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Ex_4_5.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wed May 10 08:04:14 2023
+
+@author: delvigne
+"""
+
+
+'''
+Exercice 4.5 Modelling residence time of particles inside a CSTR
+'''
+
+import numpy as np
+from matplotlib.pyplot import figure
+from matplotlib.pyplot import plot
+from matplotlib.pyplot import xlabel
+from matplotlib.pyplot import ylabel
+from matplotlib.pyplot import title
+import matplotlib.pyplot as plt 
+import math
+from numpy.random import seed
+from numpy.random import rand
+
+
+'''
+Deterministic simulation for the outflow of soluble molecules (Euler referential)
+'''
+
+Q = 100 #in L/min
+V = 1000 #in L
+N = 80 # in min -> timescale
+t = np.arange(N)
+
+C_time = []
+C0 = 1
+for x in t:
+    C = C0*math.exp(-(Q/V)*x)
+    C_time.append(C)
+    
+figure(1)
+plot(C_time)
+xlabel('Time (h)')
+ylabel('Concentration')
+title('Deterministic-Euler simulation')
+
+''' 
+Stochastic simulation for the escape of discrete particles (Lagrange referential)
+'''
+
+
+#Passage time of particles follows an exponential distribution
+#seed(3)
+r = np.random.rand(30)
+
+t_pass = []
+for y in r:
+    t_passage = -math.log(y)/(Q/V)
+    t_pass.append(t_passage)
+    
+    
+fig2, (ax1, ax2) = plt.subplots(2,1)
+ax1.eventplot(t_pass,colors='orange')
+ax1.axis('off')
+ 
+time2 = (sorted(t_pass,reverse=True))
+ax2.plot(time2,np.arange(1,len(t_pass)+1),'tab:orange')
+xlabel('Time (h)')
+ylabel('Number of particles')
+title('Stochastic-Lagrangian simulation')
+
+'''
+Note : you could also use Python built-in function np.random.exponential
+Example :
+    import numpy as np
+    import matplotlib.pyplot as plt
+    import random as rand
+
+    t_pass = np.random.exponential(-V/Q,1000)
+'''
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