def enthalpy_vector(rho,T,tau,delta,Tc,rho_c,eqn_type,parameter_set1,parameter_set2,parameter_set12,x_1,x_2):
from helmholtz_functions.ideal_helmholtz_energy_dtau_from_Cp_o_over_R_vector import ideal_helmholtz_energy_dtau_from_Cp_o_over_R_vector
from helmholtz_functions.d_alpha_d_tau_vector import d_alpha_d_tau_vector
from helmholtz_functions.d_alpha_d_delta_vector import d_alpha_d_delta_vector
from helmholtz_functions.ideal_helmholtz_from_coef_dtau_vector import ideal_helmholtz_from_coef_dtau_vector
from numpy import zeros,shape
dalpha_tau=zeros(len(tau))
dalpha_delta=zeros(len(tau))
dalpha_o=zeros(len(tau))
if(eqn_type=='mix'):
rho=rho/parameter_set12['M_amu'] #transform density to mol/L from kg/m^3
if(parameter_set1['ideal_eqn_type']=='Cp'):
dalpha_o1=ideal_helmholtz_energy_dtau_from_Cp_o_over_R_vector(parameter_set1['ni'],parameter_set1['ti'],parameter_set1['vi'],parameter_set1['ui'],parameter_set1['R'],parameter_set1['ho'],parameter_set1['so'],parameter_set1['rho_c']/parameter_set1['M_amu'],parameter_set1['Tc'],parameter_set1['Tc']/T,rho/(parameter_set1['rho_c']/parameter_set1['M_amu']),parameter_set1['n_ideal_gas_terms_pow'],parameter_set1['n_ideal_gas_terms_exp'],parameter_set1['To'],parameter_set1['rho_o'])
if(parameter_set1['ideal_eqn_type']=='Coef'):
dalpha_o1=ideal_helmholtz_from_coef_dtau_vector(rho/(parameter_set1['rho_c']/parameter_set1['M_amu']),parameter_set1['Tc']/T,parameter_set1['ideal_n'],parameter_set1['ideal_gamma'])
if(parameter_set2['ideal_eqn_type']=='Cp'):
dalpha_o2=ideal_helmholtz_energy_dtau_from_Cp_o_over_R_vector(parameter_set2['ni'],parameter_set2['ti'],parameter_set2['vi'],parameter_set2['ui'],parameter_set2['R'],parameter_set2['ho'],parameter_set2['so'],parameter_set2['rho_c']/parameter_set2['M_amu'],parameter_set2['Tc'],parameter_set2['Tc']/T,rho/(parameter_set2['rho_c']/parameter_set2['M_amu']),parameter_set2['n_ideal_gas_terms_pow'],parameter_set2['n_ideal_gas_terms_exp'],parameter_set2['To'],parameter_set2['rho_o'])
if(parameter_set2['ideal_eqn_type']=='Coef'):
dalpha_o2=ideal_helmholtz_from_coef_dtau_vector(rho/(parameter_set2['rho_c']/parameter_set2['M_amu']),parameter_set2['Tc']/T,parameter_set2['ideal_n'],parameter_set2['ideal_gamma'])
dalpha_tau1=d_alpha_d_tau_vector(tau,delta,parameter_set1)
dalpha_tau2=d_alpha_d_tau_vector(tau,delta,parameter_set2)
dalpha_tau12=d_alpha_d_tau_vector(tau,delta,parameter_set12)
dalpha_delta1=d_alpha_d_delta_vector(tau,delta,parameter_set1)
dalpha_delta2=d_alpha_d_delta_vector(tau,delta,parameter_set2)
dalpha_delta12=d_alpha_d_delta_vector(tau,delta,parameter_set12)
R_tau_dalpha_o=parameter_set1['R']*x_1*(dalpha_o1)*parameter_set1['Tc']/T+parameter_set2['R']*x_2*(dalpha_o2)*parameter_set2['Tc']/T
dalpha_tau=x_1*dalpha_tau1+x_2*dalpha_tau2+x_1*x_2*dalpha_tau12
dalpha_delta=x_1*dalpha_delta1+x_2*dalpha_delta2+x_1*x_2*dalpha_delta12
h2=tau*dalpha_tau
h3=delta*dalpha_delta
h=parameter_set12['R']*T*(1.0+h2+h3)+R_tau_dalpha_o*T
if(eqn_type=='pure_substance'):
if(parameter_set1['ideal_eqn_type']=='Cp'):
dalpha_o=ideal_helmholtz_energy_dtau_from_Cp_o_over_R_vector(parameter_set1['ni'],parameter_set1['ti'],parameter_set1['vi'],parameter_set1['ui'],parameter_set1['R'],parameter_set1['ho'],parameter_set1['so'],parameter_set1['rho_c']/parameter_set1['M_amu'],parameter_set1['Tc'],parameter_set1['Tc']/T,rho/parameter_set1['rho_c'],parameter_set1['n_ideal_gas_terms_pow'],parameter_set1['n_ideal_gas_terms_exp'],parameter_set1['To'],parameter_set1['rho_o'])
if(parameter_set1['ideal_eqn_type']=='Coef'):
dalpha_o=ideal_helmholtz_from_coef_dtau_vector(delta,tau,parameter_set1['ideal_n'],parameter_set1['ideal_gamma'])
dalpha_tau=d_alpha_d_tau_vector(tau,delta,parameter_set1)
dalpha_delta=d_alpha_d_delta_vector(tau,delta,parameter_set1)
R=parameter_set1['R']#/parameter_set1['M_amu']
h1=1.0
h2=tau*(dalpha_o+dalpha_tau)
h3=delta*dalpha_delta
h=R*T*(h1+h2+h3) #h in J/mol?
return h
def enthalpy_h2o(T,density):
from helmholtz_functions.ideal_helmholtz_from_coef import ideal_helmholtz_from_coef
from helmholtz_functions.ideal_helmholtz_from_coef_dtau import ideal_helmholtz_from_coef_dtau
from helmholtz_functions.ideal_helmholtz_from_coef_dtau_dtau import ideal_helmholtz_from_coef_dtau_dtau
from helmholtz_functions.d_alpha_d_tau import d_alpha_d_tau
from helmholtz_functions.d_alpha_d_delta import d_alpha_d_delta
from helmholtz_functions.helmholtz_energy_residual import helmholtz_energy_residual
from helmholtz_functions.d_alpha_d_tau_d_tau import d_alpha_d_tau_d_tau
from helmholtz_functions.d_alpha_d_delta_d_delta import d_alpha_d_delta_d_delta
from helmholtz_functions.d_alpha_d_delta_d_tau import d_alpha_d_delta_d_tau
from helmholtz_functions.d_alpha_d_tau_vector import d_alpha_d_tau_vector
from helmholtz_functions.d_alpha_d_delta_vector import d_alpha_d_delta_vector
from helmholtz_functions.ideal_helmholtz_from_coef_dtau_vector import ideal_helmholtz_from_coef_dtau_vector
from thermodynamic_functions.enthalpy_vector import enthalpy_vector
from helmholtz_functions.d_alpha_d_delta_d_delta_vector import d_alpha_d_delta_d_delta_vector
from helmholtz_functions.d_alpha_d_delta_vector import d_alpha_d_delta_vector
from helmholtz_functions.d_alpha_d_tau_d_tau_vector import d_alpha_d_tau_d_tau_vector
from helmholtz_functions.d_alpha_d_delta_d_tau_vector import d_alpha_d_delta_d_tau_vector
from helmholtz_functions.ideal_helmholtz_from_coef_vector import ideal_helmholtz_from_coef_vector
from helmholtz_functions.ideal_helmholtz_from_coef_dtau_dtau_vector import ideal_helmholtz_from_coef_dtau_dtau_vector
from helmholtz_functions.helmholtz_energy_residual_vector import helmholtz_energy_residual_vector
from pylab import zeros
from math import sqrt
from numpy import asarray
N_i=[0.12533547935523E-1,0.78957634722828E1, -0.87803203303561E1,
0.31802509345418,
-0.26145533859358,
-0.78199751687981E-2,
0.88089493102134E-2,
-0.66856572307965,
0.20433810950965,
-0.66212605039687E-4,
-0.19232721156002,
-0.25709043003438,
0.16074868486251,
-0.40092828925807E-1,
0.39343422603254E-6,
-0.75941377088144E-5,
0.56250979351888E-3,
-0.15608652257135E-4,
0.11537996422951E-8,
0.36582165144204E-6,
-0.13251180074668E-11,
-0.62639586912454E-9,
-0.10793600908932,
0.17611491008752E-1,
0.22132295167546,
-0.40247669763528,
0.58083399985759,
0.49969146990806E-2,
-0.31358700712549E-1,
-0.74315929710341,
0.47807329915480,
0.20527940895948E-1,
-0.13636435110343,
0.14180634400617E-1,
0.83326504880713E-2,
-0.29052336009585E-1,
0.38615085574206E-1,
-0.20393486513704E-1,
-0.16554050063734E-2,
0.19955571979541E-2,
0.15870308324157E-3,
-0.16388568342530E-4,
0.43613615723811E-1,
0.34994005463765E-1,
-0.76788197844621E-1,
0.22446277332006E-1,
-0.62689710414685E-4,
-0.55711118565645E-9,
-0.19905718354408,
0.31777497330738,
-0.11841182425981,
-0.31306260323435e2,
0.31546140237781e2,
-0.25213154341695e4,
-0.14874640856724,
0.31806110878444]
t_i=[-0.5, 0.875, 1.0, 0.5, 0.75, 0.375, 1.0, 4.0, 6.0, 12.0, 1.0,
5.0, 4.0 , 2.0, 13.0, 9.0 , 3.0 , 4.0, 11.0, 4.0, 13.0, 1.0,
7.0, 1.0 , 9.0, 10.0, 10.0 , 3.0 , 7.0, 10.0, 10.0, 6.0, 10.0,
10.0, 1.0 , 2.0, 3.0, 4.0 , 8.0 , 6.0, 9.0, 8.0, 16.0, 22.0,
23.0,23.0 , 10.0, 50.0, 44.0, 46.0 , 50.0, 0.0, 1.0, 4.0]
d_i=[1.0, 1.0, 1.0, 2.0, 2.0, 3.0, 4.0, 1.0, 1.0, 1.0, 2.0, 2.0, 3.0, 4.0,
4.0, 5.0, 7.0, 9.0, 10.0, 11.0, 13.0, 15.0, 1.0, 2.0, 2.0, 2.0, 3.0, 4.0,
4.0, 4.0, 5.0, 6.0, 6.0, 7.0, 9.0, 9.0, 9.0, 9.0, 9.0, 10.0, 10.0, 12.0,
3.0, 4.0, 4.0, 5.0, 14.0, 3.0, 6.0, 6.0, 6.0, 3.0, 3.0, 3.0]
p_i=[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0,
2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0,
2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 6.0, 6.0, 6.0, 6.0]
phi_i=zeros(51+3)
phi_i[51]=20.0 # Note, we need to use -sign here
phi_i[52]=20.0 # Note, we need to use -sign here
phi_i[53]=20.0 # Note, we need to use -sign here
Beta_i=zeros(51+5)
Beta_i[51]=150.0 #Note, we need to use - sign here
Beta_i[52]=150.0 #Note, we need to use - sign here
Beta_i[53]=250.0 #Note, we need to use - sign here
Beta_i[54]=0.3 #Note, we need to use - sign here
Beta_i[55]=0.3 #Note, we need to use - sign here
gamma_i=zeros(len(p_i)+3)
gamma_i[51]=1.21
gamma_i[52]=1.21
gamma_i[53]=1.25
D_i=zeros(51+3)
D_i[51]=1.0
D_i[52]=1.0
D_i[53]=1.0
R=8.314472
Tc = 647.096 #K
rho_c =322.0#18.015268*17.8737279956 #322.000214485 #kg m^-3 #mol/liter 17.8737279956
R_h2o = 0.46151805#R/18.015268# #kJ kg^-1 K^-1
delta=density/rho_c
tau=Tc/T
ideal_n = [-8.32044648201,6.6832105268,3.00632,0.012436,0.97315,1.27950,0.96956,0.24873]
ideal_gamma = [0.0,0.0,0.0,1.28728967,3.53734222,7.74073708,9.24437796,27.5075105]
n_power_terms=51#len(p_i)
n_gaussian_terms=3
n_critical_terms=2
#print delta,tau
#critcal terms
RES_a=zeros(len(p_i)+5)
RES_b=zeros(len(p_i)+5)
RES_B=zeros(len(p_i)+5)
RES_C=zeros(len(p_i)+5)
RES_D=zeros(len(p_i)+5)
RES_A=zeros(len(p_i)+5)
RES_a[54]=3.5
RES_a[55]=3.5
RES_b[54]=0.85
RES_b[55]=0.95
RES_B[54]=0.2
RES_B[55]=0.2
RES_C[54]=28.0
RES_C[55]=32.0
RES_D[54]=700.0
RES_D[55]=800.0
RES_A[54]=0.32
RES_A[55]=0.32
h2o_component_params={'N_i':asarray([0.12533547935523E-1,0.78957634722828E1, -0.87803203303561E1,0.31802509345418, -0.26145533859358, -0.78199751687981E-2,0.88089493102134E-2, -0.66856572307965,0.20433810950965,-0.66212605039687E-4,-0.19232721156002,-0.25709043003438,0.16074868486251,-0.40092828925807E-1,0.39343422603254E-6, -0.75941377088144E-5,0.56250979351888E-3, -0.15608652257135E-4,0.11537996422951E-8, 0.36582165144204E-6, -0.13251180074668E-11,-0.62639586912454E-9, -0.10793600908932, 0.17611491008752E-1, 0.22132295167546, -0.40247669763528,0.58083399985759, 0.49969146990806E-2, -0.31358700712549E-1,-0.74315929710341,0.47807329915480, 0.20527940895948E-1,-0.13636435110343, 0.14180634400617E-1, 0.83326504880713E-2, -0.29052336009585E-1,0.38615085574206E-1, -0.20393486513704E-1,-0.16554050063734E-2,0.19955571979541E-2, 0.15870308324157E-3, -0.16388568342530E-4, 0.43613615723811E-1, 0.34994005463765E-1, -0.76788197844621E-1,0.22446277332006E-1, -0.62689710414685E-4,-0.55711118565645E-9,-0.19905718354408, 0.31777497330738,-0.11841182425981,-0.31306260323435e2,0.31546140237781e2,-0.25213154341695e4,-0.14874640856724,0.31806110878444]),
't_i':asarray([-0.5, 0.875, 1.0, 0.5, 0.75, 0.375, 1.0, 4.0, 6.0, 12.0, 1.0,
5.0, 4.0 , 2.0, 13.0, 9.0 , 3.0 , 4.0, 11.0, 4.0, 13.0, 1.0,
7.0, 1.0 , 9.0, 10.0, 10.0 , 3.0 , 7.0, 10.0, 10.0, 6.0, 10.0,
10.0, 1.0 , 2.0, 3.0, 4.0 , 8.0 , 6.0, 9.0, 8.0, 16.0, 22.0,
23.0,23.0 , 10.0, 50.0, 44.0, 46.0 , 50.0, 0.0, 1.0, 4.0]),
'd_i':asarray([1.0, 1.0, 1.0, 2.0, 2.0, 3.0, 4.0, 1.0, 1.0, 1.0, 2.0, 2.0, 3.0, 4.0,
4.0, 5.0, 7.0, 9.0, 10.0, 11.0, 13.0, 15.0, 1.0, 2.0, 2.0, 2.0, 3.0, 4.0,
4.0, 4.0, 5.0, 6.0, 6.0, 7.0, 9.0, 9.0, 9.0, 9.0, 9.0, 10.0, 10.0, 12.0,
3.0, 4.0, 4.0, 5.0, 14.0, 3.0, 6.0, 6.0, 6.0, 3.0, 3.0, 3.0]),
'p_i':asarray([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0,
2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0,
2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 6.0, 6.0, 6.0, 6.0]),
'phi_i':phi_i,
'Beta_i':Beta_i,
'gamma_i':gamma_i,
'D_i':D_i,
'R':float(8.314472),
'Tc':float(647.096), #K
'rho_c':float(322.0),#18.015268*17.8737279956 #322.000214485 #kg m^-3 #mol/liter 17.8737279956
'M_amu':float(8.314472/0.46151805),
'ideal_n': asarray([-8.32044648201,6.6832105268,3.00632,0.012436,0.97315,1.27950,0.96956,0.24873]),
'ideal_gamma':asarray([0.0,0.0,0.0,1.28728967,3.53734222,7.74073708,9.24437796,27.5075105]),
'n_power_terms':int(51),#len(p_i)
'n_power_terms_wo_exp':int(7),
'n_power_terms_w_exp':int(51-7),
'n_gaussian_terms':int(3),
'n_critical_terms':int(2),
'RES_a':RES_a,
'RES_b':RES_b,
'RES_B':RES_B,
'RES_C':RES_C,
'RES_D':RES_D,
'RES_A':RES_A,
'ni':int(0),
'ti':int(0),
'vi':int(0),
'ui':int(0),
'ho':int(0),
'so':int(0),
'n_ideal_gas_terms_pow':int(0),
'n_ideal_gas_terms_exp':int(0),
'To':int(0),
'Po':int(0),
'rho_o':int(0),
'ideal_eqn_type':'Coef'}
#Calculate Ideal Terms
delta_v=asarray([delta,delta,delta])
tau_v=asarray([tau,tau,tau])
ideal=ideal_helmholtz_from_coef(delta,tau,ideal_n,ideal_gamma)
ideal_v=ideal_helmholtz_from_coef_vector(delta_v,tau_v,h2o_component_params['ideal_n'],h2o_component_params['ideal_gamma'])
#print ideal-ideal_v
dalpha_o=ideal_helmholtz_from_coef_dtau(delta,tau,ideal_n,ideal_gamma)
dalpha_o_vector=ideal_helmholtz_from_coef_dtau_vector(delta_v,tau_v,h2o_component_params['ideal_n'],h2o_component_params['ideal_gamma'])
#print dalpha_o-dalpha_o_vector
dalpha_o_tau_tau=ideal_helmholtz_from_coef_dtau_dtau(delta,tau,ideal_n,ideal_gamma)
dalpha_o_tau_tau_v=ideal_helmholtz_from_coef_dtau_dtau_vector(delta_v,tau_v,h2o_component_params['ideal_n'],h2o_component_params['ideal_gamma'])
#print dalpha_o_tau_tau-dalpha_o_tau_tau_v
#Calculate Residual Terms
residual=helmholtz_energy_residual(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A)
residual_v=helmholtz_energy_residual_vector(tau_v,delta_v,h2o_component_params)
print residual-residual_v
dalpha_tau=d_alpha_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A)
dalpha_tau_vector=d_alpha_d_tau_vector(tau_v,delta_v,h2o_component_params)
#print dalpha_tau-dalpha_tau_vector
dalpha_delta=d_alpha_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A)
dalpha_delta_vector=d_alpha_d_delta_vector(tau_v,delta_v,h2o_component_params)
#print dalpha_delta_vector-dalpha_delta
dalpha_tau_tau=d_alpha_d_tau_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A)
dalpha_tau_tau_vector=d_alpha_d_tau_d_tau_vector(tau_v,delta_v,h2o_component_params)
#print dalpha_tau_tau-dalpha_tau_tau_vector
dalpha_delta_delta=d_alpha_d_delta_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A)
dalpha_delta_delta_vector=d_alpha_d_delta_d_delta_vector(tau_v,delta_v,h2o_component_params)
#print T, dalpha_delta_delta-dalpha_delta_delta_vector
# print dalpha_delta_delta
dalpha_delta_tau=d_alpha_d_delta_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A)
dalpha_delta_tau_vector=d_alpha_d_delta_d_tau_vector(tau_v,delta_v,h2o_component_params)
#print dalpha_delta_tau_vector-dalpha_delta_tau
#compressibility Density<-->Pressure
Z=delta*dalpha_delta+float(1.0)
#Enthalpy
h1=R_h2o*T*1.0
h2=R_h2o*T*tau*(dalpha_o+dalpha_tau)
h3=R_h2o*T*delta*dalpha_delta
h=h1+h2+h3
h_v=enthalpy_vector(tau_v,delta_v,Tc,rho_c,'pure_substance',h2o_component_params,h2o_component_params,h2o_component_params,0,0)
#print dalpha_o,dalpha_o_vector
#print h,R_h2o*T*h_v
#Entropy
s=R_h2o*(tau*dalpha_o+tau*dalpha_tau-ideal-residual)
#Absolute Helmholtz Energy
absolute_helmholtz_energy=R_h2o*T*(ideal+residual)
#Isochoric heat capacity
cv=-1.0*R_h2o*(tau*tau*(dalpha_o_tau_tau+dalpha_tau_tau))
#Isobaric heat capacity
cp=cv+R_h2o*pow((1.0+delta*dalpha_delta-delta*tau*dalpha_delta_tau),2)/(1.0+2.0*delta*dalpha_delta+delta*delta*dalpha_delta_delta)
#print dalpha_delta,dalpha_delta_delta,dalpha_delta_tau,dalpha_tau_tau
# Speed of Sound?
#print dalpha_delta_delta,dalpha_delta_tau
#speed_o_sound_p1 = 1.0 + 2.0*delta*dalpha_delta + delta*delta*dalpha_delta_delta
#speed_o_sound_p2 = pow((1.0 + delta*dalpha_delta - delta*tau*dalpha_delta_tau),2)
#speed_o_sound_p3 = tau*tau*(dalpha_o_tau_tau + dalpha_tau_tau)
#speed_o_sound= sqrt((R_h2o*T)*(speed_o_sound_p1 - speed_o_sound_p2/speed_o_sound_p3)*1000.0)
#what it's probably not
#d_tau_tau
#d_delta
#d_o_tau_tau
a1 = 1 + delta*dalpha_delta - delta*tau*dalpha_delta_tau;
b1 = tau*tau*(dalpha_o_tau_tau + dalpha_tau_tau);
w = 1 + 2*delta*dalpha_delta + delta*delta*dalpha_delta_delta - a1*a1/b1;
speed_o_sound=sqrt(R_h2o*T*w*1000)
return Z,h,s,absolute_helmholtz_energy,cv,cp,speed_o_sound
