Handouts Handout 1: Practical reactor performance deviates from that of ideal reactor s : Packed bed reactor Channeling CSTR & Batch Dead Zones, Bypass PFR deviation from plug flow dispersion Deviation in residence times of molecules the longitudinal mixing caused by vortices and turbulence Failure of impellers /mixing devices Deviations In an ideal CSTR, the reactant concentration is uniform throughout the vessel, while in a real stirred tank, the reactant concentration is relatively high at the point where the feed enters and low in the stagnant regions that develop in corners and behind baffles. In an ideal plug flow reactor, all reactant and product molecules at any given axial position move at the same rate in the direction of the bulk fluid flow. However, in a real plug flow reactor, fluid velocity profiles, turbulent mixing, and molecular diffusion cause molecules to move with changing speeds and in different directions. The deviations from ideal reactor conditions pose several problems in the design and analysis of reactors. Non Ideal flow patterns: Short Circuiting or By-Pass Reactant flows into the tank through the inlet and then directly goes out through the outlet without reacting if the inlet and outlet are close by or if there exists an easy route between the two.
Handout 2: (Lecture 2, 3, 4) Residence Time Distribution Initially proposed by MacMullin and Weber (1935) and extensively studied by Danckwerts (1953). The time the atoms have spent in the reactor is called the residence time of the atoms in the reactor. Ideal plug-flow reactor: all the atoms of materials spend exactly the same amount of time inside the reactor. The idealized plug-flow and batch reactors are the only two classes of reactors that all the atoms in the reactor have the same residence time. The RTD of a reactor: A characteristic of the mixing within the chemical reactor. One of the most informative characterizations of the reactor. RTD Measurement: Injection (pulse/step) of a tracer (an inert chemical, molecular, or atom) into the reactor at time t = and measuring the tracer concentration in the effluent stream as a function of time. Tracer: non-reactive species easily detectable similar physical properties to those of the reacting mixture completely soluble in the mixture not adsorb on the walls/other surfaces in the reactor Colored and radioactive materials are most common types of tracers. The Pulse input of tracer:
C( E( C( C curve 2 Step Input: C out t C E(
F( t E( t 1 F ( E( Relation between F and E curve
For an ideal reactor, the space time,, (i.e., average residence time) is defined as V/v. The mean residence time, tm, is equal to in either ideal or nonideal reactors. t m te( E( te( V v vt m The spread of the distribution (variance): 2 2 t tm) ( E( If the distribution curve is only known at a number of discrete time values, ti, then the mean residence time is given by: Normalized RTD function: E( ) E( t / 1 E( 1 E( ) d
RTD in ideal Reactors: Handout 3: (Lecture 5, 6, 7) Reactor Modeling: When the fluid in a reactor is neither well mixed nor approximates plug flow (i.e., non ideal), one can use RTD data and some model to predict conversion in the reactor. Frequently used models include: Zero adjustable parameters segregation model
maximum mixedness model One parameter model tanks-in-series model dispersion model Two adjustable parameters real reactor modeled as combinations of ideal reactors Discuss the convolution method and sums based on above theory. Handout 4: (Lecture 8, 9, 1) Macromixing: a distribution of residence time without specifying how molecules of different ages encounter one another in the reactor. Micromixing: describe how molecules of different ages encounter one another in the reactor. Two extremes: complete segregation: all molecules of the same age group remain together during their staying in the reactor. complete micromixing: molecules of different age groups are completely mixed at the molecular level as soon as they enter the reactor. Segregation model: Flow is visualized in the form of globules Each globule consists of molecules belonging to the same residence time
Different globules have different Res. Times No interaction/mixing between different globules Discuss the mixing of two miscible fluids Handout 5: (Lecture 11, 12, 13) Dispersion Model: The Dispersion Model is used to describe non-ideal PFR Axial dispersion is taken into consideration Analogous to Fick s law of diffusion superimposed on the flow Backmixing or dispersion is used to represent the combined action of all phenomena, namely molecular diffusion, turbulent mixing, and non-uniform velocities, which give rise to a distribution of residence times in the reactor. If the reactor is an ideal plug flow, the tracer pulse traverses through the reactor without distortion and emerges to give the characteristic ideal plug flow response. If diffusion occurs, the tracer spreads away from the center of the original pulse in both the upstream and downstream directions.
Sums based on above theory. Handout 6: (Lecture 14, 15) Tank in Series Model: Derivation of N equal size CSTR s = n1 t E( ( n 1) n i e t / i
As the number becomes large, the behavior of the system approaches that of PFR