========================================================== Introduction to Chemical Engineering: Chemical Reaction Engineering Prof. Dr. Marco Mazzotti ETH Swiss Federal Institute of Technology Zurich Separation Processes Laboratory (SPL) July 14, 2015 Contents 1 Chemical reactions 2 1.1 Rate of reaction and dependence on temperature . .2 1.2 Material balance . .3 1.3 Conversion . .4 1.4 Energy balance . .5 2 Three types of reactors 6 2.1 Batch . .6 2.2 Continuous stirred tank reactor (CSTR) . .6 2.3 Plug flow reactor(PFR) . .7 3 Material balances in chemical reactors 9 3.1 Batch . .9 3.2 Continuous stirred tank reactor (CSTR) . .9 3.3 Plug flow reactor(PFR) . 10 4 Design of ideal reactors for first-order reactions 12 4.1 CSTR . 12 4.2 PFR . 13 4.3 Comparison of CSTR and PFR . 13 5 Dynamic behavior of CSTR during start-up 14 6 Reversible reactions 15 6.1 Material balance for reversible reaction . 15 6.2 Equilibrium-limited reactions . 16 7 Thermodynamics of chemical equilibrium 17 8 Energy balance of a CSTR 19 8.1 The general energy balance . 19 8.2 Steady-state in a CSTR with an exothermic reaction . 21 8.2.1 Stabiliy of steady-states . 21 8.2.2 Multiplicity of steady states, ignition and extinction temperatures . 22 8.3 Adiabatic CSTR . 23 1 CHEMICAL REACTIONS 8.3.1 Equilibrium limit in an adiabatic CSTR . 23 8.3.2 Multiple reactors in series . 25 Introduction Another important field of chemical engineering is that of chemical reaction engineering: considering the reactions that produce desired products and designing the necessary re- actors accordingly. The design of reactors is impacted by many of the aspects you have encountered in the previous lectures, such as the equilibrium and the reaction rate, both dependent on temperature and pressure. While there is a great variety of types of re- actors for different purposes, we will focus on three basic types: The batch reactor, the continuous stirred-tank reactor, and the plug-flow reactor. 1 Chemical reactions 1.1 Rate of reaction and dependence on temperature We will once again look at the formation of ammonia (NH3) from nitrogen and hydrogen (see section Chemical equilibrium of the thermodynamics chapter). This reaction follows the equation: N2 + 3H2 2NH3 (1) kJ ∆H0 = −92 mol J ∆S0 = −192 mol · K To find the Gibbs free energy of formation at room temperature, recall that ∆G0 = ∆H0 − T ∆S0 (2) kJ kJ kJ = −92 + (298 K) 0:192 = −35 mol mol · K mol ∆H0 Alternatively, one can also find the temperature for which ∆G = 0, T = ∆S0 = 479 K = 206◦C. At this temperature the equilibrium favors neither the reactants nor the products. At lower temperatures ∆G is negative, so the products are favored and the reaction goes forward. At higher temperatures the equilibrium shifts to favor the reactants, as is ex- pected for an exothermic reaction. We also introduced the stoichiometric coefficient νi that describes how many molecules of species i react in each occurrence of the reaction. In general, a reaction between species A and B forming C can be written as νAA + νBB ! νC C (3) The rate of generation of each component i is then the product of the stoichiometric coefficient and the rate of the reaction, and relates to the rate of generation of every other component as follows: 2 1 CHEMICAL REACTIONS ri = νir (4) ri r r r = r = A = B = C (5) νi νA νB νC Remember that the stoichiometric coefficients for reactants are negative, while those of products are positive. For systems of multiple chemical reactions the rates can be added to obtain the generation of component i for the whole network of reactions. As an example, take the oxidation of syngas, a mixture of carbon monoxide and hydrogen gas, where three reactions are to be considered, each having reaction rate rj (j = 1; 2; 3): 1 r1 :H + O −−! H O 2 2 2 2 1 r2 : CO + O −−! CO 2 2 2 r3 : CO + H2O −−! CO2 + H2 Using the stoichiometric coefficients, the rate of generation or consumption of each com- ponent is then given by: − RH2 = r1 + r3 RCO = −r2 − r3 − RH2O = r1 r3 RCO2 = r2 + r3 1 1 RO = − r1 − r2 2 2 2 Note that in these equations the subscript in rj indicates the reaction, whereas in Equations 4 and 5 it indicates the species. In general then, the rate of generation of component i in a system of reactions j = 1:::Nr is the sum of the rates of generation across all reactions: N N Xr Xr Ri = rij = νijrj i = A; B; ::: (6) j=1 j=1 The rate of each reaction then depends on the concentration of its reactants and the temperature, as described by the Arrhenius equation: a b −EA a b r = k(T )cAcB = k0e RT cAcB (7) where a and b are the reaction order with respect to reactant A and B, respectively. The overall order of the reaction is n = a + b. 1.2 Material balance Consider a system of volume V with a stream entering and one exiting, as shown in Figure 1. The accumulation of component i in this system is given by: dni in out = Fi − Fi + Gi (8) dt | {z } |{z} |{z} in−out net generation acc 3 Dx cin, Qin c, Q A 0 L 1 CHEMICAL REACTIONS W Q in out Fi Fi V in out Figure 1: System of volume V with a stream entering and one exiting. Fi and Fi are the mole flows of component i into and out of the system, respectively. W_ is the work done by the systems on its surroundings, and Q_ is the heat flow into the system. Here, the term Gi is the net generation for all reactions over the entire volume considered. Finding the net generation as well as the total amount of a component in the system requires integration over the whole volume: Z ni = cidV Z Gi = RidV (9) One assumption that is frequently made is that the system is homogeneous, at least over certain regions, so ni = V ci and Gi = VRi. This also means that the composition of the exiting stream is equal to the composition in the entire volume. Further, the mole flow of a component is often written as the product of the volumetric flow and the concentration of the component in the stream, so Fi = Qci. If one further assumes that only one reaction is taking place, the material balance becomes dni d (ciV ) in in = = Q c − Qci + riV (10) dt dt i 1.3 Conversion The conversion of component i is the fraction of the reactant that undergoes reaction. It is denoted as Xi, where moles of component i that reacted Xi = (11) number of moles of component i that were fed to the reactor For a continuous reactor at steady state this is in in Q ci − Qci Xi = in in (12) Q ci The desired conversion is a key parameter in the design of reactors, as we will see. 4 1 CHEMICAL REACTIONS 1.4 Energy balance Considering the volume in Figure 1, the energy balance can be written as: N N dE Xc Xc = Q_ − W_ + F inein − F outeout (13) dt i i i i i=1 i=1 The work in this equation consists of three terms: the so-called shaft work W_ s, and the volumetric work done by the entering stream on the system and by the system on the exiting stream. out out in in W_ = W_ s + P Q − P Q (14) The shaft work refers to the work done by the stirrer, for example, and is typically neg- ligible in chemical systems, so W_ s ≈ 0. The energy in the streams is summed for all Nc components, and can also be written in terms of concentrations and volume flow: N N N Xc Xc Q Xc Q Fiei = Q ciei = niei = E (15) V V i=1 i=1 i=1 E is the sum of the internal energy U, the kinetic energy K, and the potential energy EP . The kinetic and the potential energy are negligible in many chemical reaction engineering applications, so Equation 15 becomes Q Q ∼ Q E = (U + K + EP ) = U (16) V V V we know that U is a function of the enthalpy, pressure, and volume, so N N Q Q Q Xc Xc U = (H − PV ) = nihi − PQ = Fihi − PQ (17) V V V i=1 i=1 When this is applied for both streams, the term PQ cancels with the volumetric work from Equation 14, and the energy balance in Equation 13 becomes dU out out in in X in in X out in in out out = Q_ − W_ s + P Q − P Q + F h − F hi − P Q + P Q dt i i i i i dU X in in X out = Q_ + F h − F hi (18) dt i i i i i If we are considering a homogeneous system where only one reaction takes place, Gi = V νir, and we can rewrite Equation 8 by solving for the flow out of the system: out in dni F = F + V νir − (19) i i dt Equation 18 then becomes dU X in in X X dni = Q_ + F h − hi − V r νihi + hi (20) dt i i dt i i i Note that the sum of the enthalpies of each component multiplied by their corresponding P stoichiometric coefficient is the heat of reaction, so V r i νihi = V r∆Hr. At the same time, the difference in molar enthalpy between the entering stream and the reactor depends 5 2 THREE TYPES OF REACTORS on the temperatures and the specific heat of each component (assuming that there is no phase change): Z T in in in in ∼ in hi − hi = hi T − hi (T ) = cp;idT = cp;i T − T (21) T Further, the heat transfer into the reactor is Q_ = −UA (T − Ta), where U is the heat transfer coefficient, A is the heat transfer area, and Ta is the ambient temperature or the temperature of the heat transfer fluid.