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PFR design. Accounting for pressure drop. Chemical Reaction Engineering I Aug 2011 - Dec 2011 Dept. Chem. Engg., IIT-Madras. Overview. Notation PFR design equation (mass balance) Pressure drop equation Accounts for change in number of moles (due to reaction)

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pfr design accounting for pressure drop

PFR design. Accounting for pressure drop

Chemical Reaction Engineering I

Aug 2011 - Dec 2011

Dept. Chem. Engg., IIT-Madras

overview
Overview
  • Notation
  • PFR design equation (mass balance)
  • Pressure drop equation
  • Accounts for change in number of moles (due to reaction)
  • Does not consider phase change
  • Methodology, with examples
  • Liquid phase reaction: Calculations are simple
  • Gas phase reaction: Calculations are more involved
notation
Notation
  • Usual notation applies.
    • FA = molar flow rate of A, FT = total molar flow rate
    • V = volume of reactor, Q = volumetric flow rate
    • D = diameter and A = cross-sectional area of PFR, L = length of PFR, z = distance (between 0 and L)
    • T = temperature, R = universal gas constant, P = pressure, PA = partial pressure of A
    • x = conversion, e = fractional increase in number of moles for 100% conversion, for a given feed conditions.
    • k = rate constant, CA = concentration of A
    • r = density, m = viscosity
    • ff = friction factor, Re = Reynolds number
    • <Vav> = average velocity of the fluid in the PFR. Used sparingly.
    • Subscript “in” indicates inlet. E.g. FA-in is molar flow rate of A at the inlet.
definitions and formulas
Definitions and formulas

The following definitions are of use here:

Definition of ‘x’

Definition of ‘e’

Definition of CA

For gas phase only:

From ideal gas law

At constant temperature

formulas
Formulas

For liquid as well as gas phase

You don’t need to memorize these formulas

pfr design equation
PFR design equation
  • Steady state conditions
  • For a first order reaction
  • At constant temperature
pfr design equation7
PFR design equation
  • For any other order of reaction also, write the equation such that dx/dz = f(x,P). i.e. The only unknowns on the RHS must be x and P
    • i.e. RHS must not have Q or CA. These are not known yet.
    • But Qin and CA-in are known and hence RHS may have these terms.
  • For an ‘n’th order reaction
pressure drop equation
Pressure Drop Equation
  • Under steady state conditions, Reynolds number is a constant
    • Even though local velocity changes
    • This is because density also changes with location
    • We assume that the viscosity of the medium remains the same, even when the reaction occurs
  • Under steady state conditions, (rQ) = constant
  • Using Re, Calculate the friction factor ff.
  • Write pressure drop equation
solution
Solution
  • Solve both equations simultaneously
  • Initial conditions:
    • At z =0, P = Pin
    • At z = 0, x = 0
  • Special case:
    • When e =0, solve the first equation and find ‘P’. Then substitute for ‘P’ in the second equation and solve for ‘x’
example
Example
  • Consider a gas phase reaction under isothermal conditions. (Isomerization)
  • A B
  • Pin = 10 atm, Q = 0.005 m3/s, T = 300 K, Pure A is fed, k = 0.1 lit/s, Molecular weight M = 60 g/gmol, Viscosity of the gas = 10-5 Pa-s
  • What should be the length of the PFR if it is constructed (a) using a 2 cm pipe and the conversion desired is 10%? (b) using a 1.5 cm pipe and the conversion desired is 10% and (c) using a 1.5 cm pipe and the conversion desired is 20%
solution11
Solution
  • e= 0. This simplifies the equations

R=0.08206 atm-lit/(gmol-K)

dia 1 5 cm
Dia = 1.5 cm
  • 10% conversion is possible, but 20% is not
2 nd order reaction k 0 01
2nd order reaction, k = 0.01
  • Coupled equations give correct answer