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Many of the distillation processes of industry involve more than two components. While the principle established for binary solutions generally apply to such processes, but it becomes difficult to use graphical method. Hence we mosty use iteration ,Hit and trial method to reach solution.

In this section we will discuss Thiele-Gedde's method modified for constant liquid and vapor phase. It is assumed that we know about following specificaitons:

• Feed rate and composition temperature F , z_F, T_F
• Feed Plate Location
• Number of stages
• Distillate Fraction D/F
• Pressure of the column P
• Equilibrium vapourization constant K_ji as a fuction of temperature
• Reflux Ratio R

Assumptions made

• Constant liquid,vapor rates
• Temperature Profile is Linear

• Material Balance in Enriching section
  Vy_j+1,i = Lx_j,i + Dx_D,i ............. 1
  For plates from i = 1 to f (feed plate)
• In Striping section
  V'y_j,i = L'x_j-1,i - Bx_B,i ...........2
  For plates from i = f to N (bottom plate in column)
• From Equilibrium we have
  y_j,i = K_j,i x_j,i ........... 3
• From 1 & 3 we get
  x_j+1,i/x_D,i = 1/K_j+1,i[ (L/V)x_j,i/x_D,i + (V-L)/V].........4
  This equation is valid for all plates above feed plate
• Similarly from 2 & 3 we get
  x_j,i/x_B,i = 1/K_j,i[ L'/V' x_j-1,i/x_B,i + (V' - L')/V'].........5
  This equation is valid for all plates below feed plate
• From overall balance we get
  F = D + B
• Balance on component i
  Fz_F,i = Dx_D,i + Bx_B,i .........6
• Now we will assume a Temperature profile and will calculate ratios from 4 and 5 for all components on all plates
• Now from 4 we can get ratio
  x_F,i/x_D,i
  
• Also from 5 we can get ratio
  x_F,i/x_B,i
  
• From above equations we can get ratio
  x_B,i/x_D,i........7
• Now as we know from 6 that
  Fz_F,i = (Dx_D,i/x_B,i + B)x_B,i............8
• We can get value of x_B,i from 7 and 8
• Now we can calculate summation of all x_B,i's and can check whether it comes out to be equal to 1. If it does not comes out equal to 1 we will assume a new Temperature Profile and rework this procedure until we get summation of all x_B,i's equal to 1

Using Hit and Trial we can get correct temperature profile and hence can calculate compositions of distillate and bottom prduct. But convergence by this method takes long time . Hence some other methods have been developed like Theta convergence method which can cause a quick convergence of solutions.