def Volume_solve(T, P_bar, Pc_bar, Tc, m):
Pc = Pc_bar * 100
P = P_bar * 100
calc = Psat.Psat(T, Tc, Pc_bar, m)
P_sat_bar = calc[0]
P_sat = P_sat_bar * 100
a_eq = Psat.a(T, Tc, Pc, m)
b_eq = (R * Tc) / (8 * Pc)
def V_root(V):
return Psat.vdw(T, a_eq, b_eq, V, 0) - P
if P > P_sat:
V_guess = calc[1] * 0.95
V_root = sc_o.fsolve(V_root, V_guess)
return [V_root[0], 0]
elif P < P_sat:
V_guess = calc[2] * 1.05
V_root = sc_o.fsolve(V_root, V_guess)
return [0, V_root[0]]
else:
return [calc[1], calc[2]]
def dG_RT(T, P_bar, x1, Tc_1, Pc_bar_1, m_1, Tc_2, Pc_bar_2, m_2, Go1, Go2):
Pc_1 = Pc_bar_1 * 100
Pc_2 = Pc_bar_2 * 100
P = P_bar * 100
x2 = 1 - x1
b1 = (R * Tc_1) / (8 * Pc_1)
b2 = (R * Tc_2) / (8 * Pc_2)
bmix = b_mix(x1, x2, b1, b2)
a1 = Psat.a(T, Tc_1, Pc_1, m_1)
a2 = Psat.a(T, Tc_2, Pc_2, m_2)
amix = a_mix(x1, x2, a1, a2)
Volumes_1 = Volume_solve(T, P_bar, Pc_bar_1, Tc_1, m_1)
Volumes_2 = Volume_solve(T, P_bar, Pc_bar_2, Tc_2, m_2)
#Liquid phase:
V_l_1 = Volumes_1[0]
V_l_2 = Volumes_2[0]
if x1 != 0 and x1 != 1:
Gi = (x1 * numpy.log(x1) +
x2 * numpy.log(x2)) + (Go1 * x1 + Go2 * x2) / (R * T)
else:
Gi = 0
if V_l_1 != 0 or V_l_2 != 0:
Vmix_l = lin_mix(x1, x2, V_l_1, V_l_2)
deltaV_l = delta_V(x1, x2, V_l_1, V_l_2)
dG_l = P * deltaV_l / (R * T) + x1 * (numpy.log(
(V_l_1 - b1) / (Vmix_l - bmix))) + x2 * (numpy.log(
(V_l_2 - b2) /
(Vmix_l - bmix))) + x1 * (a1 / (R * T * V_l_1)) + x2 * (
a2 / (R * T * V_l_2)) - amix / (R * T * Vmix_l)
else:
dG_l = 0
#Vapour Phase:
V_v_1 = Volumes_1[1]
V_v_2 = Volumes_2[1]
if V_v_1 != 0 or V_v_2 != 0:
Vmix_v = lin_mix(x1, x2, V_v_1, V_v_2)
deltaV_v = delta_V(x1, x2, V_v_1, V_v_2)
dG_v = P * deltaV_v / (R * T) + x1 * (numpy.log(
(V_v_1 - b1) / (Vmix_v - bmix))) + x2 * (numpy.log(
(V_v_2 - b2) /
(Vmix_v - bmix))) + x1 * (a1 / (R * T * V_v_1)) + x2 * (
a2 / (R * T * V_v_2)) - amix / (R * T * Vmix_v)
else:
dG_v = 0
return dG_l + dG_v + Gi
def calculate_and_plot(self, event):
self.T_slider_label.SetLabel('Isotherm Temperature = ' + str(self.T_slider.GetValue()) + ' K')
Tc = 0
Pc = 0
m = 0
T = float(self.T_slider.GetValue())
T_Text = str(self.T_slider.GetValue())
Tc_text = self.Tc_input.GetValue()
Pc_text = self.Pc_input.GetValue()
m_text = self.m_input.GetValue()
if (Tc_text != '') and (Pc_text != '') and (m_text != ''):
Tc = float(Tc_text)
Pc = float(Pc_text)*100
m = float(m_text)
# Bereken aCrit
if (Tc != 0) and (Pc != 0) and (m != 0):
R = Psat.R
ac = (27*R*R*Tc*Tc)/(64*Pc)
b = (R*Tc)/(8*Pc)
calc = Psat.Psat(T, Tc, Pc/100, m)
Psatval = calc[0]
self.ac_label = str(round(ac,4))
self.b_label = str(round(b,4))
if np.isreal(Psatval):
self.Psat_label = str(round(Psatval,4))
else:
self.Psat_label = Psatval
self.ac_val.SetLabel('ac = ' + self.ac_label)
self.b_val.SetLabel('b = ' + self.b_label)
self.m_val.SetLabel('m = ' + m_text)
self.P_sat.SetLabel('Psat = '+ self.Psat_label)
#Calculate datapoints for vdw EOS
Data = np.zeros((1001))
Line_Data = np.zeros((1001))
for k in range(0,1001):
Data[k] = 100000*((0.1**(10-0.01*k))) + b+0.01
Value = max([min([Psat.vdw(T,Psat.a(T, Tc, Pc, m),b , Data[k],0)/100, 100]), -1000])
V_l = calc[1]
V_v = calc[2]
if Data[k] < V_l or Data[k] > V_v:
Line_Data[k] = Value
else:
Line_Data[k] = Psatval
Plot_Data1 = np.vstack((Data, Line_Data)).T
Isotherm = PolyLine(Plot_Data1, legend= 'Isotherm, T = ' + T_Text, colour='blue')
self.canvas.Draw(PlotGraphics([Isotherm], '', ' V', 'P'))
self.canvas.setLogScale((True, False))
def dG_RT(T, P_bar, x1, Tc_1, Pc_bar_1, m_1, Tc_2, Pc_bar_2, m_2, Go1, Go2):
Pc_1 = Pc_bar_1*100
Pc_2 = Pc_bar_2*100
P = P_bar*100
x2 = 1- x1
b1 = (R*Tc_1)/(8*Pc_1)
b2 = (R*Tc_2)/(8*Pc_2)
bmix = b_mix(x1, x2, b1, b2)
a1 = Psat.a(T, Tc_1, Pc_1, m_1)
a2 = Psat.a(T, Tc_2, Pc_2, m_2)
amix = a_mix(x1, x2, a1, a2)
Volumes_1 = Volume_solve(T, P_bar, Pc_bar_1, Tc_1, m_1)
Volumes_2 = Volume_solve(T, P_bar, Pc_bar_2, Tc_2, m_2)
#Liquid phase:
V_l_1 = Volumes_1[0]
V_l_2 = Volumes_2[0]
if x1 != 0 and x1 != 1:
Gi = (x1*numpy.log(x1) + x2*numpy.log(x2))+(Go1*x1 + Go2*x2)/(R*T)
else:
Gi = 0
if V_l_1 != 0 or V_l_2 != 0:
Vmix_l = lin_mix(x1, x2, V_l_1, V_l_2)
deltaV_l = delta_V(x1, x2, V_l_1, V_l_2)
dG_l = P*deltaV_l/(R*T) + x1*(numpy.log((V_l_1 - b1)/(Vmix_l - bmix))) + x2*(numpy.log((V_l_2 - b2)/(Vmix_l - bmix))) + x1*(a1/(R*T*V_l_1)) + x2*(a2/(R*T*V_l_2)) - amix/(R*T*Vmix_l)
else:
dG_l = 0
#Vapour Phase:
V_v_1 = Volumes_1[1]
V_v_2 = Volumes_2[1]
if V_v_1 != 0 or V_v_2 != 0:
Vmix_v = lin_mix(x1, x2, V_v_1, V_v_2)
deltaV_v = delta_V(x1, x2, V_v_1, V_v_2)
dG_v = P*deltaV_v/(R*T) + x1*(numpy.log((V_v_1 - b1)/(Vmix_v - bmix))) + x2*(numpy.log((V_v_2 - b2)/(Vmix_v - bmix))) + x1*(a1/(R*T*V_v_1)) + x2*(a2/(R*T*V_v_2)) - amix/(R*T*Vmix_v)
else:
dG_v = 0
return dG_l+ dG_v+ Gi
def V_single(T, Tc, P_bar, Pc_bar, m):
Pc = Pc_bar*100
P = P_bar*100
calc = Psat.Psat(T, Tc, Pc_bar, m)
sat_P = calc[0]*100
a_eq = Psat.a(T, Tc, Pc, m)
b = (R*Tc)/(8*Pc)
def eq(V):
return abs(Psat.vdw(T, a_eq, b, V, 0) - P)
if P > sat_P:
V_id_l = sc_o.fsolve(eq, [0.99*calc[1]])
return [V_id_l]
elif P < sat_P:
V_id_v = sc_o.fsolve(eq, [1.01*calc[2]])
return [V_id_v]
else:
V_id_l = calc[1]
V_id_v = calc[2]
return [V_id_l, V_id_v]
def vdw_residual(params, x, data):
T = params['T'].value
m = params['m'].value
Tc = params['Tc'].value
Pc = params['Pc'].value
x_range = numpy.size(x, axis=0)
model_data = numpy.zeros(x_range)
for k in range(x_range):
calc = Psat.Psat(x[k], Tc, Pc, m)
model_data[k] = calc[0]*100
return (model_data-data)/abs(model_data)
def G_RT_main(T, P_bar, x1,Tc_1, Pc_1_bar, m_1, Tc_2, Pc_2_bar, m_2):
Pc_1 = Pc_1_bar*100
Pc_2 = Pc_2_bar*100
P = P_bar*100
x2 = 1-x1
a_1 = Psat.a(T, Tc_1, Pc_1, m_1)
a_2 = Psat.a(T, Tc_2, Pc_2, m_2)
b_1 = (R*Tc_1)/(8*Pc_1)
b_2 = (R*Tc_2)/(8*Pc_2)
amix = a_mix(a_1, a_2, x1)
bmix = b_mix(b_1, b_2, x1)
volumes = dV(T, P_bar, x1, Tc_1, Pc_1_bar, Tc_2, Pc_2_bar, m_1, m_2)
delta_V = volumes[0]
V_i = [volumes[1], volumes[2]]
Vmix = volumes[3]
term_1 = P*delta_V[0]/R*T
term_2_1 = numpy.log((V_i[0]-b_1)/(Vmix-bmix))
term_2_2 = numpy.log((V_i[1]-b_2)/(Vmix-bmix))
term_2 = x1*term_2_1 + x2*term_2_2
term_3_1 = a_1/(R*T*V_i[0])
term_3_2 = a_2/(R*T*V_i[1])
term_3 = x1*term_3_1 + x2*term_3_2
term_4 = -amix/(R*T*Vmix)
terms = [term_1, term_2, term_3, term_4]
return sum(terms)
def Volume_solve(T, P_bar, Pc_bar, Tc, m):
Pc = Pc_bar*100
P = P_bar*100
calc = Psat.Psat(T, Tc, Pc_bar, m)
P_sat_bar = calc[0]
P_sat = P_sat_bar*100
a_eq = Psat.a(T, Tc, Pc, m)
b_eq = (R*Tc)/(8*Pc)
def V_root(V):
return Psat.vdw(T, a_eq, b_eq, V, 0)-P
if P > P_sat:
V_guess = calc[1]*0.95
V_root = sc_o.fsolve(V_root,V_guess)
return [V_root[0], 0]
elif P < P_sat:
V_guess = calc[2]*1.05
V_root = sc_o.fsolve(V_root,V_guess)
return [0, V_root[0]]
else:
return[calc[1], calc[2]]
def eq(V):
return abs(Psat.vdw(T, a_eq, b, V, 0) - P)
def V_root(V):
return Psat.vdw(T, a_eq, b_eq, V, 0) - P
def V_root(V):
return Psat.vdw(T, a_eq, b_eq, V, 0)-P
def calculate_and_plot(self, event):
self.T_slider_label.SetLabel('Isotherm Temperature = ' +
str(self.T_slider.GetValue()) + ' K')
Tc = 0
Pc = 0
m = 0
T = float(self.T_slider.GetValue())
T_Text = str(self.T_slider.GetValue())
Tc_text = self.Tc_input.GetValue()
Pc_text = self.Pc_input.GetValue()
m_text = self.m_input.GetValue()
if (Tc_text != '') and (Pc_text != '') and (m_text != ''):
Tc = float(Tc_text)
Pc = float(Pc_text) * 100
m = float(m_text)
# Bereken aCrit
if (Tc != 0) and (Pc != 0) and (m != 0):
R = Psat.R
ac = (27 * R * R * Tc * Tc) / (64 * Pc)
b = (R * Tc) / (8 * Pc)
calc = Psat.Psat(T, Tc, Pc / 100, m)
Psatval = calc[0]
self.ac_label = str(round(ac, 4))
self.b_label = str(round(b, 4))
if np.isreal(Psatval):
self.Psat_label = str(round(Psatval, 4))
else:
self.Psat_label = Psatval
self.ac_val.SetLabel('ac = ' + self.ac_label)
self.b_val.SetLabel('b = ' + self.b_label)
self.m_val.SetLabel('m = ' + m_text)
self.P_sat.SetLabel('Psat = ' + self.Psat_label)
#Calculate datapoints for vdw EOS
Data = np.zeros((1001))
Line_Data = np.zeros((1001))
for k in range(0, 1001):
Data[k] = 100000 * ((0.1**(10 - 0.01 * k))) + b + 0.01
Value = max([
min([
Psat.vdw(T, Psat.a(T, Tc, Pc, m), b, Data[k], 0) / 100,
100
]), -1000
])
V_l = calc[1]
V_v = calc[2]
if Data[k] < V_l or Data[k] > V_v:
Line_Data[k] = Value
else:
Line_Data[k] = Psatval
Plot_Data1 = np.vstack((Data, Line_Data)).T
Isotherm = PolyLine(Plot_Data1,
legend='Isotherm, T = ' + T_Text,
colour='blue')
self.canvas.Draw(PlotGraphics([Isotherm], '', ' V', 'P'))
self.canvas.setLogScale((True, False))
