Exam1 example1 17

CHE 3023 Exam 1 Problem 3
Coding on google colaboratory

from scipy.integrate import solve_ivp
from scipy.optimize import root
import numpy as np
from plotly.subplots import make_subplots
import plotly.graph_objects as go
import plotly.io as pio
pio.templates.default='plotly_dark'

This section of cod is calling different programing functions that will be used in the calculations

D12=8.48e-6
D13=13.72e-6
D23=19.91e-6
P=99.4e3
T=328.5
R=8.314
c=P/(R*T)
delta=0.24
F12=(c*D12)/delta
F13=(c*D13)/delta
F23=(c*D23)/delta
N1i=1e-3
N2i=1e-3
y1i=0.319
y2i=0.528

This section of code is defining our parameters

def f(N):
N1=N[0]
N2=N[1]
def dy(eta,y):
y1=y[0]
y2=y[1]
y3=1-y1-y2
return np.array([(y1*N2-y2*N1)/F12 + (0-y3*N1)/F13,
(y2*N1-y1*N2)/F12 + (0-y3*N2)/F23])
res=solve_ivp(dy,(0,1),(y1i,y2i),method='Radau',dense_output=True)
return res.sol(1)

This section of code is solving the initial value problem formulas

resR=root(f,[N1i,N2i])
N1=resR.x[0]
N2=resR.x[1]
def dy(eta,y):
y1=y[0]
y2=y[1]
y3=1-y1-y2
return np.array([(y1*N2-y2*N1)/F12 + (0-y3*N1)/F13,
(y2*N1-y1*N2)/F12 + (0-y3*N2)/F23])
resr=solve_ivp(dy,(0,1),(y1i,y2i),method='Radau',dense_output=True)

This section of code is using the root solver to calculate the iteration of the mol fraction as they go to zero
eta_plot=np.linspace(0,1,51)
sol=resr.sol(eta_plot)
fig=make_subplots(rows=1,cols=1)
fig.add_trace(go.Scatter(x=eta_plot*delta,y=sol[0],name='acetone'))
fig.add_trace(go.Scatter(x=eta_plot*delta,y=sol[1],name='methanol'))
fig.add_trace(go.Scatter(x=eta_plot*delta,y=1-sol[0]-sol[1],name='air'))

This section of code is graphing our solution of the mole fraction gradients