CRO 410

Study Themes

You should start by reading all the outcomes covered in CKN 320

• The 3 basic type of ideal reactors: batch (BR), CSTR and PFR with their corresponding mole balances.
• The essential difference between a PFR and CSTR, gradual change accompanied by a profile versus an immediate change to a single outlet state.
• Understand why a PFR and BR will always be represented by a differential equation and a CSTR by an algebraic equation.
• The rate expression with its temperature and concentration dependence, and the fact that the rate expression is independent of the reactor type.
• The different definitions of reaction rate as reflected in the units and the scalar quantities that relate the different formulations.
• The relativity of conversion – why it is always related to a chosen basis – see reactor staging in CKN320.
• The importance of understanding the ideal gas law.
• The effect of volume (BR) or volumetric flowrate (CSTR &PFR) changes on concentration. See ε description for conversion.
• When to use a PFR and when to use a CSTR (in terms of minimising the volume/catalyst amount). See Levenspiel plots.
• Reversible reactions – the effect of temperature on reaction rate (Arhenius) and reaction equilibrium (van Hoff) – and the difference between “speed” and “boundaries”.
• Understand that single reactions can be represented by one variable describing the composition change (x,Ci,Fi), while multiple reactions need a variable per reaction.

Pressure drop in packed bed reactors

• You should be able to apply Ergun equation correctly - with specific focus on units.
• You should understand the derivations done for pressure drop if an ideal gas used – this is directly linked to last year’s ideal gas law derivations.
• You should be able to simultaneously solve a packed bed mole balance combined with the pressure drop equation for a gas phase reaction. Note that the two differential equations are inter-related and need to be solved simultaneously. Lower pressure implies a decrease in concentration and thus a decrease in reaction rate.
• You should understand why liquid phase pressure drop in a packed bed was not discussed in class.

Semibatch reactors

• You should be able to perform a generic mole balance on any flow-batch reactor hybrid.
• You should be able to manipulate the balances into a solvable format – e.g. multiple differential equations with the same amount of unknowns as equations.
• You should be able to obtain the numerical solution to the system of equations.

Multiple reactions

• You should be able to determine the overall (net) rate expression correctly.
• You should be able to set up all the necessary equations to solve a multi - component system. Note that although the equations are more involved, the basics remain the same.
• Should understand why conversion accompanied by the 1+εx description for gasses cannot be used for multiple reactions.
• You should understand why a PFR will result in multiple differential equations, while a CSTR will result in multiple algebraic expressions.
• You should realise that multiple solutions are possible for a set of non-linear algebraic expressions. What does this imply in practice?

Non-isothermal reactors

• You should understand the implications of the simplified assumptions made in this section. Constant mass based heat capacity with composition change implies stoichiometric relationships between the molar based heat capacities. Temperature independent heat capacities or heat capacities with the same temperature dependency imply that heat of reaction is a constant. We will use these simplifications in all CRO problems.
• You should realise that given the above assumptions all energy balances – for any type of reactor – reduces to a straight line relationship between conversion and temperature.
• For any exothermic adiabatic reactor the rate is dependant on the increase in temperature as well as the decrease in reactant concentration – two opposing effects resulting in a maximum rate at an intermediate conversion.
• For an adiabatic CSTR there will be two simultaneous equations (mole and energy) that might have multiple solutions (or steady states). The s-curve (mole balance) intersection(s) with the straight line (energy balance) is a graphical presentation of the above statement. Remember that the CSTR has the “jump” property – the concentration as well as the temperature jumps to the outlet condition on entering the reactor.
• Unlike the CSTR, the adiabatic PFR entails a gradual change in concentration and temperature along the length of the reactor. Since concentration and temperature both influences rate, the interdependency should be modelled by simultaneous equations (one differential and one algebraic).
• You should understand that for a non-adiabatic CSTR, the temperature- conversion relationship changes according to the direction and quantity of energy flow.
• For a non-adiabatic PFR, you should be able to derive the energy balance (given as a differential equation). You should be able to solve this equation simultaneously with the mole balance. Note that due to the plug flow assumption there is no radial temperature gradient.
• You should understand the shape of the equilibrium conversion vs. temperature graph. Note that for exothermic reactions, there is a severe restriction on equilibrium at higher temperatures.
• Understand the rate-equilibrium trade-off for exothermic reactions.
• You should be able to able to easily read the x-T-rA contour map.
• Understand the principle of a maximum adiabatic rate given a certain inlet
• temperature.
• Understand the optimum temperature profile, this implies that a specific composition has an optimum temperature to maximise reaction rate.

Mixing effects in reactors

• Understand what a pulse tracer and RTD is. The fact that the RTD is based on an inert to measure mixing should be confused with the reaction also occurring in the reactor.
• Know and understand the RTD’s of ideal reactors.
• You should be able to calculate the relative distribution E, average residence time and standard deviation of a given discrete distribution.
• Clearly understand the effect of mixing on reactor performance, with specific focus on the effect of size differences for a specified high conversion (x>0.95).
• You should clearly understand from the class example why a RTD on its own is not sufficient to predict reactor conversion and why additional assumptions (in the form of a proposed model) are required.
• You should be able to calculate conversion given a RTD and the segregated model assumption.
• You should understand that the segregated model and maximum mixedness model only narrows the conversion range for a given RTD (unless for first order reactions where pinpointing is possible).
• You should be able to apply the CSTR in series model on first and higher order system. Given an experimental RTD you should be able to estimate the number of CSTR’s in series.
• You should understand the basic assumption of the dispersion model and how the Peclet number quantifies the amount of (back)mixing in a reactor.
• You should know how to use correlations to estimate the Peclet number.
• You should be aware of the link between the dispersion model and the CSTR in series model and understand why this is very useful when determining reactor performance.

External mass transfer (fluid-solid)

• Understand the analogy with the beer drinkers and the waitresses and why there will be a rate controlling (or rate determining) party.
• Understand that the rate of mass transfer is always equal to the rate of reaction at steady state no matter whether the reaction is rate or mass transfer controlled.
• Understand the boundary layer description with its simplifications.
• Be very comfortable with all the different rate definitions (in terms of the basis) – and always check the dimensions of an equation.
• Understand that the mole balance from CKN applies to the bulk concentration and never to the surface concentration.
• Clearly understand how mass transfer can lower the surface concentration and accordingly slow down the rate.
• Clearly understand the extremes of simultaneous mass transfer and reaction (surface concentration almost zero compared to the surface concentration the same as bulk concentration)
• Make sure you realise that the keff description used on the slides is only for first order reactions.
• Understand the notion of apparent kinetics with the implication that all measured kinetics are either slower or the same as the true kinetics.
• You should be able to estimate the mass transfer coefficient.
• Note the effect of diameter on kc and external area as well as the effect of velocity on kc.
• Be familiar with the concept of equimolar counter diffusion and why this implies that mass transfer for products is exactly opposite to that of reactants.
• You should be able to use the shrinking core model for ash-diffusion and rate controlled processes.

Intra-particle mass transfer

• Understand that there exist different diffusional lengths to different active sites.
• Understand that slow diffusion (compared to the reaction needs) results in a depleted zone (low reactant concentrations) in the center of a spherical catalyst.
• Understand how the depleted zone (where the concentration of reactant on the active site is lower than the reactant external surface concentration) results in the catalyst giving a smaller overall rate than what the rate would have been if the reactant external concentration was present on all active sites. The ratio if the rates is defined as the effectiveness factor.
• Understand that the mole balance over a single particle results in the parameter called the Thiele modulus and that this parameter is a direct indication of the effect (or non-effect) of intraparticle diffusion.
• Note that this parameter can only be determined if the true potential (intrinsic rate constant and order) of the catalyst is known.
• Note the handy relationship between effectiveness factor and Thiele modulus for first order reactions on spherical catalysts.
• Be very comfortable with the 3 possible regimes and note that some relationships can only be used in certain regimes.
• Understand how the internal mass transfer controlled regime can alter the rate constants, activation energy as well as rate orders.
• Be familiar with the Weisz-Prater parameter and its usefulness when dealing with measured results (of which the regime is unknown)
• Realise that external and internal mass transfer effects can simultaneously affect the observed rate.

Slurry Bed reactors

• Understand the additional mass transfer step and its description (gas to liquid)
• Understand how the overall reaction rate can be expressed in terms of the 3 mass transfer processes (G-L, L-S and internal) and the intrinsic rate constant.
• Understand how the rate as a function of catalyst concentration can be visualised in a simple manner and how this graph is very useful in determining the rate controlling steps.