Question 1 of 6: Uncertainties in Reactor Scale-up — Homogeneous vs. Heterogeneous Systems

Question 1: Uncertainties in Reactor Scale-up — Homogeneous vs. Heterogeneous Systems (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Overview. Scale-up magnifies every transport process that competes with the chemical reaction. In the laboratory a reactor is small, nearly isothermal and well mixed, so the measured performance is close to the intrinsic kinetics. As size increases, the ratio of heat-transfer surface to reacting volume falls (surface $\propto L^2$, volume $\propto L^3$, so $S/V\propto 1/L$), mixing times lengthen, and residence-time distributions broaden. Because the governing dimensionless groups (Reynolds, Péclet, Damköhler, Nusselt) cannot all be held constant at once, geometric and dynamic similarity cannot be preserved simultaneously — which is why staged scale-up through pilot units is required. The specific problem areas differ between single-phase (homogeneous) and multiphase (heterogeneous) systems.

Homogeneous reaction systems (single fluid phase). The reaction proceeds throughout the bulk fluid, so the dominant uncertainties are thermal and mixing related rather than interphase transport:

• Heat removal / thermal control. This is the classic homogeneous scale-up problem. The falling surface-to-volume ratio makes it progressively harder to add or remove the heat of reaction, so large vessels develop temperature gradients and hot spots; for exothermic reactions this raises the risk of thermal runaway and shifts selectivity and equilibrium.
• Mixing and micromixing. Achieving uniform concentration and temperature is far harder at scale. For fast or complex (series/parallel) reactions, imperfect micromixing and local segregation change the product distribution (selectivity/yield) even when the mean residence time is matched.
• Residence-time distribution and flow regime. Large vessels develop dead zones, short-circuiting and bypassing; the RTD broadens and departs from the ideal plug-flow or perfectly-mixed model assumed in the laboratory, and laminar/turbulent transitions may occur.
• Kinetic-data extrapolation. Rate constants and activation energies measured over a narrow lab window must be extrapolated to plant temperatures and pressures; unrecognised side reactions or trace-impurity/catalytic-wall effects may emerge only at scale.
• Hydraulics and control. Pressure drop, pump/compressor duty, larger thermal inertia, and the possibility of multiple steady states complicate stable control.

Heterogeneous reaction systems (two or more phases). Here the reaction occurs at an interface or within a catalyst particle, so interphase and intraparticle transport couple to the kinetics and usually govern scale-up:

• Mass- and heat-transfer (diffusion) disguise of the kinetics. Film (interphase) and pore (intraparticle) diffusion limit the observed rate; the effectiveness factor $\eta<1$, so the apparent rate and activation energy measured in the laboratory differ from the intrinsic values and do not extrapolate cleanly to plant particle sizes.
• Catalyst behaviour. Deactivation by coking, poisoning or sintering, mechanical attrition (in fluidized beds), and changes in activity/selectivity with time-on-stream are difficult to reproduce at scale; pellet size and shape affect both diffusion and pressure drop.
• Phase contacting and distribution. Gas–liquid mass-transfer coefficient $k_La$, interfacial area, gas hold-up, wetting efficiency in trickle beds, and liquid/gas maldistribution all change with diameter; poor distribution causes channelling and bypassing.
• Multiphase hydrodynamics. Fluidization regime transitions (bubbling → slugging → turbulent), minimum fluidization velocity, particle entrainment/elutriation, and packed-bed pressure drop (Ergun equation) are strongly scale-dependent; wall effects matter when the tube-to-particle diameter ratio $D/d_p$ is small.
• Thermal management. Radial and axial temperature gradients and local hot spots on catalyst pellets are severe in fixed beds for exothermic reactions (e.g. partial oxidations), threatening runaway and catalyst damage.

In short, homogeneous scale-up is dominated by heat transfer and mixing, whereas heterogeneous scale-up adds the harder problems of interphase/intraparticle transport, catalyst life and multiphase contacting. In both cases the safe route is to obtain rate and transport data on a pilot scale and to scale up in stages rather than to rely on a single large step.