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Mole balance for chemical reaction engineering (Design Equations for reactors) Lec 3 week 3 The General Mole Balance Equation • To perform a mole balance on any system, the system boundaries must first be specified. The volume enclosed by these boundaries is referred to as the system volume. where Nj , represents the number of moles of species j in the system at time t. • The rate of generation of species j is expressed as The product of the reaction term and can be written in more familiar terms, GA = rA V • V is volume of the system. • Note that the units for this relation are consistent: mass mass volume time volume.time • If GA (and hence rA) varies with position in the system volume, we can take this into account by evaluating this term at several locations. Then DGA1 = rA1 DV1, • Summing the reactions over the entire volume yields: k k i 1 i 1 G A DG Ai rAi DVi k • As (that is, as we decrease the size of these cubes and increase their number) then DV 0 which gives V GA r A dV we now replace G in equation (1) to get : • From this general mole balance equation we can develop the design equations for the various types of industrial reactors: batch, semi-batch. and continuous- flow. Types of Reactors • Batch – No flow of material in or out of reactor – Changes with time • Fed- Batch (semi batch) – Either an inflow or an outflow of material but not both – Changes with time • Continuous – Flow in and out of reactor – Continuous Stirred Tank Reactor (CSTR) – Plug Flow Reactor (PFR) – Steady State Operation ( no change with time) General Mole Balance in terms of number of moles Batch reactor mole balance • Generalized Design Equation for Reactors • No flow into or out of the reactor, then, FA = FA0 = 0 • Good mixing, constant volume dN A rAV dt Batch Reactor Batch Reactor Fed Batch Reactor • Reactor Design Equation V FA0 FA dN A rA dV dt • No outflow FA = 0 • Good Mixing rA dV term out of the integral dN A FA0 rA V dt Continuous Stirred Tank Reactor CSTR • General Reactor Design Equation V FA0 FA dN A rA dV dt • Assume Steady State • Well Mixed • So V dN A 0 dt rA dV VrA FA0 FA VrA 0 or FA0 FA V rA CSTR Tubular Reactor (Plug Flow Reactor) (PFR) • Tubular Reactor • Pipe through which fluid flows and reacts. • Poor mixing • Difficult to control temperature variations. • An advantage is the simplicity of construction PFR Design Equation • Design Equation V FA0 FA dN A rA dV dt • Examine a small volume element (DV) with length Dy and the same radius as the entire pipe. Flow of A into Element Flow of A out of Element • If the element is small, then spatial variations in rA are negligible, and Assumption of “good mixing” V rA dV rA DV applies only to the small volume element • If volume element is very small, then assume steady state with no changes in the concentration of A. dN A 0 dt • Simplify design equation to: FA y FA y Dy rADV 0 • rA is a function of position y, down the length of the pipe and reactant concentration • take the limit where the size of a volume element becomes infinitesimally small dFA rA lim Dv 0 dV This is the Design Equation for a PFR • take the limit where the size of a volume element becomes infinitesimally small dFA rA lim Dv 0 dV • or because Dy A = V, dFA rA dV • This is the Design Equation for a PFR • Bioapplications - Sometimes hollow fiber reactor analysis is simplified to a PFR Plug Flow Reactor Mole Balance PFR: The integral form is: dFA FA 0 r A V FA This is the volume necessary to reduce the entering molar flow rate (mol/s) from FA0 to the exit molar flow rate of FA. Packed Bed Reactor PBR FA0 FA rdW dNdt A A The integral form to find the catalyst weight is: dFA FA 0 rA W FA Reactor Mole Balance Summary