Industrial and applied chemistry

Reaction engineering, heat and mass transfer

Connect intrinsic reaction kinetics with reactor-scale mixing, residence time, heat removal and diffusion to predict conversion, selectivity and stability.

1 Lower secondary 2 Upper secondary 3 Undergraduate 4 Advanced 5 Research

IntuitionFrom molecules to reactors

A rate law measured under well-mixed, isothermal conditions is not yet a reactor design. Flow, mixing, heat exchange and transport through catalyst pores reshape local concentrations and temperatures; reactor engineering couples these effects to the chemistry.

Definition: Residence time

For a steady flow reactor, the nominal space time is reactor volume divided by volumetric feed rate, $\tau=V/\dot V_0$ . It is a useful scale, not a guarantee that every fluid element spends exactly that long in the reactor; the residence-time distribution describes the spread.

SchoolIdeal reactor models

\text{Batch: }\frac{dC_A}{dt}=r_A;\quad \text{CSTR: }F_{A0}-F_A+r_A V=0;\quad \text{PFR: }\frac{dF_A}{dV}=r_A

A batch reactor has no inlet or outlet during reaction. A continuous stirred-tank reactor (CSTR) assumes uniform conditions at its outlet and throughout the tank; a plug-flow reactor (PFR) assumes axial progression with negligible back-mixing. These idealizations provide balances whose predictions are starting points for equipment design.

Example: First-order conversion

For an irreversible first-order liquid reaction with rate $-r_A=kC_A$ , an ideal PFR gives $X=1-e^{-k\tau}$ . At $k\tau=1$ , conversion is about 0.63. The same rate law in an ideal CSTR gives $X=k\tau/(1+k\tau)=0.50$ , because the whole tank remains at the lower outlet concentration.

Solution

The design equation integrates the local rate along reactor volume. A PFR sees high reactant concentration near its inlet; a CSTR operates everywhere at its outlet concentration. Thus the PFR gives higher conversion for this positive-order reaction at equal volume and feed rate.

UndergraduateHeat transfer changes the kinetics

\frac{dT}{dt}\;\text{or}\;\frac{dT}{dV}\sim\frac{(-\Delta H_r)(-r_A)}{\rho C_p}-\frac{UA(T-T_c)}{\rho C_p V}

For an exothermic reaction, heat release raises temperature; Arrhenius kinetics then often accelerates the reaction, raising heat release further. Cooling duty, mixing and reactor geometry determine whether this feedback is controlled or produces hot spots and thermal runaway. Endothermic reactions instead require heat supplied at a sufficient rate to avoid quenching the chemistry.

AdvancedMass transfer and catalyst effectiveness

A reactant may cross a fluid film, diffuse through catalyst pores, and only then react at an active site. If diffusion is slow relative to reaction, the measured pellet-scale rate falls below the intrinsic rate. The effectiveness factor $\eta$ compares these rates; external-film resistance and internal pore diffusion are distinct limitations and call for different remedies.

\eta=\frac{\text{observed rate in porous catalyst}}{\text{rate if the whole catalyst were at surface conditions}},\qquad 0<\eta\le 1

Definition: Damköhler number

A Damköhler number compares a characteristic reaction rate with a transport or flow timescale. For a first-order reaction in a plug-flow setting, $Da=k\tau$ ; large $Da$ means reaction is fast relative to residence, while small $Da$ signals that contact time or intrinsic kinetics may limit conversion. Other geometries define corresponding Damköhler groups differently.

ResearchResearch frontier

References

Chemical Reaction Engineering · Octave Levenspiel, 1999
Elements of Chemical Reaction Engineering · H. Scott Fogler, 2016
Transport Phenomena · R. Byron Bird, Warren E. Stewart, Edwin N. Lightfoot, 2002
Diffusion and Reaction in Porous Catalysts · E. W. Thiele, 1939