energy Balances The unsteady-state energy balance for an open well-mixed system that has n species, entering and leaving the system at their respective molar flow rates Fi (moles of i per time) and their respective energy Ei (joules per mole of i)

The Energy Balances Evaluating work term W is separated into flow work (W) or other work (Ws) Ws is shaft work and produce such stirrer in CSTR or turbine in PFR Flow work is the work necessary to get the mass into and out of the system J/s

The Energy Balances Combining the energy balance term derived earlier and work term we get We know that In chemical reactor these energies are often negligible as compared to enthalpy, heat transfer and work term J/mol

The Energy Balances Enthalpy in case of into and out of the system can be expressed as the sum of the net internal energy carried into (or out of) the system by mass flow plus the flow work Combining we get We can also write

The Energy Balances Adiabatic (Q=0) CSTR, PFR, Batch or PBR. The relationship between conversion, XEB and temperature for Ws = 0, constant CPi and ∆CP = 0 For an exothermic reaction

CSTRs with Heat Exchange. Evaluating the Heat Exchange Term, Q

Evaluating the Heat Exchange Term, Q Rate of heat transfer from Exchanger

Evaluating the Heat Exchange Term, Q Energy transferred between the reactor and the coolant Assuming the temperature inside the CSTR, T, is spatially uniform Page 555

Evaluating the Heat Exchange Term, Q

Evaluating the Heat Exchange Term, Q Sub into the energy balance

CSTR sizing Algorithm Example AB 1. Design Eqn 2. Rate Law 3. Stoichiometry 4. Combining X specified Calculate V & T V specified Calculate X & T Calculate T Calculate k and KC Calculate V=FA0X/kCA0(1-X) Calculate XMB Calculate XEB Plot XEB vs T Plot XMB vs T Evaluate V from the graph Page 557

CSTR Algorithm

CSTR Algorithm XMB Conversion from mole balance XEB Conversion from energy balance

Example: Adiabatic Liquid Phase in A CSTR Given T Find X and V Also given k, E, CPA=CPB, ΔHRx  , CAo, and vo

Example: Adiabatic Liquid Phase in A CSTR

Example: Adiabatic Liquid Phase in A CSTR

Sketch XEB versus T

Mole Balance to Determine XMB=f(T) rearranging...

At the intersection of XMB vs. T and XEB vs. T both the mole balance and the energy balances are satisfied. The steady-state conditions (XSS,TSS) occur here. Examples 8-8, Example 8-9 (Page 563) Both the mole and energy balances are satisfied when XMB=XEB. The steady state temperature and conversion are TSS and XSS respectively for an entering temperature TO

Energy Balance on a PFR Page 496 , pdf page 528 a = heat exchange area per unit volume of reactor; for a tubular reactor, a = 4/D

Energy Balance on a PFR Energy Balance ΔQ+∑Fi0Hi0 -∑FiHi=            Catalyst weight is related to reactor volume by: Differentiate with respect to W

Energy Balance on a PFR Conversion as Variable or Flow Rate as Variable

Energy Balance on a PFR

Energy Balance on a PBR If we want to include pressure drop:

Balance on Heat Exchanger Coolant If Ta is not constant, then we must add an additional energy balance on the coolant fluid: with Ta = Tao at W = 0

Example 8-4 When we checked the vapor pressure at the exit to the adiabatic reactor in Example 8-3 where the temperature is 360K, we found the vapor pressure to be 1.5MPa for isobutane, which is greater than the rupture pressure of

P8-2 (d) How would the answers change if the reactor were in a counter current exchanger where the coolant temperature was not constant along the length of the reactor

P8-5 (3rd edn) The elementary irreversible organic liquid phase reaction A + B  C is carried out adiabatically in a flow reactor. An equal molar feed in A and B enters at 27C and volumetric flow is 2 dm3/s. Additional information HAo (273) = -20kcal/mol HBo (273)= -15kcal/mol HCo (273)= -41kcal/mol CA0= 0.1kmol/m3 CPA=CPB=15cal/mol.K CPC=30cal/mol.K k = 0.01 / dm3/mol.s at 300K E= 10000 cal/mol

(a) Calculate the PFR and CSTR volumes necessary to achieve 85% conversion A + B  C

(a) Calculate the PFR and CSTR volumes necessary to achieve 85% conversion

PFR X T k -rA FA0/-rA 300 0.01 1 2000

PFR X T k -rA FA0/-rA 300 0.01 1 2000 0.2 340 0.072 4.6 435 0.4 380 0.34 12.3 163 0.6 420 1.21 19.3 103 0.8 460 3.42 13.7 146 0.85 470 4.31 9.71 206

(b) What is the maximum inlet temperature one could have so that the boiling point of the liquid (550K) would not be exceeded even for complete conversion?

(b) What is the maximum inlet temperature one could have so that the boiling point of the liquid (550K) would not be exceeded even for complete conversion?

(b) What is the maximum inlet temperature one could have so that the boiling point of the liquid (550K) would not be exceeded even for complete conversion?

(c) Plot the conversion and temperature as a function of PFR volume (c) Plot the conversion and temperature as a function of PFR volume. Use Polymath

(d) Calculate the conversion that can achieved in one 500dm3 CSTR volume and in two 250dm3 CSTR in series Use Polymath for CSTR