ANFIS based Control Scheme for Binary Distillation Column

Component material balance equations

The constant molar holdup in reboiler has been considered i. e. dM_B/dt=0, so by this

B=L₁-V_B

Component material balance around reboiler is given by

Where

M_B= Liquid molar hold up in reboiler, kmoles,

L₁= Total liquid flow rate from tray-1 entering to reboiler, kmole/h,

x_B,j = Liquid fraction of component j in bottom product,% mole fractions,

V_B = Total vapor flow rate leaving reboiler, kmole/h,

y_B,j = Vapor fraction of component j in bottom product,% mole fractions,

B = Total bottom product rate, kmole/h,

The vapor fraction of component j from reboiler is given by

_Where

η1,jv= vaporization efficiency of component j in reboiler,

k1,j = Equilibrium constant of component j in reboiler

_{Total enthalpy balance equations}

_{Total enthalpy balance equation for reboiler is given by}

Where

h₁ = Total molar enthalpy of liquid entering from tray-1 to reboiler, kJ/kmole,

h_B = Total molar enthalpy of liquid leaving reboiler, kJ/kmole,

H_B = Total molar enthalpy of vapor leaving reboiler, kJ/kmole,

Q_B = Reboiler heat duty, kW

Component material balance equations

Component material balance equation for i^th tray is given by

y_ij is calculated as

Where

M_i= Molar liquid hold up on tray I, kmole

x_ij = Liquid fraction of component j, leaving the tray i, % mole fraction

L_i = Total liquid flow rate leaving tray-i, kmole/h

V_i = Total vapor flow rate leaving tray-i, kmole/h

F_i = Total feed flow rate injected to tray-i, kmole/h

x_Fij = Liquid fraction of component j in feed on tray i,% mole fractions,

y_ij = vapor fraction of component j leaving the tray i,% mole fractions,

ƞ_ij = Murphree stage efficiency based on vapor phase of component j on tray i

y_ij^* = Equilibrium vapor fraction of component j on tray i

L_i is an additional variable and it is related to M_i through

Where

l_w = Length of the weir, ft

A_net = Net area of the tray, ft²

h_w = Height of the weir, ft

M_Di = Average molar density of liquid on tray I, kmole/ft³

Total material balance equation for i^th general tray is calculated as

Where

L_i+1 = Total liquid flow rate entering to tray i, kmole/h,

V_i–1 = Total vapor flow rate entering to tray i, kmole/h,

F_i = Total feed flow rate injected on tray i, kmole/h

_{Enthalpy balance equation for general tray i}

_{Enthalpy balance equation for general tray i is given as}

Where

h_i = Total molar enthalpy of liquid leaving tray I, kJ/kmole,

H_i = Total molar enthalpy of vapor leaving tray I, kJ/kmole

Enthalpy on any tray are calculated by mixing rule as given by

Where

hl_ij = Pure component enthalpy of component j in liquid, kJ/kmole,

Hv_ij = Pure component enthalpy of component j in liquid, kJ/kmole

Next section i. e. III^rd section produces the modeling of condenser.

Component material balance equations

Reflux drum level is considered constant. This means at any time D=V_NT-R.

Component material balance around condenser is given by

Where

M_D= Liquid molar hold up in the reflux drum, kmole,

D = Distillate flow rate, kmole/h,

x_D,j = Liquid fraction of component j in reflux drum, % mole fractions

y_NT,j = Vapor fraction of component j leaving tray NT,% mole fractions,

R = Total liquid flow rate entering to the tray NT from reflux drum, kmole/h,

V_NT = Total vapor flow rate leaving the tray NT, kmole/h,

_{Enthalpy balance equation}

_{The enthalpy balance equation for liquid and vapor for condenser is}

Where

h_D = Total molar enthalpy of liquid leaving the reflux drum, kJ/kmole,

H_NT = Total molar enthalpy of vapor leaving the last tray NT, kJ/kmole,

Q_C = Condenser duty, kW

Simulation Algorithm

All the above equations have been utilized to simulate the model. The flow diagram of the simulation algorithm to develop the equation based model of binary distillation column is given in Figure 15. To simulate open loop binary distillation column the environment of MATLAB^®/SIMULINK^® is used.

Figure 15:

Simulation algorithm.

As mention in step 3, all the differential equations are solved by ode15 s, which is a variable-order multi step solver, based on the numerical differentiation formulas (NDFs). Optionally it uses the backward differentiation formulas, BDFs, (also known as Gear’s method). It works efficiently when the problem is suspected to be stiff.