Material balances (moles) Maurizio Fermeglia DIA Maurizio.fermeglia@untis.it Mose.units.it

Mole Balances, Conversion & Reactor Sizing What we expect to cover: general definitions - homogeneous/heterogeneous reactions, reaction rate. development of general mole balance and its application to common industrial reactors (batch and continuous) development of reactor design equations in terms of conversions application of design equations in reactor sizing

Chemical reaction A detectable number of molecules of one or more species have lost their identity and assumed a new form by a change in the kind or number of atoms in the compound and/or by a change in structure or configuration of these atoms. Decomposition Combination Isomerization Rate of reaction How fast a number of moles of one chemical species are being consumed to form another chemical species.

Homogeneous & Heterogeneous Reactions Homogeneous Reactions: reactions that occur in a single phase (gas or liquid) NO + O 2  NO 2 C 2 H 6  C 2 H 4 + H 2 Can be catalithic Heterogeneous Reactions: reactions that require the presence of two distinct phases Coal combustion SO 2 + 1/2 O 2  SO 3 (for sulphuric acid production) Reaction types Decomposition Combination Isomerization

Reaction Rate (-rA) for Homogeneous Reactions (-r A ) = rate of consumption of species A = moles of A consumed per unit volume per unit time The rate of formation of A is denoted as (r A ) Note: “minus” sign denotes consumption or disappearance Units of (-r A ) o (r A ) moles (or kilo moles) per unit volume and unit time mol/l-s or kmol/m3-s

Reaction rate (-r A ') for heterogeneous reaction For a heterogeneous reaction, rate of consumption of species A is denoted as (-r A ') Units of (-r A ') Moles per unit time per mass of catalyst mol/s-g or kmol/hr-kg catalyst

Is (-r A ) = dCa/dt ?? Steady state operation = no change with time C AO C A 10:00 am 50.0 10.0 12:00 pm 50.0 10.0 3:00 pm 50.0 10.0 5:00 pm 50.0 10.0 Neither C AO nor C A are changing with time  dca /dt = 0  ra=0 … which is impossible. Ethylene Oxide + water Ethylene Glycol

Reaction Rate - Functional form Reaction rate is NOT defined by a differential equation but it is defined by an algebraic equation Reaction rate is Function of T and concentrations Is independent from reaction type Reaction rate is described by a kinetic expression or rate law an algebraic equation that relates reaction rate to species concentration (-rA) = [k f (T)] · [f´(Concentrations)] (-rA)= k · [concentration terms] e.g. (-r A )= k C A ; (-r A )= k C A 2 or more complex (-r A )= k1 C A / (1 + k2 C A ) Note: a more appropriate description of functionality should be in terms of “activities” rather than concentration.

General Mole Balance Considers chemical species In and OUT of the reactor Mole balance in terms of chemical species, NOT atomic species Reaction rate --> number of reacting moles per unit time and volume (r, -r) Reactor sizing equations are different for types of reactors IN OUT GEN ACCUMULATION Ga= generation term = (ra) V (for homogeneous volume) Otherwise the integral holds

Reactor types Batch reactor Flow reactor Other Reactor Types Continuous-Stirred Tank Reactor (CSTR) Plug Flow Reactor (PFR) Packed Bed Reactor (PBR) Other Reactor Types Fluidized Bed Reactor Trickle Bed Reactor …..

Mole Balance for Batch Reactor Two different cases: 1. Constant Volume 2. Constant Pressure If reactor is perfectly mixed

Mole Balance for Batch Reactor Constant Volume (NA = CA V) Constant Pressure (NA = CA V)

Mole Balance for CSTR V V V Design equation valid with the following hypothesis: Steady state Reaction rate constant in space FAO X=0 V FA X=X

Example: CSTR One L/min of liquid containing A and B (C AO = 0.10 mol/l, C BO = 0.01 mol/l) flows into a mixed flow reactor of volume Vr=1.0 L. The materials react in a complex manner for which the stoichiometry is unknown. The outlet stream from the reactor contains of A, B and C at concentrations of C Af = 0.02 mol/l, C Bf =0.03 mol/l and C Cf =0.04 mol/l. Find the rate of reaction of A, B and C at conditions of the reactor.

Solution VR = 1.0 L vf = ?? CAO = 0.10 mol/L Basic Design Equation CBO = 0.01 mol/L CCO = 0.00 mol/L Basic Design Equation (-rj) = [Fjo - Fjf]/[VR] Approach Fj = Cj x v (molar flow rate) vf = vi = v conc. inside reactor = conc. in exit (-rj) = [Cjo-Cjf] [v]/ [VR] (-rA) = [0.10-0.02] [1]/[1] = 0.08 mol/min (-rB) = [0.01-0.03] [1]/[1] = – 0.02 mol/min (-rC) = [0.00-0.04] [1]/[1] = – 0.04 mol/min VR = 1.0 L vi = 1.0 L/min vf = ?? CAF = 0.02 mol/L CBF = 0.03 mol/L CCF = 0.04 mol/L

Mole Balance for a PFR Differential Form Integral Form Design equation valid with the following hypothesis: Steady state Reaction rate constant in space Note: conversion depends from VOLUME only (and not from shape) Differential Form Integral Form

PFR: derivation Mole balance for a generic volume V Steady state The derivative

Summary - Design Equations of Ideal Reactors Differential Equation Algebraic Integral Remarks Conc. changes with time but is uniform within the reactor. Reaction rate varies with time. Batch CSTR Conc. inside reactor is uniform. (rj) is constant. Exit conc = conc inside reactor. PFR Concentration and hence reaction rates vary spatially.

Exercise: PFR reactor sizing Reaction A  B cis-2-butene  trans-2-butene PFR First order reaction: -ra= kCa Constant volumetric flow rate v=v0 Determine A qualitative graph with the concentration profile as a function of V The equation giving the reactor’s volume as a function of inlet and outlet concentrations, constant k and volumetric flow rate v. The volume needed to reduce the concentration of A at 10% of the inlet one. Assume v= 10 liters /min and k = 0.23 min-1

PFR reactor sizing: solution A qualitative graph with the concentration profile Ca0 Ca V

PFR reactor sizing: solution Design equation for a PFR: For a first order kinetic: Volumetric flow rate v0 is constant: Substituiting rA: BC: V=0 for CA=CA0 With numbers …

Reactor Characteristics Batch Reactor mainly used for small scale operation suitable for slow reactions mainly used for liquid-phase reaction charge-in/clean-up times can be large CSTR steady state operation; used in series good mixing leads to uniform concentration and temperature mainly used for liquid phase reaction suitable for viscous liquids PFR suitable for fast reaction gas phase reaction temperature control is difficult there are no moving parts

Mole balance for Packet Bed Reactor - PBR Considers INLET and OUTLET species in the control volume Mole balance Rate law --> number of reacting moles for unity of time and volume (r, -r) Different sizing equations for different reactor types -r’A specific rate law for mass of catalyst IN OUT GEN ACCUMULATION Ga= generation term = r’ W mole balance in terms of mass of catalyst W

PBR: derivation Mass balance in terms of W Steady state Differentiation with respect to W

Mole balance for Packed Bed Reactor W Integral form Differential form

Industrial reactors

Hydrogenation reactors

Industrial reactors: liquid phase Batch Used for low scale productions, good for high value product (pharma, bio,…) Difficult temperature control High conversions High cost of labor, complex operation Semi Batch Like batch but with a better temperature control Good for minimizing secondary reactions Used for two-phase reactions (bubbles)

Industrial reactors: liquid phase CSTR Characterized by a strong mixing Used in series or in parallel Conversion is the lowest among flux reactors Easy to reuse old reactors (flexibility)

Industrial reactors: gas phase PFR Easy maintenance High conversion (the highest among flux reactors) Difficult temperature control Parallel pipes Cost (and construction) is similar to heat exchangers PBR (fixed bed) Similar to PFR, contains solid phase Catalytic reactions Fluidized bed Similar to CSTR (good mixing an temperature control) Must be modelled with specific equations Used for high productions

Industrial reactors Fixed bed Fluidized bed

Industrial reactors Slurry reactor

Reforming reactors (BP)

Reactor modelling in process simulators Demo on the use of: Aspen + PRO II COCO - COFE