Effects of Pressure Drop

Effects of Pressure Drop Effects of Pressure Drop

Analyze the following second order gas phase reaction that occurs isothermally in a PBR:

Mole Balance
Must use the differential form of the mole balance to separate variables:

Rate Law
Second order in A and irreversible:

Stoichiometry

Isothermal, T = T₀

Combine

Need to find (P/P₀) as a function of W (or V if you have a PFR).

Pressure Drop in Packed Bed Reactors

Ergun Equation

Variable Density

let

Catalyst Weight

where

let

then

Isothermal Operation

let

then

recall that

notice that

The two expressions are coupled ordinary differential equations. We can solve them simultaneously using an ODE solver such as Polymath. For the special case of isothermal operation and epsilon = 0, we can obtain an analytical solution.

Polymath will combine the mole balance, rate law and stoichiometry.

Analytical Solution

Combine

Solve

Could now solve for X given W, or for W given X.

Pressure and Reaction Orders

Engineering Analysis

We want to learn how the various parameters (particle diameter, porosity, etc.) affect the pressure drop and hence conversion. We need to know how to respond to "What if…" questions, such as:

"If we double the particle size, decrease the porosity by a factor of 3, and double the pipe size, what will happen to D P and X?"

To answer these questions we need to see how a varies with these parameters.

Turbulent Flow

Compare Case 1 and Case 2:

For example, Case 1 might be our current situation and Case 2 might be the parameters we want to change to.

For constant mass flow through the system = constant

Laminar Flow

Effect of Reducing Particle Size on Conversion in a PBR

POLYMATH

Consider the following gas phase reaction carried out isothermally in a packed bed reactor. Pure A is fed at a rate of 2.5 moles/s and with , and a = 0.0002 kg^-1.

2A B

Mole Balance

Elementary

Rate Law

Stoichiometry

Gas with T = T₀

A B/2

POLYMATH will combine everything

________________

Profiles

"What Four Things are Wrong with this Solution?" (Chapter 4)

Spherical Reactors

Mole Balance
Stoichiometry
Cross-sectional Area
Pressure Drop Equations



Combine	Polymath will combine for you

Go Back

Ergun Equation
Variable Density

let

Catalyst Weight
where


let
then



Isothermal Operation

let
then
recall that
notice that
	The two expressions are coupled ordinary differential equations. We can solve them simultaneously using an ODE solver such as Polymath. For the special case of isothermal operation and epsilon = 0, we can obtain an analytical solution. Polymath will combine the mole balance, rate law and stoichiometry.