Chemical Reaction Engineering

Asynchronous Video Series

Chapter 8, Part 1:

Developing the Energy Balance. Adiabatic Operation

H. Scott Fogler, Ph.D.

Energy Balances

Energy Balances

User Friendly EquationsThese equations relate X and T, and Fi and T

User Friendly EquationsThese equations relate X and T, and Fi and T

User Friendly EquationsThese equations relate X and T, and Fi and T

User Friendly Equations

User Friendly Equations

User Friendly Equations

User Friendly Equations

User Friendly Equations

Energy Balance

Energy Balance

Energy Balance

Energy Balance

Energy Balance

€

H i = H io TR( ) + ˜ C p T − TR( )

Energy Balance

€

H i = H io TR( ) + ˜ C p T − TR( )

Energy Balance

€

H i = H io TR( ) + ˜ C p T − TR( )

Energy Balance

€

H i = H io TR( ) + ˜ C p T − TR( )

Energy Balance

€

H i = H io TR( ) + ˜ C p T − TR( )

From Chapter 1 we have:

€

Fi = Fi0 + υ iFA 0 X

From Chapter 1 we have:

€

˙ Q − ˙ W S + Fi 0H i 0 − Fi 0 H i − H i Fi 0 + υ iFA 0 X( )∑∑∑

€

Fi = Fi0 + υ iFA 0 X

From Chapter 1 we have:

€

˙ Q − ˙ W S + Fi 0H i 0 − Fi 0 H i − H i Fi 0 + υ iFA 0 X( )∑∑∑

€

H i∑ Fi 0 + υ iFA 0 X( ) = H iFi 0 + υ∑ 0H i

ΔHRX

1 2 4 3 4 FA 0 X

€

Fi = Fi0 + υ iFA 0 X

From Chapter 1 we have:

€

˙ Q − ˙ W S + Fi 0H i 0 − Fi 0 H i − H i Fi 0 + υ iFA 0 X( )∑∑∑

€

H i∑ Fi 0 + υ iFA 0 X( ) = H iFi 0 + υ∑ 0H i

ΔHRX

1 2 4 3 4 FA 0 X

€

˙ Q − ˙ W S − Fi 0 H i − H i 0( ) + ΔH RX FA 0 X = 0∑

€

Fi = Fi0 + υ iFA 0 X

From Chapter 1 we have:

€

˙ Q − ˙ W S + Fi 0H i 0 − Fi 0 H i − H i Fi 0 + υ iFA 0 X( )∑∑∑

€

H i∑ Fi 0 + υ iFA 0 X( ) = H iFi 0 + υ∑ 0H i

ΔHRX

1 2 4 3 4 FA 0 X

€

˙ Q − ˙ W S − Fi 0 H i − H i 0( ) + ΔH RX FA 0 X = 0∑

Heat of Reaction

€

H i T( ) = H i TR( ) + ˆ C pi T− TR( )

€

ΔH RX = H iυ i = υ iH io TR( ) + υ 0

ˆ C pi∑∑∑ T− TR( )

€

ΔH RX = ΔH Ro TR( ) + Δ ˆ C p T− TR( )

€

Fi = Fi0 + υ iFA 0 X

From Chapter 1 we have:

€

˙ Q − ˙ W S + Fi 0H i 0 − Fi 0 H i − H i Fi 0 + υ iFA 0 X( )∑∑∑

€

H i∑ Fi 0 + υ iFA 0 X( ) = H iFi 0 + υ∑ 0H i

ΔHRX

1 2 4 3 4 FA 0 X

€

˙ Q − ˙ W S − Fi 0 H i − H i 0( ) + ΔH RX FA 0 X = 0∑

Heat of Reaction

€

H i T( ) = H i TR( ) + ˆ C pi T− TR( )

€

ΔH RX = H iυ i = υ iH io TR( ) + υ 0

ˆ C pi∑∑∑ T− TR( )

€

ΔH RX = ΔH Ro TR( ) + Δ ˆ C p T− TR( )

€

Fi = Fi0 + υ iFA 0 X

€

ΔH RX =da

H D TR( ) +ca

H C TR( ) −ba

H B TR( ) − H A TR( )

€

=H io TR( )+ CPi T− TR( )

€

Fi0 H i − H i0( ) = Fi0Cpi T −Ti0( )∑∑

€

˙ Q − ˙ W S − Fi 0 H i − H i 0( ) + ΔH RX FA 0 X = 0∑

If Ti0=T0

€

˙ Q − ˙ W S + Fi 0C pi T − T0( ) − ΔH RX FA 0 = 0 X∑

€

FA = FA0 1− X( )

Writing the energy balance in terms of conversion:

€

rA

V

∫ dV = FA0 X

Writing the energy balance in terms of conversion:

€

FA = FA0 1− X( )

€

rA

V

∫ dV = FA0 X

Writing the energy balance in terms of conversion:

€

FA = FA0 1− X( )

€

Fi 0C pi T − T0( )∑ = FA 0θ iCpi∑ T − T0( )

€

rA

V

∫ dV = FA0 X

Writing the energy balance in terms of conversion:

€

FA = FA0 1− X( )

€

Fi 0C pi T − T0( )∑ = FA 0θ iCpi∑ T − T0( )

€

˙ Q − ˙ W S + FA 0 X ΔH RX TR( ) + ΔC p T − TR( )[ ] = FA 0 θ iCpi T − T0( )∑

€

rA

V

∫ dV = FA0 X

Writing the energy balance in terms of conversion:

€

FA = FA0 1− X( )

€

Fi 0C pi T − T0( )∑ = FA 0θ iCpi∑ T − T0( )

€

˙ Q − ˙ W S + FA 0 X ΔH RX TR( ) + ΔC p T − TR( )[ ] = FA 0 θ iCpi T − T0( )∑

Neglecting and rearranging:

€

˙ W S

€

˙ Q − FA 0 θ iCpi T − T0( )∑ + FA 0 X ΔH RX TR( ) + ΔC p T − TR( )[ ] = 0

€

FA = FA0 + rAdVV

∫ = FA 0 1− X( )

€

rA

V

∫ dV = FA0 X

€

Fi 0C pi T − T0( )∑ = FA 0θ iCpi∑ T − T0( )

€

˙ Q − ˙ W S + FA 0 X ΔH RX TR( ) + ΔC p T − TR( )[ ] = FA 0 θ iCpi T − T0( )∑

€

FA = FA0 + rAdVV

∫ = FA 0 1− X( )

€

rA

V

∫ dV = FA0 X

€

Fi 0C pi T − T0( )∑ = FA 0θ iCpi∑ T − T0( )

€

˙ Q − ˙ W S + FA 0 X ΔH RX TR( ) + ΔC p T − TR( )[ ] = FA 0 θ iCpi T − T0( )∑

€

FA = FA0 + rAdVV

∫ = FA 0 1− X( )

€

rA

V

∫ dV = FA0 X

€

Fi 0C pi T − T0( )∑ = FA 0θ iCpi∑ T − T0( )

€

˙ Q − ˙ W S + FA 0 X ΔH RX TR( ) + ΔC p T − TR( )[ ] = FA 0 θ iCpi T − T0( )∑

T

X

Slope ≈

€

ΔH Rxn

θ iC pi∑