def enthalpy(tau,delta,ni,ti,vi,ui,R,ho,so,rho_c,Tc,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o,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,M_amu,ideal_n,ideal_gamma,ideal_eqn_type):
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.d_alpha_d_tau import d_alpha_d_tau
from helmholtz_functions.d_alpha_d_delta import d_alpha_d_delta
from helmholtz_functions.ideal_helmholtz_from_coef_dtau import ideal_helmholtz_from_coef_dtau
from pylab import zeros
dalpha_tau=zeros(len(tau))
dalpha_delta=zeros(len(tau))
dalpha_o=zeros(len(tau))
#M_H2=2.01594
T=Tc/tau
if(ideal_eqn_type=='Cp'):
for i in range(0,len(tau)):
dalpha_o[i]=ideal_helmholtz_energy_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/M_amu,Tc,tau[i],delta[i],n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o)
if(ideal_eqn_type=='Coef'):
for i in range(0,len(tau)):
dalpha_o[i]=ideal_helmholtz_from_coef_dtau(delta[i],tau[i],ideal_n,ideal_gamma)
if(ideal_eqn_type=='none'):
dalpha_o[1]==0.0
for i in range(0,len(tau)):
dalpha_tau[i]=d_alpha_d_tau(tau[i],delta[i],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[i]=d_alpha_d_delta(tau[i],delta[i],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)
R_specific=R/M_amu
h1=R_specific*T*1.0
h2=R_specific*T*tau*(dalpha_o+dalpha_tau)
h3=R_specific*T*delta*dalpha_delta
h=h1+h2+h3
return h
def cp_h2_mod(T,Pin):
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.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 numpy import asarray,zeros
from scipy.optimize import fsolve
from residual_pressure import residual_pressure
bars_to_kPa=100
P=Pin*bars_to_kPa
R=8.314472
R_hydrogen=R/2.01594
M_amu=2.01594
density_guess=P/(R_hydrogen*T)
rho_c=15.508*2.01594 # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel
delta_guess=density_guess/rho_c
########################################
#Hydrogen parameters from Leachman,2007
########################################
Tc=33.145
tau=Tc/T
R=8.314472
R_hydrogen=R/2.01594
N_i=[-6.93643,0.01,2.1101,4.52059,0.732564,-1.34086,0.130985,-0.777414,0.351944,-0.0211716,0.0226312,0.032187,-0.0231752,0.0557346];
t_i=[0.6844,1,0.989,0.489,0.803,1.1444,1.409,1.754,1.311,4.187,5.646,0.791,7.249,2.986]
d_i=[1,4,1,1,2,2,3,1,3,2,1,3,1,1]
p_i=[0,0,0,0,0,0,0,1,1,0/1,0/1,0/1,0/1,0/1]
phi_i=[0,0,0,0,0,0,0,0,0,1.685,0.489,0.103,2.506,1.607]# Not, we need to use -sign here
Beta_i=[0,0,0,0,0,0,0,0,0, 0.171,0.2245,0.1304,0.2785,0.3967] #Note, we need to use - sign here
gamma_i=[0,0,0,0,0,0,0,0,0,0.7164,1.3444,1.4517,0.7204,1.5445]
D_i=[0,0,0,0,0,0,0,0,0,1.506,0.156,1.736,0.67,1.6620]
Tc=33.145
rho_c=15.508*2.01594 # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel
#delta=density/rho_c
tau=Tc/T
ni=2.5
ti=0.0
vi=[1.616,-0.4117,-0.792,0.758,1.217]
ui=[531,751,1989,2484,6859]
R=8.314472 #J/mol/K
ho = 7206.9069892047 #J/mol
so = 143.4846187346 #J/mol/K
n_power_terms=9
n_gaussian_terms=5
n_critical_terms=0
n_power_terms_w_exp=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))
To=273.15
rho_o=((0.001/(R*To))*1000)
#############################################
## End parameters -> should be data structure
#############################################
delta=fsolve(residual_pressure,delta_guess,args=(P,tau,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,R,Tc,rho_c,M_amu))
dalpha_o_tau_tau=ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/2.01594,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o)
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)
#Isochoric heat capacity
cv=-1.0*R_hydrogen*(tau*tau*(dalpha_o_tau_tau+dalpha_tau_tau))
#Isobaric heat capacity
cp=cv+R_hydrogen*pow((1.0+delta*dalpha_delta-delta*tau*dalpha_delta_tau),2)/(1.0+2.0*delta*dalpha_delta+delta*delta*dalpha_delta_delta)
#default is in kJ/kg-K convert to erg/K/mol for DeBoer's TCM
# kJ 1000J 1e7 ergs 1 kg M_amu g erg
#----- * ----- * --------- * ------ * -------- = -------
# kg*K kJ 1J 1000 g mol K mol
return cp*M_amu*1e7
def enthalpy_normal_h2(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_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=[-6.93643,0.01,2.1101,4.52059,0.732564,-1.34086,0.130985,-0.777414,0.351944,-0.0211716,0.0226312,0.032187,-0.0231752,0.0557346];
t_i=[0.6844,1,0.989,0.489,0.803,1.1444,1.409,1.754,1.311,4.187,5.646,0.791,7.249,2.986]
d_i=[1,4,1,1,2,2,3,1,3,2,1,3,1,1]
p_i=[0,0,0,0,0,0,0,1,1,0/1,0/1,0/1,0/1,0/1]
phi_i=[0,0,0,0,0,0,0,0,0,1.685,0.489,0.103,2.506,1.607]# Not, we need to use -sign here
Beta_i=[0,0,0,0,0,0,0,0,0, 0.171,0.2245,0.1304,0.2785,0.3967] #Note, we need to use - sign here
gamma_i=[0,0,0,0,0,0,0,0,0,0.7164,1.3444,1.4517,0.7204,1.5445]
D_i=[0,0,0,0,0,0,0,0,0,1.506,0.156,1.736,0.67,1.6620]
Tc=33.145
rho_c=15.508*2.01594 # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel
delta=density/rho_c
tau=Tc/T
R=8.314472
R_hydrogen=R/2.01594
ni=2.5
ti=0.0
vi=[1.616,-0.4117,-0.792,0.758,1.217]
ui=[531,751,1989,2484,6859]
R=8.314472 #J/mol/K
ho = 7206.9069892047 #J/mol
so = 143.4846187346 #J/mol/K
n_power_terms=9
n_gaussian_terms=5
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))
To=273.15
rho_o=((0.001/(R*To))*1000)
h2_component_params={'N_i':asarray([-6.93643,0.01,2.1101,4.52059,0.732564,-1.34086,0.130985,-0.777414,0.351944,-0.0211716,0.0226312,0.032187,-0.0231752,0.0557346]),
't_i':asarray([0.6844,1,0.989,0.489,0.803,1.1444,1.409,1.754,1.311,4.187,5.646,0.791,7.249,2.986]),
'd_i':asarray([1,4,1,1,2,2,3,1,3,2,1,3,1,1]),
'p_i':asarray([0,0,0,0,0,0,0,1,1,0/1,0/1,0/1,0/1,0/1]),
'phi_i':asarray([0,0,0,0,0,0,0,0,0,1.685,0.489,0.103,2.506,1.607]),
'Beta_i':asarray([0,0,0,0,0,0,0,0,0, 0.171,0.2245,0.1304,0.2785,0.3967]),
'gamma_i':asarray([0,0,0,0,0,0,0,0,0,0.7164,1.3444,1.4517,0.7204,1.5445]),
'D_i':asarray([0,0,0,0,0,0,0,0,0,1.506,0.156,1.736,0.67,1.6620]),
'Tc':float(33.145),
'rho_c':float(15.508*2.01594), # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel
'R':float(8.314472),
'ni':float(2.5),
'ti':float(0.0),
'vi':asarray([1.616,-0.4117,-0.792,0.758,1.217]),
'ui':asarray([531,751,1989,2484,6859]),
#'R':float(8.314472) #J/mol/K
'ho':float(7206.9069892047), #J/mol
'so':float(143.4846187346), #J/mol/K
'n_power_terms':int(9),
'n_power_terms_wo_exp':int(7),
'n_power_terms_w_exp':int(2),
'n_gaussian_terms':int(5),
'n_critical_terms':int(0),
'n_ideal_gas_terms_pow':int(0),
'n_ideal_gas_terms_exp':int(5),
'RES_a':zeros(5),
'RES_b':zeros(5),
'RES_B':zeros(5),
'RES_C':zeros(5),
'RES_D':zeros(5),
'RES_A':zeros(5),
'To':float(273.15),
'rho_o':float((0.001/(8.314472*273.15))*1000),
'M_amu':float(2.01594),
'ideal_eqn_type':'Cp'}
tau_v=asarray([tau,tau])
delta_v=asarray([delta,delta])
Virial_b=Virial_B_vector(tau_v,h2_component_params,h2_component_params,h2_component_params,1.0,1.0,rho_c/2.01594,Tc,'pure')
#Calculate Ideal Terms
ideal=ideal_helmholtz_energy_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/2.01594,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/2.01594,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/2.01594,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o)
dalpha_o_tau_tau=ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/2.01594,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/2.01594,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)
print T, Virial_b,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_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_hydrogen*T*1.0
h2=R_hydrogen*T*tau*(dalpha_o+dalpha_tau)
h3=R_hydrogen*T*delta*dalpha_delta
h=h1+h2+h3
#Entropy
s=R_hydrogen*(tau*dalpha_o+tau*dalpha_tau-ideal-residual)
#Absolute Helmholtz Energy
absolute_helmholtz_energy=R_hydrogen*T*(ideal+residual)
#Isochoric heat capacity
cv=-1.0*R_hydrogen*(tau*tau*(dalpha_o_tau_tau+dalpha_tau_tau))
#Isobaric heat capacity
cp=cv+R_hydrogen*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_hydrogen*T*w*1000)
return Z,h,s,absolute_helmholtz_energy,cv,cp,speed_o_sound,R_hydrogen*T*ideal,residual*R_hydrogen*T
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
def enthalpy_helium(T,density):
from math import sqrt,exp
from numpy import sort,asarray,shape,concatenate,power
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.mBWR_to_Helmholtz import mBWR_to_Helmholtz
from helmholtz_functions.helmholtz_energy_residual import helmholtz_energy_residual
from helmholtz_functions.d_alpha_d_tau import d_alpha_d_tau
from helmholtz_functions.d_alpha_d_tau_d_tau import d_alpha_d_tau_d_tau
from helmholtz_functions.d_alpha_d_delta import d_alpha_d_delta
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
M_He=4.0026#02 g/mol
R=8.314310 #
R_He=R/M_He
To=4.230359714841141 #Kelvin
rho_o=31.163394763964778 # mol/L
ho=108.78863197310453 # J/mol
so=3.6929233790579463 # J/mol/K
Tc=5.19530# Kelvin
rho_c=17.3990 #(mol/L)
mBWR_Coef=[0.4558980227431e-4,#1
0.1260692007853e-2,#2
-0.7139657549318e-2,#3
0.9728903861441e-2,#4
-0.1589302471562e-1,#5
0.1454229259623e-5,#6
-0.4708238429298e-4,#7
0.1132915232587e-2,#8
0.2410763742104e-2,#9
-0.5093547838381e-8,#10
0.2699726927900e-5,#11
-0.3954146691114e-4,#12`
0.1551961438127e-8,#13
0.1050712335785e-7,#14
-0.5501158366750e-7,#15
-0.1037673478521e-9,#16
0.6446881346448e-12,#17
0.3298960057071e-10,#18
-0.3555585738784e-12,#19
-0.6885401367690e-2,#20
0.9166109232806e-2,#21
-0.6544314242937e-5,#22
-0.3315398880031e-4,#23
-0.2067693644676e-7,#24
0.3850153114958e-7,#25
-0.1399040626999e-10,#26
-0.1888462892389e-11,#27
-0.4595138561035e-14,#28
0.6872567403738e-14,#29
-0.6097223119177e-18,#30
-0.7636186157005e-17,#31
0.3848665703556e-17]#32
rho=density/M_He #mol/L
# delta=rho/rho_c
# tau=Tc/T
# tau_o=Tc/To
# delta_o=rho_o/rho_c
ni=2.5
ti=0.0
vi=[0.0]
ui=[0.0]
npower=1
n_exp=0
tau=Tc/T
delta=rho/rho_c
n_power=1
#phi_o=ideal_helmholtz_energy_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c,Tc,tau,delta,n_power,n_exp,To,rho_o)
#N=mBWR_Coef
#abwr=ABWR(N,T,rho,rho_c)
#residual=abwr/(R*T)
[N_i,d_i,t_i,p_i]=mBWR_to_Helmholtz(mBWR_Coef,T,rho,rho_c,Tc,R)
#print shape(sorted_array)
#print d_i
#print t_i
#N_i=sorted_array[3,:]
#d_i=sorted_array[2,:]
#t_i=sorted_array[1,:]
#p_i=sorted_array[0,:]
#print 'heres p_i',p_i,p_ii
Beta_i=0
gamma_i=0
D_i=0
n_power_terms=len(N_i)
n_gaussian_terms=0
n_critical_terms=0
RES_a=0
RES_b=0
RES_B=0
RES_C=0
RES_D=0
RES_A=0
phi_i=0
#residual2=helmholtz_energy_residual(tau,delta,ni,ti,di,pi,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)
#helmholtz=residual2#-residual#residual2#(ideal+residual)/M_He#(ideal+residual)/M_He
#print residual,residual2
#Calculate Ideal Terms
ideal=ideal_helmholtz_energy_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c,Tc,tau,delta,n_power,n_exp,To,rho_o)
dalpha_o=ideal_helmholtz_energy_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c,Tc,tau,delta,n_power,n_exp,To,rho_o)
dalpha_o_tau_tau=ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c,Tc,tau,delta,n_power,n_exp,To,rho_o)
#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_He*T*1.0
h2=R_He*T*tau*(dalpha_o+dalpha_tau)
h3=R_He*T*delta*dalpha_delta
h=h1+h2+h3
#Entropy
s=R_He*(tau*dalpha_o+tau*dalpha_tau-ideal-residual)
#Absolute Helmholtz Energy
absolute_helmholtz_energy=R_He*T*(ideal+residual)
#Isochoric heat capacity
cv=-1.0*R_He*(tau*tau*(dalpha_o_tau_tau+dalpha_tau_tau))
#Isobaric heat capacity
cp=cv+R_He*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=power(R_He*T*w*1000,0.5)
return Z,h,s,absolute_helmholtz_energy,cv,cp,speed_o_sound,ideal,residual
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
