Figure 6.26:

Phase portrait of conversion versus temperature for feed initial condition; \tau =35~min.

Code for Figure 6.26

Text of the GNU GPL.

main.py

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# Converted from limit_cycle.m - CSTR limit cycle: theta=35
import numpy as np
from scipy.integrate import solve_ivp
from misc import save_ascii

p = dict(
    k_m      = 0.004,
    T_m      = 298.,
    E        = 15000.,
    c_Af     = 2.,
    C_p      = 4.,
    rho      = 1000.,
    T_f      = 298.,
    T_a      = 298.,
    DeltaH_R = -2.2e5,
    U        = 340.,
    theta    = 35.,
    T_set    = 321.53,
    c_set    = 0.48995,
    T_fs     = 298.,
    Kc       = 0.,
)
p['C_ps'] = p['C_p'] * p['rho']

def rhs(t, x, p):
    c_A = x[0]; T = x[1]
    k   = p['k_m'] * np.exp(-p['E'] * (1./T - 1./p['T_m']))
    T_f = p['T_fs'] + p['Kc'] * (T - p['T_set'])
    return [
        (p['c_Af'] - c_A)/p['theta'] - k*c_A,
        p['U']/p['C_ps']*(p['T_a']-T) + (T_f-T)/p['theta'] - k*c_A*p['DeltaH_R']/p['C_ps']
    ]

x0     = [p['c_Af'], p['T_f']]
tfinal = 15. * p['theta']
tout   = np.linspace(0., tfinal, 1000)

sol = solve_ivp(lambda t, x: rhs(t, x, p), [0., tfinal], x0,
                method='Radau', t_eval=tout,
                rtol=np.sqrt(np.finfo(float).eps),
                atol=np.sqrt(np.finfo(float).eps))

x    = sol.y.T
u    = (x[:, 1] - p['T_set']) * p['Kc'] + p['T_fs']
conv = (p['c_Af'] - x[:, 0]) / p['c_Af']
table = np.column_stack([tout, x, conv, u])
save_ascii('limit_cycle.dat', table)