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_methane(T,density):
from helmholtz_functions.ideal_helmholtz_energy_from_Cp_o_over_R import ideal_helmholtz_energy_from_Cp_o_over_R
from helmholtz_functions.ideal_helmholtz_energy_dtau_from_Cp_o_over_R import ideal_helmholtz_energy_dtau_from_Cp_o_over_R
from helmholtz_functions.ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R import ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R
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.ideal_helmholtz_energy_from_Cp_o_over_R_vector import ideal_helmholtz_energy_from_Cp_o_over_R_vector
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.ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R_vector import ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R_vector
from thermodynamic_functions.Virial_B_vector import Virial_B_vector
from math import sqrt
from pylab import zeros
from numpy import asarray
N_i=[0.43679010280e-01,
0.67092361990,
-0.17655778590e01,
0.85823302410,
-0.12065130520e01,
0.51204672200,
-0.40000107910e-03 ,
-0.12478424230e-01,
0.31002697010e-01,
0.17547485220e-02,
-0.31719216050e-05,
-0.22403468400e-05,
0.29470561560e-06,
0.18304879090,
0.15118836790,
-0.42893638770,
0.68940024460e-01,
-0.14083139960e-01,
-0.30630548300e-01,
-0.29699067080e-01,
-0.19320408310e-01,
-0.11057399590,
0.99525489950e-01,
0.85484378250e-02,
-0.61505556620e-01,
-0.42917924230e-01,
-0.18132072900e-01,
0.34459047600e-01,
-0.23859194500e-02,
-0.11590949390e-01,
0.66416936020e-01,
-0.23715495900e-01,
-0.39616249050e-01,
-0.13872920440e-01,
0.33894895990e-01,
-0.29273787530e-02,
0.93247999460e-04,
-0.62871715180e01,
0.12710694670e02,
-0.64239534660e01]
t_i= [-0.5,
0.5,
1.0,
0.5,
1.0,
1.5,
4.5,
0.0,
1.0,
3.0,
1.0,
3.0,
3.0,
0.0,
1.0,
2.0,
0.0,
0.0,
2.0,
2.0,
5.0,
5.0,
5.0,
2.0,
4.0,
12.0,
8.0,
10.0,
10.0,
10.0,
14.0,
12.0,
18.0,
22.0,
18.0,
14.0,
2.0,
0.0,
1.0,
2.0]
d_i=[1.0,
1.0,
1.0,
2.0,
2.0,
2.0,
2.0,
3.0,
4.0,
4.0,
8.0,
9.0,
10.0,
1.0,
1.0,
1.0,
2.0,
4.0,
5.0,
6.0,
1.0,
2.0,
3.0,
4.0,
4.0,
3.0,
5.0,
5.0,
8.0,
2.0,
3.0,
4.0,
4.0,
4.0,
5.0,
6.0,
2.0,
0.0,
0.0,
0.0]
p_i=[0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
2,
2,
2,
2,
2,
3,
3,
3,
3,
4,
4,
4,
4,
4,
4,
4,
0/1,
0/1,
0/1,
0/1]
phi_i=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,20.0,40.0,40.0,40.0]# Not, we need to use -sign here
Beta_i=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,200,250,250,250] #Note, we need to use - sign here
gamma_i=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1.07,1.11,1.11,1.11]
D_i=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1.0,1.0,1.0,1.0]
Tc=190.564
rho_c=10.139128*16.0428 # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel
delta=density/rho_c
tau=Tc/T
R=8.31451
R_methane=R/16.0428
ni=4.0016
ti=0
vi=[0.84490000e-02,4.6942000,3.4865000,1.6572000,1.4115000]
ui=[648.0,1957.0,3895.0,5705.0,15080.0]
R=8.31451 #J/mol/K
ho = 8295.6883966242294 #J/mol - -
so = 28.384819963016852 #J/mol/K
rho_o=26.326811491312679 #mol/L
To=111.66720547358069
n_power_terms=36
n_gaussian_terms=4
n_critical_terms=0
n_ideal_gas_terms_pow=0
n_ideal_gas_terms_exp=5
RES_a = zeros(len(ui))
RES_b = zeros(len(ui))
RES_B = zeros(len(ui))
RES_C = zeros(len(ui))
RES_D = zeros(len(ui))
RES_A = zeros(len(ui))
ch4_component_params={'N_i':asarray([0.43679010280e-01,0.67092361990, -0.17655778590e01, 0.85823302410, -0.12065130520e01,0.51204672200, -0.40000107910e-03 ,-0.12478424230e-01,0.31002697010e-01,0.17547485220e-02,-0.31719216050e-05,-0.22403468400e-05,0.29470561560e-06,0.18304879090, 0.15118836790,-0.42893638770,0.68940024460e-01,-0.14083139960e-01,-0.30630548300e-01,-0.29699067080e-01,-0.19320408310e-01,-0.11057399590,0.99525489950e-01,0.85484378250e-02, -0.61505556620e-01,-0.42917924230e-01,-0.18132072900e-01,0.34459047600e-01,-0.23859194500e-02,-0.11590949390e-01,0.66416936020e-01,-0.23715495900e-01, -0.39616249050e-01, -0.13872920440e-01,0.33894895990e-01,-0.29273787530e-02,0.93247999460e-04,-0.62871715180e+01,0.12710694670e+02,-0.64239534660e+01]),
't_i':asarray([-0.5, 0.5,1.0,0.5,1.0,1.5,4.5,0.0,1.0,3.0,1.0,3.0,3.0,0.0,1.0,2.0,0.0,0.0,2.0,2.0,5.0,5.0,5.0,2.0,4.0,12.0,8.0,10.0,10.0,10.0,14.0,12.0,18.0,22.0,18.0,14.0,2.0,0.0,1.0,2.0]),
'd_i':asarray([1.0,1.0,1.0,2.0,2.0,2.0,2.0,3.0,4.0,4.0,8.0,9.0,10.0,1.0,1.0,1.0,2.0,4.0,5.0,6.0,1.0,2.0,3.0,4.0,4.0,3.0,5.0,5.0,8.0,2.0,3.0,4.0,4.0,4.0,5.0,6.0,2.0,0.0,0.0,0.0]),
'p_i':asarray([0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,2,2,2,2]),
'phi_i':asarray([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,20.0,40.0,40.0,40.0]),
'Beta_i':asarray([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,200,250,250,250]),
'gamma_i':asarray([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1.07,1.11,1.11,1.11]),
'D_i':asarray([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1]),
'Tc':float(190.564),
'rho_c':float(10.139128*16.0428), # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel
'R':float(8.31451),
'ni':float(4.0016),
'ti':float(0.0),
'vi':asarray([0.84490000e-02,4.6942000,3.4865000,1.6572000,1.4115000]),
'ui':asarray([648.0,1957.0,3895.0,5705.0,15080.0]),
#'R':float(8.314472) #J/mol/K
'ho':float(8295.6883966242294), #J/mol
'so':float(28.384819963016852), #J/mol/K
'n_power_terms':int(36),
'n_power_terms_wo_exp':int(13),
'n_power_terms_w_exp':int(36-13),
'n_gaussian_terms':int(4),
'n_critical_terms':int(0),
'n_ideal_gas_terms_pow':int(0),
'n_ideal_gas_terms_exp':int(5),
'RES_a':zeros(4),
'RES_b':zeros(4),
'RES_B':zeros(4),
'RES_C':zeros(4),
'RES_D':zeros(4),
'RES_A':zeros(4),
'To':float(111.66720547358069),
'rho_o':float(26.326811491312679),
'M_amu':float(16.0428),
'ideal_eqn_type':'Cp'}
tau_v=asarray([tau,tau])
delta_v=asarray([delta,delta])
Virial_b=Virial_B_vector(tau_v,ch4_component_params,ch4_component_params,ch4_component_params,1.0,1.0,rho_c/16.0428,Tc,'pure')
#Calculate Ideal Terms
ideal=ideal_helmholtz_energy_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o)
ideal_v=ideal_helmholtz_energy_from_Cp_o_over_R_vector(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau_v,delta_v,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o)
#print ideal-ideal_v
dalpha_o=ideal_helmholtz_energy_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o)
dalpha_o_v=ideal_helmholtz_energy_dtau_from_Cp_o_over_R_vector(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau_v,delta_v,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o)
print dalpha_o-dalpha_o_v
dalpha_o_tau_tau=ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o)
dalpha_o_tau_tau_vector=ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R_vector(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau_v,delta_v,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o)
#print dalpha_o_tau_tau-dalpha_o_tau_tau_vector
#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)
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_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_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_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_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)
#compressibility Density<-->Pressure
Z=delta*dalpha_delta+float(1.0)
#Enthalpy
h1=R_methane*T*1.0
h2=R_methane*T*tau*(dalpha_o+dalpha_tau)
h3=R_methane*T*delta*dalpha_delta
h=h1+h2+h3
#Entropy
s=R_methane*(tau*dalpha_o+tau*dalpha_tau-ideal-residual)
#Absolute Helmholtz Energy
absolute_helmholtz_energy=R_methane*T*(ideal+residual)
#Isochoric heat capacity
cv=-1.0*R_methane*(tau*tau*(dalpha_o_tau_tau+dalpha_tau_tau))
#Isobaric heat capacity
cp=cv+R_methane*pow((1.0+delta*dalpha_delta-delta*tau*dalpha_delta_tau),2)/(1.0+2.0*delta*dalpha_delta+delta*delta*dalpha_delta_delta)
# Speed of Sound?
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_methane*T*w*1000)
return Z,h,s,absolute_helmholtz_energy,cv,cp,speed_o_sound,R_methane*T*ideal,residual*R_methane*T
