#!/usr/bin/env python
# coding: utf-8

# # Liquid/Vapor Equilibrium : dew and boiling curve
# 
# The vapor pressure of benzene and toluene are given by the following equation
# $$log_{lO} P_A^0 (Pa)=\frac{- 0,05223 A}{T} + B$$
# Where T is the temperature in Kelvin and A et B are constant given below.
#   
# 			    A (K)            B
# 	Benzene		32295		9,7795
# 	Toluene		39198		10,45449
#  
# By considering that the mixture benzene-toluene is ideal, calculate the molar fraction of benzene in :
# 
# a) the mixture boiling at 97°C under the normal pressure (101300 Pa)
# 
# b) the first drop of distillate
# 
# c) Plot the boiling and the dew point curves. 
# 
# d) Plot the square diagram.
# 
# e) Determine the boiling temperature of a mixture having a molar fraction of 0.3

# In[66]:


import numpy as np
import matplotlib.pyplot as plt
#Data for Antoine Laws
K=0.05223
A_BZ=32295
B_BZ=9.7795
A_TL=39198
B_TL=10.45449
P=101300 #Pa
#calculation of the boiling temperature of pure A and B at atm pressure
T_BZ=(-K*A_BZ)/(np.log10(P)-B_BZ)
T_TL=(-K*A_TL)/(np.log10(P)-B_TL)
print ('At a pressure of {} Pa the boiling temperature of Benzene is {:.2f} K and of toluene is {:.2f} K'.format(P,T_BZ,T_TL))

def P0_BZ(T):
    return 10**(B_BZ-K*A_BZ/T)
def P0_TL(T):
    return 10**(B_TL-K*A_TL/T)
def x_BZ(T):
    return (P-P0_TL(T))/(P0_BZ(T)-P0_TL(T))
def y_BZ(T):
    return x_BZ(T)*P0_BZ(T)/P

T97=97+273.15
print ('At a temperature of {} T the vapor pressure of Benzene is {:.0f} Pa and of toluene is {:.0f} Pa'.format(T97,P0_BZ(T97),P0_TL(T97)))
print ('')
print ('The molar fraction in Benzene of a mixture boiling at', T97, 'K is',round(x_BZ(T97),3))
print ('The first condensate obtained at ', T97, 'is',round(y_BZ(T97),3), 'in Benzene')
T=np.linspace(T_BZ,T_TL,100)
plt.plot(x_BZ(T),T,label='Boiling curve')
plt.plot(y_BZ(T),T,label='Dew point curve')
plt.plot([x_BZ(T97),x_BZ(T97),y_BZ(T97),y_BZ(T97)],[T_BZ,T97,T97,T_BZ], 'r--',label='x and y at 97°C')
plt.legend(loc='best')
plt.xlabel('x and y of Benzene')
plt.ylabel('T (K)')
plt.grid()
plt.show()




# In[67]:


import numpy as np
import matplotlib.pyplot as plt
alpha1=P0_BZ((T_BZ+T_TL)/2)/P0_TL((T_BZ+T_TL)/2)
print ('The mean relative volatility is', round(alpha1,3))
print ('determined at the mean temperature of the boiling temperature of benzene and toluene')


# In[68]:


#plot of square diagram y=f(x)
x=np.linspace(0,1,100)
y=alpha1*x/(1+(alpha1-1)*x)
yb=x
plt.plot(x,y, 'b--', label='From relative volatility')
plt.plot(x_BZ(T),y_BZ(T), 'g--', label='From Antoine law')
plt.plot([0,x_BZ(T97),x_BZ(T97)],[y_BZ(T97),y_BZ(T97),0], 'r--',label='x and y at 97°C')
plt.plot(x,yb,'b')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.grid()
plt.show()


# In[69]:


from scipy.optimize import fsolve

x_BZX=0.3 #Fraction molaire en benzene dont on recherche la temperature d'ebulition 
#Fonction dont il faut trouver la racine pour trouver la temperature d'ebulition d'un mélange à x_BZX
def xeb(T):
    return x_BZ(T)-x_BZX
#Résolution 
Teb = fsolve(xeb, x0=T_BZ)[0]
print('Un mélange de composition',x_BZX, 'en Benzène a une température d ébulition', round(Teb,2), 'K')

plt.plot(x,y, 'b--', label='From relative volatility')
plt.plot(x_BZ(T),y_BZ(T), 'g--', label='From Antoine law')
plt.plot([0,x_BZ(Teb),x_BZ(Teb)],[y_BZ(Teb),y_BZ(Teb),0], 'r--')
plt.plot(x,yb,'b')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.grid()
plt.show()

plt.plot(x_BZ(T),T,label='Boiling curve')
plt.plot(y_BZ(T),T,label='Dew point curve')
plt.plot([x_BZ(Teb),x_BZ(Teb),y_BZ(Teb),y_BZ(Teb)],[T_BZ,Teb,Teb,T_BZ], 'r--')
plt.legend(loc='best')
plt.xlabel('x and y of Benzene')
plt.ylabel('T (K)')
plt.grid()
plt.show()


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