def Excess_Enthalpy_vector(rho,T,tau,delta,Tc,rho_c,parameter_set1,parameter_set2,parameter_set12,x_1,x_2): from thermodynamic_functions.enthalpy_vector import enthalpy_vector from thermodynamic_functions.pressure_vector import pressure_vector from residual_pressure_pure_substance import residual_pressure_pure_substance from scipy.optimize import leastsq Enthalpy_of_mixture=enthalpy_vector(rho,T,tau,delta,Tc,rho_c,'mix',parameter_set1,parameter_set2,parameter_set12,x_1,x_2) Pressure_of_mixture=pressure_vector(rho,T,tau,delta,'mix',parameter_set1,parameter_set2,parameter_set12,x_1,x_2,Tc,rho_c) density_guess_component_1=Pressure_of_mixture/((parameter_set1['R']/parameter_set1['M_amu'])*T) density_guess_component_2=Pressure_of_mixture/((parameter_set2['R']/parameter_set2['M_amu'])*T) [density_component_1,message_1]=leastsq(residual_pressure_pure_substance,density_guess_component_1,args=(Pressure_of_mixture,T,parameter_set1)) [density_component_2,message_2]=leastsq(residual_pressure_pure_substance,density_guess_component_2,args=(Pressure_of_mixture,T,parameter_set2)) Tc1=parameter_set1['Tc'] Tc2=parameter_set2['Tc'] rho_c1=parameter_set1['rho_c'] rho_c2=parameter_set2['rho_c'] tau_1=Tc1/T tau_2=Tc2/T delta_1=density_component_1/parameter_set1['rho_c'] delta_2=density_component_2/parameter_set2['rho_c'] Enthalpy_component_1=enthalpy_vector(density_component_1,T,tau_1,delta_1,Tc1,rho_c1,'pure_substance',parameter_set1,parameter_set1,parameter_set1,1,1) Enthalpy_component_2=enthalpy_vector(density_component_2,T,tau_2,delta_2,Tc2,rho_c2,'pure_substance',parameter_set2,parameter_set2,parameter_set2,1,1) Excess_Enthalpy=Enthalpy_of_mixture-x_1*Enthalpy_component_1-x_2*Enthalpy_component_2 return Excess_Enthalpy
[tau, delta, Tc, rho_c] = scale_tau_and_delta_kw( T, density / h2_ch4_mix_params["M_amu"], x_h2, x_ch4, h2_params["Tc"], ch4_params["Tc"], h2_params["rho_c"] / h2_params["M_amu"], ch4_params["rho_c"] / ch4_params["M_amu"], h2_ch4_mix_params["BetaT"], h2_ch4_mix_params["BetaV"], h2_ch4_mix_params["GammaT"], h2_ch4_mix_params["GammaV"], ) P = pressure_vector(density, T, tau, delta, "mix", h2_params, ch4_params, h2_ch4_mix_params, x_h2, x_ch4, rho_c, Tc) h = enthalpy_vector(density, T, tau, delta, Tc, rho_c, "mix", h2_params, ch4_params, h2_ch4_mix_params, x_h2, x_ch4) Excess_h = Excess_Enthalpy_vector( density, T, tau, delta, Tc, rho_c, h2_params, ch4_params, h2_ch4_mix_params, x_h2, x_ch4 ) B = Virial_B_vector(tau, h2_params, ch4_params, h2_ch4_mix_params, x_h2, x_ch4, rho_c, Tc, "mix") C = Virial_C_vector(tau, h2_params, ch4_params, h2_ch4_mix_params, x_h2, x_ch4, rho_c, Tc, "mix") print Excess_h # Excess Enthalpy in J/mol print P - 1000 * P_refprop # Pressure in kPa print h - M_amu * enthalpy_refprop # Enthalpy in J/mol M_amu used to convert from kJ/kg print B print C print tau, delta print P # ...and BEHOLD! IT WORKS!
def enthalpy_h2_h2o_mixture(T,P,x_h2,x_h2o,h2o_h2_mix_params): from thermodynamic_functions.enthalpy_vector import enthalpy_vector from thermodynamic_functions.pressure import pressure from scale_tau_and_delta_kw import scale_tau_and_delta_kw #from pylab import zeros,shape from numpy import asarray,shape,zeros from scipy.optimize import leastsq from residual_pressure import residual_pressure from residual_pressure_pure_substance import residual_pressure_pure_substance # equations written to get values for a T (K), and density (kg/m^3) 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'} h2o_phi_i=zeros(51+3) h2o_phi_i[51]=20.0 # Note, we need to use -sign here h2o_phi_i[52]=20.0 # Note, we need to use -sign here h2o_phi_i[53]=20.0 # Note, we need to use -sign here h2o_Beta_i=zeros(51+5) h2o_Beta_i[51]=150.0 #Note, we need to use - sign here h2o_Beta_i[52]=150.0 #Note, we need to use - sign here h2o_Beta_i[53]=250.0 #Note, we need to use - sign here h2o_Beta_i[54]=0.3 #Note, we need to use - sign here h2o_Beta_i[55]=0.3 #Note, we need to use - sign here h2o_gamma_i=zeros(51+3) h2o_gamma_i[51]=1.21 h2o_gamma_i[52]=1.21 h2o_gamma_i[53]=1.25 h2o_D_i=zeros(51+3) h2o_D_i[51]=1.0 h2o_D_i[52]=1.0 h2o_D_i[53]=1.0 h2o_RES_a=zeros(51+5) h2o_RES_b=zeros(51+5) h2o_RES_B=zeros(51+5) h2o_RES_C=zeros(51+5) h2o_RES_D=zeros(51+5) h2o_RES_A=zeros(51+5) h2o_RES_a[54]=3.5 h2o_RES_a[55]=3.5 h2o_RES_b[54]=0.85 h2o_RES_b[55]=0.95 h2o_RES_B[54]=0.2 h2o_RES_B[55]=0.2 h2o_RES_C[54]=28.0 h2o_RES_C[55]=32.0 h2o_RES_D[54]=700.0 h2o_RES_D[55]=800.0 h2o_RES_A[54]=0.32 h2o_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':h2o_phi_i, 'Beta_i':h2o_Beta_i, 'gamma_i':h2o_gamma_i, 'D_i':h2o_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':h2o_RES_a, 'RES_b':h2o_RES_b, 'RES_B':h2o_RES_B, 'RES_C':h2o_RES_C, 'RES_D':h2o_RES_D, 'RES_A':h2o_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'} Rmix=h2o_h2_mix_params['R']/((x_h2o*h2o_component_params['M_amu']+(x_h2*h2_component_params['M_amu']))) density_guess=P/(Rmix*T) #Here we need to iteratively solve (using total Pressure to calculate error) for the right density for a given set of mixture parameters, mole fractions, and total pressure #leastsq usage plsq=leastsq(residuals,p0,args=(y_meas,x)) [density,message]=leastsq(residual_pressure,density_guess,args=(P,T,h2_component_params,h2o_component_params,h2o_h2_mix_params,x_h2,x_h2o)) [tau,delta,Tc,rho_c]=scale_tau_and_delta_kw(T,density,x_h2,x_h2o,h2_component_params['Tc'],h2o_component_params['Tc'],h2_component_params['rho_c'],h2o_component_params['rho_c'],h2o_h2_mix_params['BetaT'],h2o_h2_mix_params['BetaV'],h2o_h2_mix_params['GammaT'],h2o_h2_mix_params['GammaV']) enthalpy_of_mixture=enthalpy_vector(tau,delta,Tc,rho_c,'mix',h2_component_params,h2o_component_params,h2o_h2_mix_params,x_h2,x_h2o) #need two things here: # 1. solve for density as if each component were at full pressure # 2. Get tau and delta such that they're respective to each pure component's critical points density_guess=P/((h2_component_params['R']/h2_component_params['M_amu'])*T) [density_h2,message_h2]=leastsq(residual_pressure_pure_substance,density_guess,args=(P,T,h2_component_params)) density_guess=P/((h2o_component_params['R']/h2o_component_params['M_amu'])*T) [density_h2o,message_h2o]=leastsq(residual_pressure_pure_substance,density_guess,args=(P,T,h2o_component_params)) enthalpy_of_hydrogen=enthalpy_vector(h2_component_params['Tc']/T,density_h2/h2_component_params['rho_c'],h2_component_params['Tc'],h2_component_params['rho_c'],'pure_substance',h2_component_params,h2_component_params,h2_component_params,1,1)#use mix params here to get back density and T in function for ideal components enthalpy_of_water=enthalpy_vector(h2o_component_params['Tc']/T,density_h2o/h2o_component_params['rho_c'],h2o_component_params['Tc'],h2o_component_params['rho_c'],'pure_substance',h2o_component_params,h2o_component_params,h2o_component_params,1,1)#use mix params here to get back densith and T in function for ideal components enthalpy_excess=enthalpy_of_mixture-x_h2*enthalpy_of_hydrogen-x_h2o*enthalpy_of_water #print shape(enthalpy_of_mixture) #print enthalpy_excess #print 'mix', enthalpy_of_mixture #print'h2', x_h2*enthalpy_of_hydrogen #print 'h2o',x_h2o*enthalpy_of_water #print enthalpy_excess return enthalpy_excess
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