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Ex_2_10.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wed Mar 15 21:11:16 2023
+
+@author: delvigne
+"""
+
+
+
+'''
+Exercice 2.10 - Simulation of a fed-batch bioreactor with oxygen transfer
+'''
+
+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]
+    CL = state[2]
+    V = state[3]
+    
+    mumax = 0.6 #in h-1
+    Ks = 0.01 #in g/L
+    Yxs = 0.5 #in g per g
+    D = 0.01 #Dilution rate in h-1
+    Sin = 500
+    Yxo = 1
+    Ko = 0.001
+    KLa = 350
+    C0L = 0.01
+    
+    rx = mumax*(S/(Ks+S))*X*(CL/(Ko+CL))
+    
+    
+    if t<5:
+        D=0
+    
+    dXdt = rx -D*X
+    dSdt = -rx/Yxs - D*S + D*Sin
+    dCLdt = KLa * (C0L - CL)- (rx/Yxo)-D*CL
+    dVdt = D*V
+    state = [dXdt,dSdt,dCLdt,dVdt]
+    return state
+
+'''Specify the time range for running the simulation'''
+t = np.linspace(0,30)
+
+
+'''Specify the initial conditions'''
+state0 = [0.1,5,0.01,10] #We have 0.1 g/L of biomass, 5 g/L of substrate, 10 mg/L of dissolved oxygen 
+                         #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('CL (g/L)')
+
+figure(3)
+plot(r.t,a[:,3])
+xlabel('Time (h)')
+ylabel('V (L)')