IMPORTANT CONCEPTS in Kinetics/Reactor Design:

Thermodynamics:

• Thermodynamics does not predict kinetics.  A more-negative, free-energy change  (i.e., a larger equilibrium constant) does not imply a faster reaction rate.
  
• Catalysts can only increase the rate of processes that are thermodynamically favored;  they cannot initiate reactions that are not thermodynamically feasible.  A catalyst does not change ΔG, ΔH, or the equilibrium constant.
  
• Three of the most important calculations for a reactor are:
  adiabatic temperature: if the heat released for an exothermic reaction is not removed, this temperature will be attained at complete conversion.
  equilibrium composition: no reactor can produce yields of products beyond those predicted by equilibrium, but we can often choose which reactions to consider in the equilibrium calculations (see below).
  isothermal heat load: heat must be removed (added) at the same rate at which it is generated (consumed) by a reaction.  The isothermal heat load will vary with time in a batch reactor, with distance in a plug flow reactor, and be invariant in a continuous stirred tank reactor operating at steady-state.
  
• As temperature increases for an exothermic reaction, equilibrium conversion decreases.  For an endothermic reaction, conversion increases.
  

Kinetics: Rate Laws and Mechanisms

• As long as a reaction is not limited by equilibrium or mass transfer, longer reaction times, higher temperatures, and more catalyst all increase conversion.  A reaction that takes place in 1 hr at 200^oC could take place in less than 1 s at 400^oC.
• The rate of reaction is often the product of a rate constant, which usually increases exponentially with temperature (relatively few reaction rates decrease with temperature), and reactant concentrations raised to some power.  The activation energy is the term in the exponential that determines how fast the rate increases with temperature.
• Most chemical processes involve multiple reactions. High temperature favors reactions with higher activation energies.  High reactant concentrations favor reactions with higher reaction orders.
• Local concentrations determine reaction rates (e.g., if a solid product forms from a pure liquid reactant, the concentration of reactant does not change).
• The steady-state approximation can be applied to a series of reaction steps by assuming that all reaction steps proceed at the same rate.
• The rate-determining step in a series of reaction steps is the step furthest from equilibrium, and all the other steps are assumed to be in quasi-equilibrium.
• For homogeneous reactions, rates are proportional to volume.  In contrast, for heterogeneous reactions, rates are proportional to surface area (catalyst surface area or interphase area).
  

Kinetics: Determination of Rate Parameters

• A kinetic rate expression cannot reliably be extrapolated outside the concentration, conversion, or temperature regime where the data were obtained.  The rate law is an intrinsic property of the reaction and not the reactor.
• For a first-order, isothermal reaction, fractional conversion (X) depends on time but not the initial concentration: 
  X = 1 - e^-kt .  Thus, half life (t_1/2: the time for X=0.5) contains the same information as the rate constant (k).  
  t_1/2 = (ln 2)/k
• A reaction mechanism can be suggested, but not proven, by fitting data to a rate expression derived from a reaction sequence.
• Four main techniques are used to determine rate parameters from experimental kinetic data:  isolation, half-lives, integration, and differentiation.  The method of integration, which makes use of conversion/time data available in integrated form, is usually used and is strongly preferred over the method of differentiation (which exacerbates the impact of experimental error on calculated rate coefficients).
  

Material & Energy Balances

• Material balances on individual components are most useful for reactor design:
  Accumulation(+ or -) = In(+) - Out(+) + Generation by reaction(+ or -)
• For systems with multiple reactions, solve at least as many material balances as the number of independent reactions.  A material balance can be solved for each component in the system.
• The first law of thermodynamics applies to reactors, both closed and open systems:
        dU/dt = Σ_i(F_iH_i)in – Σ_i(F_iH_i)out + Q - W
  where U = total internal energy of the system
  F_i = molar flow rate into or out of the reactor of a given component
  H_i = enthalpy per mole of a given component at inlet or outlet conditions (the heat of reaction is contained in these terms)
  Q = heat added (removed) per time;      W = work done by (to) system per time
• In an adiabatic reactor, the temperature change is approximately directly linearly proportional to the conversion.
• In viscous reaction systems, heat developed by agitator work is often an important term in the energy balance.
  

Ideal Reactors

• Not all molecules spend the same amount of time in a flow reactor, and the residence time distribution can affect both rate and selectivity.
• The material balances for batch reactors (BR) and plug flow reactors (PFR) are mathematically equivalent; time in a BR is equivalent to residence time in a PFR.
• Material entering an ideal continuous stirred tank reactor (CSTR) undergoes a step change in concentration and temperature. A CSTR operates at the exit temperature and concentrations.
• Though all reaction occurs in an ideal CSTR at constant concentration and temperature, molecules flowing through both ideal and real CSTRs have a broad distribution of residence times.  The residence time distribution of an ideal CSTR is exactly known.
• CSTRs are often used in series to decrease the average residence time required for a given conversion (relative to a single, large CSTR) or to narrow the residence time distribution to one closer to that of a PFR.
• Reactor temperature and concentrations can be sensitive to feed conditions. Reactor behavior is nonlinear because of the exponential Arrhenius rate constant, and reactors are the most likely equipment in a plant to explode.
• For an exothermic reaction in a nonisothermal CSTR (t_feed - t_reactor), multiple steady-states can exist (i.e., the material and energy balances have multiple solutions).  Multiple steady states are the result of energy feedback and the nonlinear behavior of the rate constant.  This can result in an unstable operating condition leading to a quench (the reaction stops) or a runaway (the reactor overheats).  Either situation can be dangerous and is to be avoided.
• Reactor volume, and thus heat generated for a homogeneous exothermic reaction, increase as the cube of the reactor dimension, but heat transfer through the external surface increases only as the square, so temperature control is much more difficult for larger reactors.  For exothermic reactions in jacketed reactors, an upper limit on reactor volume exists.  If the reaction is carried out in a reactor larger than this,  the heat cannot be removed as fast as it is generated without other means for cooling.
• For gas-phase reactions, when the number of moles change due to reaction, the concentrations of reactants change as a result, and flow rates and reaction rates also change.
• For series reactions, the more important variable is space time or reaction time and for positive order kinetics, higher selectivity to an intermediate is obtained in a PFR then in CSTR.
  

Catalysis & Mass Transfer

• A catalyst usually lowers the activation energy for reaction.
• The three most important attributes of a catalyst are selectivity, activity, and stability.  Often selectivity is the most important aspect.
• All catalysts deactivate, usually due to a loss of catalytic sites.
• A catalyst does more than allow a system to achieve its most thermodynamically stable state; it can selectively accelerate a desired reaction.  In the majority of industrial processes, the products are not those expected from full conversion.
• Many industrial reactions are limited by diffusion (mass transfer limited).  Concentration gradients external to a catalyst particle are determined from mass transfer coefficient correlations.  Concentration gradients within a porous catalyst particle are accounted for by an effectiveness factor.
• When catalytic reactions are not limited by mass transfer, the reaction rate for a given catalyst is proportional to its surface area.
• If a catalyst increases the rate constant of a forward reaction, it also increases the rate constant of the reverse reaction (microscopic reversibility).
  

The 'Real World' and Mixing

• Real processes involve multiple reactions.
• Most industrial chemical reactions are exothermic and heat transfer is often the most important design criteria.  Most biotech reactions are essentially athermal and, like other heterogeneous reactions, mass transfer is often the most important design criteria.
• Most chemical reactions are run in batch reactors, which are especially common in the pharmaceutical, biotech, polymer, and cosmetics industries.  Sizes vary from a few liters to over 200,000 liters.
• CSTRs are the next most common reactors, followed by PFRs and then by hybrid reactor types (catalytic fixed beds, fluidized beds, etc.)
• Whenever reaction rates are of the same magnitude as or faster than the mixing rate in a stirred reactor, mixing will have a serious impact on results. Poor mixing is a primary source of variability in products made in batch reactors.  The results for a reaction run in a poorly mixed CSTR may deviate strongly from those expected.
• There is no single "correct" agitator type.  Different agitator designs may perform equally well (or equally poorly) for a given application. Though some detailed design calculations can be carried out, workable designs are often developed by trial-and-error.
• Many reactions involve shear-sensitive materials, which severely limit the maximum mixing rate and make impeller and reactor design important.  Mixing becomes the limiting factor.