Pressure Drop in Reactor Design

Why does pressure drop matter in reactor design?

C_A \propto P

C_A is gas-phase concentration
P is pressure

In which reactors is pressure drop most important?

Gas-phase PFRs and packed-bed reactors

Why is pressure drop usually negligible for liquids?

\rho \approx \text{constant}

Why is pressure drop irrelevant in batch reactors?

\dot V = 0

What is the concentration–pressure relationship for an ideal gas?

CA = \frac{PA}{RT}

P_A is partial pressure of A
R is the gas constant
T is absolute temperature

What is the chain of effects caused by pressure drop?

P \downarrow \Rightarrow CA \downarrow \Rightarrow -rA \downarrow \Rightarrow X_A \downarrow

Why does pressure decrease along a reactor?

Friction, reactor length, volume change, change in moles, temperature effects

What is the dominant pressure-drop cause in CH4415 problems?

Frictional pressure loss

How does pressure vary along a PFR?

P = P(z), \quad \frac{dP}{dz} < 0

How does pressure drop affect residence time in a PFR?

\dot V \uparrow \Rightarrow \tau \downarrow

Why does pressure drop reduce conversion in a PFR?

-rA = f(CA), \quad C_A = f(P)

How is gas-phase concentration written including pressure drop and expansion?

CA = C{A,0}\frac{P}{P0}\frac{1 - XA}{1 + \varepsilon X_A}

C{A,0} is inlet concentration

P0 is inlet pressure
\varepsilon is expansion factor

What does the term \frac{P}{P_0}represent?

Pressure drop along the reactor

What does the term 1+εXA represent?

Stoichiometric expansion or contraction

Why must both pressure drop and stoichiometry be included?

CA = CA(P, X_A)

Why are packed-bed reactors especially sensitive to pressure drop?

Gas flows through catalyst particles causing high friction losses

Which equation is used to model pressure drop in packed beds?

Ergun equation

What qualitative trends follow from the Ergun equation?

\Delta P \uparrow \text{ with } \dot V \uparrow,\; L \uparrow,\; d_p \downarrow

L is bed length
d_p is particle diameter

Why must pressure drop be coupled with reactor design equations?

-rA = f(CA), \quad C_A = f(P), \quad P = f(z)

How many equations must be solved for a PFR with pressure drop?

Two: mole balance and pressure-drop equation

How are PFRs with pressure drop usually solved?

Numerically

What happens if pressure drop is neglected when it is significant?

V{\text{predicted}} < V{\text{actual}}

Why does ignoring pressure drop overpredict conversion?

C_A \text{ assumed constant}

What is the effect of pressure drop on required reactor volume?

P \downarrow \Rightarrow V \uparrow \text{ (for fixed } X_A\text{)}

When may pressure drop be neglected?

Short reactors, low flow rates, high gas density, liquid-phase systems

What must be done in exams if pressure drop is neglected?

Justify the assumption

Why is pressure drop rarely ignored in packed-bed reactors?

\Delta P_{\text{PBR}} \text{ is large}

What is the key design risk of ignoring pressure drop?

Underestimating reactor size

One-sentence exam definition of pressure drop effects

In gas-phase plug flow reactors, pressure drop reduces reactant concentration and reaction rate, leading to lower conversion and requiring larger reactor volumes than constant-pressure models predict