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Additional_exercice_3.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Feb 29 10:38:19 2024
+
+@author: delvigne
+"""
+'''
+Additional exercice 3
+'''
+
+import numpy as np
+from scipy.integrate import solve_ivp
+from matplotlib.pyplot import figure
+from matplotlib.pyplot import plot
+from matplotlib.pyplot import xlabel
+from matplotlib.pyplot import ylabel
+
+
+def Fedbatch(t, state):
+    X = state[0]
+    S = state[1]
+    V = state[2]
+    
+    mumax = 0.7 #in h-1
+    Ks = 0.01 #in g/L
+    Yxs = 0.46 #in g per g
+    D = 0.1/10 #Dilution rate in h-1 (D = Q/V)
+    Sin = 200
+
+    
+    rx = mumax*(S/(Ks+S))*X
+    
+    
+    if t<5:
+        D=0
+    
+    dXdt = rx -D*X
+    dSdt = -rx/Yxs - D*S + D*Sin
+    dVdt = D*V
+    state = [dXdt,dSdt,dVdt]
+    return state
+
+'''Specify the time range for running the simulation'''
+t = np.linspace(0,30)
+
+
+'''Specify the initial conditions'''
+state0 = [0.2,10,10] #We have 0.2 g/L of biomass, 10 g/L of substrate 
+                         #and a volume of 10L at the beginning of the simulation
+
+'''Solve the ODEs'''
+r = solve_ivp(fun=Fedbatch, t_span=[t[0],max(t)],y0=state0, t_eval=t, method='LSODA')
+
+a = r.y.T
+
+figure(1)
+plot(r.t,a[:,0],r.t,a[:,1])
+xlabel('Time (h)')
+ylabel('X, S (g/L)')
+
+figure(2)
+plot(r.t,a[:,2])
+xlabel('Time (h)')
+ylabel('V (L)')