def transport_equation_plot():
'''Check the transport equation integrator'''
w = 5
tend = 5
dx = 0.1
length = 100
phi = 1
dt = 0.001
lab = Column(length, dx, tend, dt, w)
D = 5
lab.add_species(phi,
'O2',
D,
0,
bc_top_value=1,
bc_top_type='dirichlet',
bc_bot_value=0,
bc_bot_type='dirichlet')
lab.solve()
x = np.linspace(0, lab.length, lab.length / lab.dx + 1)
sol = 1 / 2 * (special.erfc(
(x - lab.w * lab.tend) / 2 / np.sqrt(D * lab.tend)) +
np.exp(lab.w * x / D) * special.erfc(
(x + lab.w * lab.tend) / 2 / np.sqrt(D * lab.tend)))
plt.figure()
plt.plot(x, sol, 'k', label='Analytical solution')
plt.scatter(lab.x[::10],
lab.species['O2'].concentration[:, -1][::10],
marker='x',
label='Numerical')
plt.xlim([x[0], x[-1]])
ax = plt.gca()
ax.ticklabel_format(useOffset=False)
ax.grid(linestyle='-', linewidth=0.2)
plt.legend()
plt.tight_layout()
plt.show()
def fun(k0):
w, k_w_in, k_w_out, k_g_in, k_g_out = k0
print(*k0)
# try:
ftc1 = Column(L, dx, tend, dt)
ftc1.add_species(
theta=((phi_g**(10 / 3)) / (phi**2)),
name='SF6g',
D=D_SF6g,
init_C=0,
bc_top=0,
bc_top_type='constant',
bc_bot=0,
bc_bot_type='constant',
w=-0.00) #-0.055
ftc1.add_species(
theta=((phi_w**(10 / 3)) / (phi**2)),
name='SF6w',
D=D_SF6w,
init_C=0,
bc_top=0,
bc_top_type='constant',
bc_bot=0,
bc_bot_type='constant',
w=w)
# SF6mp stands for SF6 gas in micro pores, it is immobile and only collects SF6;
ftc1.add_species(
theta=phi_p,
name='SF6mp',
D=1e-18,
init_C=0,
bc_top=0,
bc_top_type='flux',
bc_bot=0,
bc_bot_type='flux')
#((phi_g**(10/3))/(phi**2))*
#((phi_w**(10/3))/(phi**2))*
# # Constants
ftc1.constants['k_w_in'] = k_w_in #from FTR w
ftc1.constants['k_w_out'] = k_w_out
#0.4
ftc1.constants['k_g_in'] = k_g_in
ftc1.constants['k_g_out'] = k_g_out
ftc1.constants['phi_w'] = phi_w
ftc1.constants['phi_g'] = phi_g
ftc1.constants['phi_p'] = phi_p
# # Rates of diffusion into pores and out
ftc1.rates['R_w_in'] = 'k_w_in * SF6w'
ftc1.rates['R_w_out'] = 'k_w_out * SF6mp'
ftc1.rates['R_g_in'] = 'k_g_in * SF6w'
ftc1.rates['R_g_out'] = 'k_g_out * SF6g'
# # dcdt
ftc1.dcdt['SF6w'] = '-R_g_in + R_g_out * phi_g - R_w_in + R_w_out * phi_p'
ftc1.dcdt['SF6g'] = 'R_g_in / phi_g - R_g_out'
ftc1.dcdt['SF6mp'] = 'R_w_in / phi_p - R_w_out'
for i in range(0, len(ftc1.time)):
if (ftc1.time[i] > F1T_frz - 16 and ftc1.time[i] < T1T_thw - 16) or (
ftc1.time[i] > F2T_frz - 16 and
ftc1.time[i] < T2T_thw - 16) or (ftc1.time[i] > F3T_frz - 16):
ftc1.change_boundary_conditions(
'SF6g', i, bc_top=0, bc_top_type='flux')
ftc1.change_boundary_conditions(
'SF6w', i, bc_top=0, bc_top_type='flux')
else:
ftc1.change_boundary_conditions(
'SF6g', i, bc_top=0, bc_top_type='constant')
ftc1.change_boundary_conditions(
'SF6w', i, bc_top=0, bc_top_type='constant')
if any([ftc1.time[i] == T_inj for T_inj in Ti]):
SF6_add = np.zeros(x.size)
SF6_add[x > 0] = 0
SF6_add[x > 18 - (h_inj / 2)] = Ci[Ti == ftc1.time[i]]
SF6_add[x > 18 + (h_inj / 2)] = 0
new_profile = ftc1.profiles['SF6w'] + SF6_add #
ftc1.change_concentration_profile('SF6w', i, new_profile)
ftc1.integrate_one_timestep(i)
time_idxs = find_indexes_of_intersections(ftc1.time, Tm)
zm = 9
M1D9 = (
ftc1.SF6w.concentration[ftc1.x == zm, time_idxs] * phi_w[ftc1.x == zm] +
ftc1.SF6g.concentration[ftc1.x == zm, time_idxs] * phi_g[ftc1.x == zm]
) / (
phi_w[ftc1.x == zm] + phi_g[ftc1.x == zm])
zm = 21
M1D21 = (
ftc1.SF6w.concentration[ftc1.x == zm, time_idxs] * phi_w[ftc1.x == zm] +
ftc1.SF6g.concentration[ftc1.x == zm, time_idxs] * phi_g[ftc1.x == zm]
) / (
phi_w[ftc1.x == zm] + phi_g[ftc1.x == zm])
zm = 33
M1D33 = (
ftc1.SF6w.concentration[ftc1.x == zm, time_idxs] * phi_w[ftc1.x == zm] +
ftc1.SF6g.concentration[ftc1.x == zm, time_idxs] * phi_g[ftc1.x == zm]
) / (
phi_w[ftc1.x == zm] + phi_g[ftc1.x == zm])
fx_time_idxs = find_indexes_of_intersections(ftc1.time, Tm_nz)
F1 = ftc1.estimate_flux_at_top('SF6g')[fx_time_idxs]
F2 = ftc1.estimate_flux_at_top('SF6w')[fx_time_idxs]
F3 = ftc1.estimate_flux_at_top('SF6mp')[fx_time_idxs]
fx_mod = F1 + F2 + F3
fx_meas = dC1h * Vh1 / SA / 2
err = rmse(M1D9, C1D9[:len(M1D9) - len(C1D9)]) + rmse(
M1D21, C1D21[:len(M1D21) - len(C1D21)]) + rmse(
M1D33, C1D33[:len(M1D33) - len(C1D33)]) + 100 * rmse(
fx_mod, fx_meas[:len(fx_mod)])
def fun(k0):
w, k_w_in, k_w_out, k_g_in, k_g_out, phi_1, phi_2, phi_3 = k0
print(*k0)
try:
tend = periods[0]
# tend = 457
dt = 0.01
dx = 0.2 ## cm
L = 40 ## cm
x = np.linspace(0, L, L / dx + 1)
t = np.linspace(0, tend, round(tend / dt) + 1)
#phi = 0.8
Chs = np.zeros(t.shape) #
Fx = np.zeros(t.shape)
phi = (phi_1 - 0.91) * np.exp(-x / 10) + 0.91
phi_w = phi * (0.875 / 0.97)
phi_g = phi * ((0.97 - 0.875) / 0.97)
phi_p = 1 - phi
ftc1 = Column(L, dx, tend, dt)
ftc1.add_species(
theta=((phi_g) / (1-np.log(phi))),
element='SF6g',
D=D_SF6g,
init_C=0,
bc_top=0,
bc_top_type='constant',
bc_bot=0,
bc_bot_type='constant',
w=-0.00) #-0.055
ftc1.add_species(
theta=((phi_w) / (1-np.log(phi))),
element='SF6w',
D=D_SF6w,
init_C=0,
bc_top=0,
bc_top_type='constant',
bc_bot=0,
bc_bot_type='constant',
w=w)
# SF6mp stands for SF6 gas in micro pores, it is immobile and only collects SF6;
ftc1.add_species(
theta=phi_p,
element='SF6mp',
D=1e-18,
init_C=0,
bc_top=0,
bc_top_type='flux',
bc_bot=0,
bc_bot_type='flux')
# # Constants
ftc1.constants['k_w_in'] = k_w_in #from FTR w
ftc1.constants['k_w_out'] = k_w_out
#0.4
ftc1.constants['k_g_in'] = k_g_in
ftc1.constants['k_g_out'] = k_g_out
ftc1.constants['phi_w'] = phi_w
ftc1.constants['phi_g'] = phi_g
ftc1.constants['phi_p'] = phi_p
# # Rates of diffusion into pores and out
ftc1.rates['R_w_in'] = 'k_w_in * SF6w'
ftc1.rates['R_w_out'] = 'k_w_out * SF6mp'
# ftc1.rates['R_w_in'] = '0'
# ftc1.rates['R_w_out'] = '0'
ftc1.rates['R_g_in'] = 'k_g_in * SF6w'
ftc1.rates['R_g_out'] = 'k_g_out * SF6g'
# # dcdt
ftc1.dcdt[
'SF6w'] = '-R_g_in + R_g_out * phi_g - R_w_in + R_w_out * phi_p'
ftc1.dcdt['SF6g'] = 'R_g_in / phi_g - R_g_out'
ftc1.dcdt['SF6mp'] = 'R_w_in / phi_p - R_w_out'
Fx = np.zeros(t.size)
for i in range(0, len(ftc1.time)):
if (ftc1.time[i] > periods[0] and ftc1.time[i] < periods[1]) or (
ftc1.time[i] > periods[2] and ftc1.time[i] < periods[3]) or (
ftc1.time[i] > periods[4] and ftc1.time[i] < periods[5]):
ftc1.change_boundary_conditions(
'SF6g', i, bc_top=0, bc_top_type='flux')
ftc1.change_boundary_conditions(
'SF6w', i, bc_top=0, bc_top_type='flux')
Fx[i] = 0
else:
ftc1.change_boundary_conditions(
'SF6g', i, bc_top=0, bc_top_type='constant')
ftc1.change_boundary_conditions(
'SF6w', i, bc_top=0, bc_top_type='constant')
F1 = ftc1.estimate_flux_at_top('SF6g', i)
F2 = ftc1.estimate_flux_at_top('SF6w', i)
F3 = ftc1.estimate_flux_at_top('SF6mp', i)
Fx[i] = F1[i] + F2[i] + F3[i]
if any([ftc1.time[i] == T_inj for T_inj in Ti_1]):
SF6_add = np.zeros(x.size)
SF6_add[x > 0] = 0
SF6_add[x > 18 - (h_inj / 2)] = Ci[Ti_1 == ftc1.time[i]]
SF6_add[x > 18 + (h_inj / 2)] = 0
new_profile = ftc1.profiles['SF6w'] + SF6_add #
ftc1.change_concentration_profile('SF6w', i, new_profile)
ftc1.integrate_one_timestep(i)
Ti_2 = Ti - periods[0]
tend = periods[2] - periods[0]
dt = 0.01
dx = 0.2 ## cm
L = 40 ## cm
x = np.linspace(0, L, L / dx + 1)
t = np.linspace(0, tend, round(tend / dt) + 1)
#phi = 0.8
Chs = np.zeros(t.shape) #
Fx = np.zeros(t.shape)
phi = (phi_2 - 0.91) * np.exp(-x / 10) + 0.91
phi_w = phi * (0.875 / 0.97)
phi_g = phi * ((0.97 - 0.875) / 0.97)
phi_p = 1 - phi
ftc2 = Column(L, dx, tend, dt)
ftc2.add_species(
theta=((phi_g) / (1-np.log(phi))),
element='SF6g',
D=D_SF6g,
init_C=ftc1.profiles.SF6g,
bc_top=0,
bc_top_type='constant',
bc_bot=0,
bc_bot_type='constant',
w=-0.00) #-0.055
ftc2.add_species(
theta=((phi_w) / (1-np.log(phi))),
element='SF6w',
D=D_SF6w,
init_C=ftc1.profiles.SF6w,
bc_top=0,
bc_top_type='constant',
bc_bot=0,
bc_bot_type='constant',
w=w)
# SF6mp stands for SF6 gas in micro pores, it is immobile and only collects SF6;
ftc2.add_species(
theta=phi_p,
element='SF6mp',
D=1e-18,
init_C=ftc1.profiles.SF6mp,
bc_top=0,
bc_top_type='flux',
bc_bot=0,
bc_bot_type='flux')
# # Constants
ftc2.constants['k_w_in'] = k_w_in #from FTR w
ftc2.constants['k_w_out'] = k_w_out
#0.4
ftc2.constants['k_g_in'] = k_g_in
ftc2.constants['k_g_out'] = k_g_out
ftc2.constants['phi_w'] = phi_w
ftc2.constants['phi_g'] = phi_g
ftc2.constants['phi_p'] = phi_p
# # Rates of diffusion into pores and out
ftc2.rates['R_w_in'] = 'k_w_in * SF6w'
ftc2.rates['R_w_out'] = 'k_w_out * SF6mp'
# ftc2.rates['R_w_in'] = '0'
# ftc2.rates['R_w_out'] = '0'
ftc2.rates['R_g_in'] = 'k_g_in * SF6w'
ftc2.rates['R_g_out'] = 'k_g_out * SF6g'
# # dcdt
ftc2.dcdt[
'SF6w'] = '-R_g_in + R_g_out * phi_g - R_w_in + R_w_out * phi_p'
ftc2.dcdt['SF6g'] = 'R_g_in / phi_g - R_g_out'
ftc2.dcdt['SF6mp'] = 'R_w_in / phi_p - R_w_out'
for i in range(0, len(ftc2.time)):
if (ftc2.time[i] + periods[0] > periods[0]
and ftc2.time[i] + periods[0] < periods[1]) or (
ftc2.time[i] + periods[0] > periods[2]
and ftc2.time[i] + periods[0] < periods[3]) or (
ftc2.time[i] + periods[0] > periods[4]
and ftc2.time[i] + periods[0] < periods[5]):
ftc2.change_boundary_conditions(
'SF6g', i, bc_top=0, bc_top_type='flux')
ftc2.change_boundary_conditions(
'SF6w', i, bc_top=0, bc_top_type='flux')
Fx[i] = 0
else:
ftc2.change_boundary_conditions(
'SF6g', i, bc_top=0, bc_top_type='constant')
ftc2.change_boundary_conditions(
'SF6w', i, bc_top=0, bc_top_type='constant')
F1 = ftc2.estimate_flux_at_top('SF6g', i)
F2 = ftc2.estimate_flux_at_top('SF6w', i)
F3 = ftc2.estimate_flux_at_top('SF6mp', i)
Fx[i] = F1[i] + F2[i] + F3[i]
if any([ftc2.time[i] == T_inj for T_inj in Ti_2]):
SF6_add = np.zeros(x.size)
SF6_add[x > 0] = 0
SF6_add[x > 18 - (h_inj / 2)] = Ci[Ti_2 == ftc2.time[i]]
SF6_add[x > 18 + (h_inj / 2)] = 0
new_profile = ftc2.profiles['SF6w'] + SF6_add #
ftc2.change_concentration_profile('SF6w', i, new_profile)
ftc2.integrate_one_timestep(i)
Ti_3 = Ti - periods[2]
tend = periods[4] - periods[2]
dt = 0.01
dx = 0.2 ## cm
L = 40 ## cm
x = np.linspace(0, L, L / dx + 1)
t = np.linspace(0, tend, round(tend / dt) + 1)
#phi = 0.8
Chs = np.zeros(t.shape) #
Fx = np.zeros(t.shape)
phi = (phi_3 - 0.91) * np.exp(-x / 10) + 0.91
phi_w = phi * (0.875 / 0.97)
phi_g = phi * ((0.97 - 0.875) / 0.97)
phi_p = 1 - phi
ftc3 = Column(L, dx, tend, dt)
ftc3.add_species(
theta=((phi_g) / (1-np.log(phi))),
element='SF6g',
D=D_SF6g,
init_C=ftc2.profiles.SF6g,
bc_top=0,
bc_top_type='constant',
bc_bot=0,
bc_bot_type='constant',
w=-0.00) #-0.055
ftc3.add_species(
theta=((phi_w) / (1-np.log(phi))),
element='SF6w',
D=D_SF6w,
init_C=ftc2.profiles.SF6w,
bc_top=0,
bc_top_type='constant',
bc_bot=0,
bc_bot_type='constant',
w=w)
# SF6mp stands for SF6 gas in micro pores, it is immobile and only collects SF6;
ftc3.add_species(
theta=phi_p,
element='SF6mp',
D=1e-18,
init_C=ftc2.profiles.SF6mp,
bc_top=0,
bc_top_type='flux',
bc_bot=0,
bc_bot_type='flux')
# # Constants
ftc3.constants['k_w_in'] = k_w_in #from FTR w
ftc3.constants['k_w_out'] = k_w_out
#0.4
ftc3.constants['k_g_in'] = k_g_in
ftc3.constants['k_g_out'] = k_g_out
ftc3.constants['phi_w'] = phi_w
ftc3.constants['phi_g'] = phi_g
ftc3.constants['phi_p'] = phi_p
# # Rates of diffusion into pores and out
ftc3.rates['R_w_in'] = 'k_w_in * SF6w'
ftc3.rates['R_w_out'] = 'k_w_out * SF6mp'
# ftc3.rates['R_w_in'] = '0'
# ftc3.rates['R_w_out'] = '0'
ftc3.rates['R_g_in'] = 'k_g_in * SF6w'
ftc3.rates['R_g_out'] = 'k_g_out * SF6g'
# # dcdt
ftc3.dcdt[
'SF6w'] = '-R_g_in + R_g_out * phi_g - R_w_in + R_w_out * phi_p'
ftc3.dcdt['SF6g'] = 'R_g_in / phi_g - R_g_out'
ftc3.dcdt['SF6mp'] = 'R_w_in / phi_p - R_w_out'
for i in range(0, len(ftc3.time)):
if (ftc3.time[i] + periods[2] > periods[0]
and ftc3.time[i] + periods[2] < periods[1]) or (
ftc3.time[i] + periods[2] > periods[2]
and ftc3.time[i] + periods[2] < periods[3]) or (
ftc3.time[i] + periods[2] > periods[4]
and ftc3.time[i] + periods[2] < periods[5]):
ftc3.change_boundary_conditions(
'SF6g', i, bc_top=0, bc_top_type='flux')
ftc3.change_boundary_conditions(
'SF6w', i, bc_top=0, bc_top_type='flux')
Fx[i] = 0
else:
ftc3.change_boundary_conditions(
'SF6g', i, bc_top=0, bc_top_type='constant')
ftc3.change_boundary_conditions(
'SF6w', i, bc_top=0, bc_top_type='constant')
F1 = ftc3.estimate_flux_at_top('SF6g', i)
F2 = ftc3.estimate_flux_at_top('SF6w', i)
F3 = ftc3.estimate_flux_at_top('SF6mp', i)
Fx[i] = F1[i] + F2[i] + F3[i]
if any([ftc3.time[i] == T_inj for T_inj in Ti_3]):
SF6_add = np.zeros(x.size)
SF6_add[x > 0] = 0
SF6_add[x > 18 - (h_inj / 2)] = Ci[Ti_3 == ftc3.time[i]]
SF6_add[x > 18 + (h_inj / 2)] = 0
new_profile = ftc3.profiles['SF6w'] + SF6_add #
ftc3.change_concentration_profile('SF6w', i, new_profile)
ftc3.integrate_one_timestep(i)
zm = 9
M1D9 = (ftc1.SF6w.concentration[ftc1.x == zm, :] * phi_w[ftc1.x == zm] +
ftc1.SF6g.concentration[ftc1.x == zm, :] * phi_g[ftc1.x == zm]) / (
phi_w[ftc1.x == zm] + phi_g[ftc1.x == zm])
M2D9 = (ftc2.SF6w.concentration[ftc2.x == zm, :] * phi_w[ftc2.x == zm] +
ftc2.SF6g.concentration[ftc2.x == zm, :] * phi_g[ftc2.x == zm]) / (
phi_w[ftc2.x == zm] + phi_g[ftc2.x == zm])
M3D9 = (ftc3.SF6w.concentration[ftc3.x == zm, :] * phi_w[ftc3.x == zm] +
ftc3.SF6g.concentration[ftc3.x == zm, :] * phi_g[ftc3.x == zm]) / (
phi_w[ftc3.x == zm] + phi_g[ftc3.x == zm])
MD9 = np.concatenate((M1D9[0], M2D9[0], M3D9[0]))
zm = 21
M1D21 = (ftc1.SF6w.concentration[ftc1.x == zm, :] * phi_w[ftc1.x == zm] +
ftc1.SF6g.concentration[ftc1.x == zm, :] * phi_g[ftc1.x == zm]) / (
phi_w[ftc1.x == zm] + phi_g[ftc1.x == zm])
M2D21 = (ftc2.SF6w.concentration[ftc2.x == zm, :] * phi_w[ftc2.x == zm] +
ftc2.SF6g.concentration[ftc2.x == zm, :] * phi_g[ftc2.x == zm]) / (
phi_w[ftc2.x == zm] + phi_g[ftc2.x == zm])
M3D21 = (ftc3.SF6w.concentration[ftc3.x == zm, :] * phi_w[ftc3.x == zm] +
ftc3.SF6g.concentration[ftc3.x == zm, :] * phi_g[ftc3.x == zm]) / (
phi_w[ftc3.x == zm] + phi_g[ftc3.x == zm])
MD21 = np.concatenate((M1D21[0], M2D21[0], M3D21[0]))
zm = 33
M1D33 = (ftc1.SF6w.concentration[ftc1.x == zm, :] * phi_w[ftc1.x == zm] +
ftc1.SF6g.concentration[ftc1.x == zm, :] * phi_g[ftc1.x == zm]) / (
phi_w[ftc1.x == zm] + phi_g[ftc1.x == zm])
M2D33 = (ftc2.SF6w.concentration[ftc2.x == zm, :] * phi_w[ftc2.x == zm] +
ftc2.SF6g.concentration[ftc2.x == zm, :] * phi_g[ftc2.x == zm]) / (
phi_w[ftc2.x == zm] + phi_g[ftc2.x == zm])
M3D33 = (ftc3.SF6w.concentration[ftc3.x == zm, :] * phi_w[ftc3.x == zm] +
ftc3.SF6g.concentration[ftc3.x == zm, :] * phi_g[ftc3.x == zm]) / (
phi_w[ftc3.x == zm] + phi_g[ftc3.x == zm])
MD33 = np.concatenate((M1D33[0], M2D33[0], M3D33[0]))
MF1 = ftc1.estimate_flux_at_top('SF6g') + ftc1.estimate_flux_at_top(
'SF6w') + ftc1.estimate_flux_at_top('SF6mp')
MF2 = ftc2.estimate_flux_at_top('SF6g') + ftc2.estimate_flux_at_top(
'SF6w') + ftc2.estimate_flux_at_top('SF6mp')
MF3 = ftc3.estimate_flux_at_top('SF6g') + ftc3.estimate_flux_at_top(
'SF6w') + ftc3.estimate_flux_at_top('SF6mp')
MF = np.concatenate((MF1, MF2, MF3))
MT = np.concatenate((ftc1.time, ftc2.time + ftc1.time[-1],
ftc3.time + ftc2.time[-1] + ftc1.time[-1]))
idxs = find_indexes_of_intersections(MT, Tm, dt)
idxs_f = find_indexes_of_intersections(MT, Tm[::2] + 1, dt)
if np.isnan(MF).any() or np.isnan(MD9).any() or np.isnan(
MD21).any() or np.isnan(MD33).any():
err = 1e8
else:
err = norm_rmse(MD9[idxs], CD9_mean[:len(MD9[idxs])]) + norm_rmse(
MD21[idxs], CD21_mean[:len(MD21[idxs])]) + norm_rmse(
MD33[idxs], CD33_mean[:len(MD33[idxs])]) + 10 * norm_rmse(
MF[idxs_f], Fx_mean[:len(MF[idxs_f])])
except:
err = 1e8
print(":::::: {}".format(err))
return err