Ahmed Abdala

Department of Chemical EngineeringThe Petroleum InstituteAbu Dhabi, UAE

𝑟𝑖 =1

𝑉

𝑑𝑁𝑖𝑑𝑡

= 𝑓 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 𝑟𝑒𝑔𝑖𝑜𝑛 𝑜𝑓 𝑣𝑜𝑙𝑢𝑚𝑒 𝑉

Homogenous reactor type◦ Batch reactors◦ Steady state flow reactors◦ Unsteady state semibatch reactor

1

Fj

Consider the volume enclosed by the boundaries (system volume)

The mole balance of species j:

𝐼𝑛 − 𝑂𝑢𝑡 + 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛

𝑟𝑎𝑡𝑒 𝑜𝑓𝑓𝑙𝑜𝑤

𝑜𝑓 𝑗 into𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚

𝑚𝑜𝑙𝑒𝑠/𝑡𝑖𝑚𝑒

−

𝑟𝑎𝑡𝑒 𝑜𝑓 𝑓𝑙𝑜𝑤𝑜𝑓 𝑗 𝑜𝑢𝑡 𝑜𝑓𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚

𝑚𝑜𝑙𝑒𝑠/𝑡𝑖𝑚𝑒

+

𝑟𝑎𝑡𝑒 𝑜𝑓 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑜𝑓 𝑗 𝑏𝑦 𝑐ℎ𝑒𝑚𝑖𝑐𝑎𝑙𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 𝑤𝑖𝑡ℎ𝑖𝑛𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚

𝑚𝑜𝑙𝑒𝑠/𝑡𝑖𝑚𝑒

=

𝑟𝑎𝑡𝑒 𝑜𝑓 𝑎𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑜𝑓 𝑗 𝑤𝑖𝑡ℎ𝑖𝑛𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚

𝑚𝑜𝑙𝑒𝑠/𝑡𝑖𝑚𝑒

𝐹𝑗0 − 𝐹𝑗 + 𝐺𝑗 =𝑑𝑁𝑗

𝑑𝑡

The energy balance equation

𝑟𝑎𝑡𝑒 𝑜𝑓ℎ𝑒𝑎𝑡𝑓𝑙𝑜𝑤 𝑖𝑛𝑡𝑜𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑜𝑓 𝑣𝑜𝑙𝑢𝑚𝑒

𝐽𝑜𝑢𝑙𝑒/𝑡𝑖𝑚𝑒

−

𝑟𝑎𝑡𝑒 𝑜𝑓ℎ𝑒𝑎𝑡𝑓𝑙𝑜𝑤 𝑜𝑢𝑡 𝑜𝑓𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑜𝑓 𝑣𝑜𝑙𝑢𝑚𝑒

𝐽𝑜𝑢𝑙𝑒/𝑡𝑖𝑚𝑒

+

𝑟𝑎𝑡𝑒 𝑜𝑓 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑜𝑓 ℎ𝑒𝑎𝑡 𝑏𝑦 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛𝑤𝑖𝑡ℎ𝑖𝑛 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑜𝑓 𝑣𝑜𝑙𝑢𝑚𝑒

𝐽𝑜𝑢𝑙𝑒/𝑡𝑖𝑚𝑒

=

𝑟𝑎𝑡𝑒 𝑜𝑓𝑎𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 ℎ𝑒𝑎𝑡

𝑤𝑖𝑡ℎ𝑖𝑛 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑜𝑓𝑣𝑜𝑙𝑢𝑚𝑒

𝐽𝑜𝑢𝑙𝑒/𝑡𝑖𝑚𝑒

Fj0

System volume

Gj

Constant density batch or flow reactor

◦ 𝑋𝐴 = 1 −𝐶𝐴

𝐶𝐴0and d𝑋𝐴 = −

𝑑𝐶𝐴

𝐶𝐴0

◦𝐶𝐴

𝐶𝐴0= 1 − 𝑋𝐴 and d𝐶𝐴 = −𝐶𝐴0𝑑𝑋𝐴

3

Flow Reactor

Batch Reactor

Gas phase and Constant and T◦ 𝑉 = 𝑉0 1 + 𝜀𝐴𝑋𝐴

◦ 𝑋𝐴 =𝐶𝐴0−𝐶𝐴

𝐶𝐴0+𝜀𝐴𝐶𝐴and d𝑋𝐴 = −

𝐶𝐴0 1+𝜀𝐴

𝐶𝐴0+𝜀𝐴𝐶𝐴2

◦𝐶𝐴

𝐶𝐴0=

1−𝑋𝐴

1+𝜀𝐴𝑋𝐴and

d𝐶𝐴

𝐶𝐴0= −

1+𝜀𝐴

1+𝜀𝐴𝑋𝐴2 𝑑𝑋𝐴

◦ ε𝐴 =𝑉𝑋𝐴=1−𝑉𝑋𝐴=0

𝑉𝑋𝐴=0

𝑎𝜀𝐴

𝐶𝐴0=

−𝑖𝜀𝑖𝐶𝑖0

𝐶𝐴0𝑋𝐴

𝑎=

−𝐶𝑖0𝑋𝑖

𝑖

4

Gas phase and variable and T

◦ 𝑋𝐴 =1−

𝐶𝐴0𝐶𝐴

𝑍𝑇0𝑍0𝑇0

1+𝜀𝐴𝐶𝐴0𝐶𝐴

𝑍𝑇0𝑍0𝑇0

◦𝐶𝐴

𝐶𝐴0=

1−𝑋𝐴

1+𝜀𝐴𝑋𝐴

𝑍0𝑇0𝑍𝑇0

◦𝐶𝑖

𝐶𝐴0=

𝑖

𝑎+𝑖

𝑎𝑋𝐴

1+𝜀𝐴𝑋𝐴

𝑇0𝑇0

𝑎𝜀𝐴

𝐶𝐴0=

−𝑖𝜀𝑖𝐶𝑖0

𝐶𝐴0𝑋𝐴

𝑎=

−𝐶𝑖0𝑋𝑖

𝑖

5

A continuous stream of fluid enters a vessel at

temperature T0 and pressure 0, reacts there,

and leaves at T and .

a) A gaseous feed, T0 = 400 K, 0= 4 atm, CA0= 100,

CBO= 200, A + B 2 R , T = 300 K , = 3 atm, C A = 20 .

Find XA, XB, CB .

b) A gaseous feed, T0 = 1000 K, B= 5 atm, CA0= 100,

CBO= 200, A + B 5R, T = 400 K, = 4 atm, CA = 20.

Find XA,XB,CB.

6