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Ex_2_11.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wed Mar  9 09:58:19 2022
+
+@author: delvigne
+"""
+
+import numpy as np
+
+
+'''
+Exercice 2.11 :  Scale-up of areated bioreactors
+5 bioreactors : 15L, 300L, 3000L, 30000L et 100000L
+'''
+
+
+#Technical specifications
+
+#Vessel diameters in m (from exisiting equipments) 
+D = np.array([0.18, 0.39, 0.85, 2.4, 3.8])
+
+d = D/3
+
+
+#Computation of effective volume based on standard geometry
+n = 3 #Number of agitation stages
+
+V = []
+
+for y in D:
+    V2 = n*3.14159*((y**3)/4)
+    V.append(V2)
+
+
+
+#Scale-up based on a volumic power of 2KW/m3
+
+ro = 1000 #Kg/m3
+Np = 5 
+P_V = 2000 #W/m3
+
+
+StirringRate1 = ((P_V*V[0]/(ro*Np*((D[0]/3)**5)))**(1/3))
+StirringRate2 = ((P_V*V[1]/(ro*Np*((D[1]/3)**5)))**(1/3))
+StirringRate3 = ((P_V*V[2]/(ro*Np*((D[2]/3)**5)))**(1/3))
+StirringRate4 = ((P_V*V[3]/(ro*Np*((D[3]/3)**5)))**(1/3))
+StirringRate5 = ((P_V*V[4]/(ro*Np*((D[4]/3)**5)))**(1/3))
+N = np.array([StirringRate1, StirringRate2,StirringRate3, StirringRate4,StirringRate5])
+
+#Circulation flow rate
+Nqc = 1.51 
+
+Qc1 = Nqc*N[0]*(D[0]/3)**3
+Qc2 = Nqc*N[1]*(D[1]/3)**3
+Qc3 = Nqc*N[2]*(D[2]/3)**3
+Qc4 = Nqc*N[3]*(D[3]/3)**3
+Qc5 = Nqc*N[4]*(D[4]/3)**3
+
+Qc = np.array([Qc1, Qc2, Qc3, Qc4, Qc5])
+    
+#G/L Dispersion when G/S is kept constant 
+G_s = 0.02 #  %m/s
+g = 9.81 # m/s2
+
+Fr1 = (((N[0])**2)*d[0])/g #Froude number
+Fr2 = (((N[1])**2)*d[1])/g
+Fr3 = (((N[2])**2)*d[2])/g
+Fr4 = (((N[3])**2)*d[3])/g
+Fr5 = (((N[4])**2)*d[4])/g
+
+Fl1 = (G_s*(3.14159*((D[0]/2)**2)))/((N[0]*(d[0]**3))) #Flow number
+Fl2 = (G_s*(3.14159*((D[1]/2)**2)))/((N[1]*(d[1]**3)))
+Fl3 = (G_s*(3.14159*((D[2]/2)**2)))/((N[2]*(d[2]**3)))
+Fl4 = (G_s*(3.14159*((D[3]/2)**2)))/((N[3]*(d[3]**3)))
+Fl5 = (G_s*(3.14159*((D[4]/2)**2)))/((N[4]*(d[4]**3)))
+
+Fr = np.array([Fr1,Fr2,Fr3,Fr4,Fr5])
+Fl = np.array([Fl1,Fl2,Fl3,Fl4,Fl5])
+
+#Mixing time
+
+tm1 = 5*(V[0]/Qc[0])
+tm2 = 5*(V[1]/Qc[1])
+tm3 = 5*(V[2]/Qc[2])
+tm4 = 5*(V[3]/Qc[3])
+tm5 = 5*(V[4]/Qc[4])
+
+tm = np.array([tm1, tm2, tm3, tm4, tm5])
+