@neutrium/thermo.eos.iapws97
Version:
A javascript implementation of the IAWPS formulations for the thermodynamic properties of water and steam.
661 lines • 55.9 kB
JavaScript
"use strict";
var thermo_1 = require('@neutrium/thermo');
var NS = require('./base');
var R = NS.constants['R'];
//
// Comments : Calculate the steam properties using IAWPS for a given pressure and temperature
//
// @param P is the pressure of the water in MPa
// @param T is the temperature in K
//
function solve(P, T, v) {
v = (typeof v == "undefined") ? -1 : v;
var region = findRegion_PT(P, T), result = null;
switch (region) {
case 1:
result = r1(P, T);
break;
case 2:
result = r2(P, T);
break;
case 3:
result = r3(P, T, v);
break;
case 5:
result = r5(P, T);
break;
default: throw new Error('Input valves are outside the range of the IAPWS97 correlations');
}
return result;
}
exports.solve = solve;
//
// Comments : Determines which IAPWS-IF97 region a pressure and temperature combination lie in.
//
// @param P is the pressure of the water in MPa
// @param T is the temperature in K
//
function findRegion_PT(P, T) {
if (P >= NS.CONST('MIN_P') && P <= NS.CONST('MAX_P') && T >= NS.CONST('MIN_T') &&
(T <= NS.CONST('R5_MIN_T') || (P <= NS.CONST('R5_MAX_P') && T <= NS.CONST('MAX_T')))) {
if (T > NS.CONST('R5_MIN_T')) {
if (P <= NS.CONST('R5_MAX_P')) {
return 5;
}
else {
return -1;
}
}
else if (T > NS.CONST('R3_MIN_T')) {
if (P > b23_T_P(T)) {
return 3;
}
else {
return 2;
}
}
else {
if (r4_T_Psat(T) > P) {
return 2;
}
else {
return 1;
}
}
}
return -1;
}
function generateResult(r) {
// Calculate the density from the specific volume
r.rho = 1 / r.v;
// Caculate additional properties using the auxillary equations
// Viscosity cP,
r.mu = NS.viscosity(r.t, r.rho) / 1000;
// Thermal Conductivity W/m.K
r.k = NS.thermal_conductivity(r.t, r.rho) / 1000;
// Surface Tension mN/m
r.sigma = NS.surface_tension(r.t);
// Dielectric constant
r.epsilon = NS.dielectric_constant(r.t, r.rho);
// Ionisation constant
r.ic = NS.ionization_constant(r.t, r.rho);
// Convert properties to the default units specified in NeutriumJs.thermo (where required)
r.p = r.p * 1000000; // Pressure MPa -> Pa
return new thermo_1.State(r);
}
// Auxillary equations for Regions 2 and 3
// Equation 5 (pp. 5) of IAPWS-97
// Returns the pressure for a given temperature along the region 2-3 boundary
function b23_T_P(T) {
return 348.05185628969 - 1.1671859879975 * T + 0.0010192970039326 * T * T;
}
exports.b23_T_P = b23_T_P;
// Equation 6 (pp. 6) of IAPWS-97
// Returns the temperature for a given pressure along the region 2-3 boundary
// Exported for use in the PH module
function b23_P_T(P) {
return 572.54459862746 + Math.pow((P - 13.91883977887) / 0.0010192970039326, 0.5);
}
exports.b23_P_T = b23_P_T;
// Region 1 forwards equation
function r1(P, T) {
var R1_PT_N = [0.14632971213167, -0.84548187169114, -3.756360367204, 3.3855169168385, -0.95791963387872, 0.15772038513228, -0.016616417199501, 8.1214629983568E-4, 2.8319080123804E-4, -6.0706301565874E-4, -0.018990068218419, -0.032529748770505, -0.021841717175414, -5.283835796993E-5, -4.7184321073267E-4, -3.0001780793026E-4, 4.7661393906987E-5, -4.4141845330846E-6, -7.2694996297594E-16, -3.1679644845054E-5, -2.8270797985312E-6, -8.5205128120103E-10, -2.2425281908E-6, -6.5171222895601E-7, -1.4341729937924E-13, -4.0516996860117E-7, -1.2734301741641E-9, -1.7424871230634E-10, -6.8762131295531E-19, 1.4478307828521E-20, 2.6335781662795E-23, -1.1947622640071E-23, 1.8228094581404E-24, -9.3537087292458E-26], R1_PT_J = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41], R1_PT_I = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32], tau = 1386.0 / T, pi = P / 16.53, g = 0, g_p = 0, g_pp = 0, g_t = 0, g_tt = 0, g_pt = 0;
for (var i = 0; i < 34; i++) {
var I = R1_PT_I[i], J = R1_PT_J[i], N = R1_PT_N[i];
g += N * Math.pow(7.1 - pi, I) * Math.pow(tau - 1.222, J);
g_p += -N * I * Math.pow(7.1 - pi, I - 1) * Math.pow(tau - 1.222, J);
g_pp += N * I * (I - 1) * Math.pow(7.1 - pi, I - 2) * Math.pow(tau - 1.222, J);
g_t += N * Math.pow(7.1 - pi, I) * J * Math.pow(tau - 1.222, J - 1);
g_tt += N * Math.pow(7.1 - pi, I) * J * (J - 1) * Math.pow(tau - 1.222, J - 2);
g_pt += -N * I * Math.pow(7.1 - pi, I - 1) * J * Math.pow(tau - 1.222, J - 1);
}
return generateResult({
p: P,
t: T,
v: R * T * pi * g_p / (1000 * P),
u: R * T * (tau * g_t - pi * g_p),
s: R * (tau * g_t - g),
h: R * T * tau * g_t,
cp: R * (-Math.pow(tau, 2) * g_tt),
cv: R * (-Math.pow(tau, 2) * g_tt + Math.pow(g_p - tau * g_pt, 2) / g_pp),
w: Math.pow(1000 * R * T * Math.pow(g_p, 2) / (Math.pow(g_p - tau * g_pt, 2) / (Math.pow(tau, 2) * g_tt) - g_pp), 0.5)
});
}
exports.r1 = r1;
function r2(P, T) {
var R2I_PT_N = [-9.6927686500217, 10.086655968018, -0.005608791128302, 0.071452738081455, -0.40710498223928, 1.4240819171444, -4.383951131945, -0.28408632460772, 0.021268463753307], R2I_PT_J = [0, 1, -5, -4, -3, -2, -1, 2, 3], R2R_PT_N = [-1.7731742473213E-3, -0.017834862292358, -0.045996013696365, -0.057581259083432, -0.05032527872793, -3.3032641670203E-5, -1.8948987516315E-4, -3.9392777243355E-3, -0.043797295650573, -2.6674547914087E-5, 2.0481737692309E-8, 4.3870667284435E-7, -3.227767723857E-5, -1.5033924542148E-3, -0.040668253562649, -7.8847309559367E-10, 1.2790717852285E-8, 4.8225372718507E-7, 2.2922076337661E-6, -1.6714766451061E-11, -2.1171472321355E-3, -23.895741934104, -5.905956432427E-18, -1.2621808899101E-6, -0.038946842435739, 1.1256211360459E-11, -8.2311340897998, 1.9809712802088E-8, 1.0406965210174E-19, -1.0234747095929E-13, -1.0018179379511E-9, -8.0882908646985E-11, 0.10693031879409, -0.33662250574171, 8.9185845355421E-25, 3.0629316876232E-13, -4.2002467698208E-6, -5.9056029685639E-26, 3.7826947613457E-6, -1.2768608934681E-15, 7.3087610595061E-29, 5.5414715350778E-17, -9.436970724121E-7], R2R_PT_J = [0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58], R2R_PT_I = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24], pi = P, tau = 540 / T, gi = Math.log(pi), gi_p = 1 / pi, gi_pp = -1 / (pi * pi), gi_t = 0, gi_tt = 0, gi_pt = 0, N, J, I;
for (var i = 0; i < 9; i++) {
N = R2I_PT_N[i];
J = R2I_PT_J[i];
gi += N * Math.pow(tau, J);
gi_t += N * J * Math.pow(tau, J - 1);
gi_tt += N * J * (J - 1) * Math.pow(tau, J - 2);
}
var gr = 0, gr_p = 0, gr_pp = 0, gr_t = 0, gr_tt = 0, gr_pt = 0;
for (var j = 0; j < 43; j++) {
N = R2R_PT_N[j];
J = R2R_PT_J[j];
I = R2R_PT_I[j];
gr += N * Math.pow(pi, I) * Math.pow(tau - 0.5, J);
gr_p += N * I * Math.pow(pi, I - 1) * Math.pow(tau - 0.5, J);
gr_pp += N * I * (I - 1) * Math.pow(pi, I - 2) * Math.pow(tau - 0.5, J);
gr_t += N * Math.pow(pi, I) * J * Math.pow(tau - 0.5, J - 1);
gr_tt += N * Math.pow(pi, I) * J * (J - 1) * Math.pow(tau - 0.5, J - 2);
gr_pt += N * I * Math.pow(pi, I - 1) * J * Math.pow(tau - 0.5, J - 1);
}
return generateResult({
p: P,
t: T,
v: (R * T / (1000 * P)) * pi * (gi_p + gr_p),
u: R * T * (tau * (gi_t + gr_t) - pi * (gi_p + gr_p)),
s: R * (tau * (gi_t + gr_t) - (gi + gr)),
h: R * T * tau * (gi_t + gr_t),
cp: -R * tau * tau * (gi_tt + gr_tt),
cv: R * (-tau * tau * (gi_tt + gr_tt) - Math.pow(1 + pi * gr_p - tau * pi * gr_pt, 2) / (1 - pi * pi * gr_pp)),
w: Math.pow(1000 * R * T * (1 + 2 * pi * gr_p + pi * pi * gr_p * gr_p) / ((1 - pi * pi * gr_pp) + Math.pow(1 + pi * gr_p - tau * pi * gr_pt, 2) / (tau * tau * (gi_tt + gr_tt))), 0.5)
});
}
exports.r2 = r2;
//
// Region 3
//
// Use a optional argument to calculate density
function r3(P, T, rho) {
var v = 1 / rho;
if (rho == -1 || typeof rho == 'undefined') {
v = r3_PT_v(P, T);
rho = 1 / v;
}
var R3_PT_N = [1.0658070028513, -15.732845290239, 20.944396974307, -7.6867707878716, 2.6185947787954, -2.808078114862, 1.2053369696517, -8.4566812812502E-03, -1.2654315477714, -1.1524407806681, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 4.8972281541877, -3.0502617256965, 0.039420536879154, 0.12558408424308, -0.2799932969871, 1.389979956946, -2.018991502357, -8.2147637173963E-03, -0.47596035734923, 0.0439840744735, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.022175400873096, 0.094260751665092, 0.16436278447961, -0.013503372241348, -0.014834345352472, 5.7922953628084E-04, 3.2308904703711E-03, 8.0964802996215E-05, -1.6557679795037E-04, -4.4923899061815E-05], R3_PT_J = [0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26], R3_PT_I = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11], g = rho / 322, tau = 647.096 / T, s = R3_PT_N[0] * Math.log(g), s_g = R3_PT_N[0] / g, s_gg = -R3_PT_N[0] / Math.pow(g, 2), s_t = 0, s_tt = 0, s_gt = 0;
// Need to start from i = 1 because j[0] and i[0] are NA and not used
for (var i = 1; i < 40; i++) {
var N = R3_PT_N[i], J = R3_PT_J[i], I = R3_PT_I[i];
s += N * Math.pow(g, I) * Math.pow(tau, J);
s_g += N * I * Math.pow(g, I - 1.0) * Math.pow(tau, J);
s_gg += N * I * (I - 1.0) * Math.pow(g, I - 2.0) * Math.pow(tau, J);
s_t += N * Math.pow(g, I) * J * Math.pow(tau, J - 1.0);
s_tt += N * Math.pow(g, I) * J * (J - 1.0) * Math.pow(tau, J - 2.0);
s_gt += N * I * Math.pow(g, I - 1.0) * J * Math.pow(tau, J - 1.0);
}
return generateResult({
p: rho * R * T * g * s_g / 1000,
t: T,
v: v,
u: R * T * tau * s_t,
s: R * (tau * s_t - s),
h: R * T * (tau * s_t + g * s_g),
cp: R * (-Math.pow(tau, 2) * s_tt + Math.pow(g * s_g - g * tau * s_gt, 2) / (2 * g * s_g + Math.pow(g, 2) * s_gg)),
cv: R * (-Math.pow(tau, 2) * s_tt),
w: Math.pow(1000 * R * T * (2 * g * s_g + Math.pow(g, 2) * s_gg - Math.pow(g * s_g - g * tau * s_gt, 2) / (Math.pow(tau, 2) * s_tt)), 0.5)
});
}
exports.r3 = r3;
// Selection criteria from table 2, page 10 of PT Region 3 supplementary release
function r3_PT_v(P, T) {
var Tsat = r4_P_Tsat(P), b3cd = b3cd_P_T(P);
if (40.0 < P && P <= 100.0) {
if (T <= b3ab_P_T(P)) {
return r3a_PT_v(P, T);
}
else {
return r3b_PT_v(P, T);
}
}
else if (25.0 < P && P <= 40.0) {
if (T <= b3cd) {
return r3c_PT_v(P, T);
}
else if (T <= b3ab_P_T(P)) {
return r3d_PT_v(P, T);
}
else if (T <= b3ef_P_T(P)) {
return r3e_PT_v(P, T);
}
else {
return r3f_PT_v(P, T);
}
}
else if (22.5 < P && P <= 25.0) {
if (T <= b3cd) {
return r3c_PT_v(P, T);
}
else if (T <= b3gh_P_T(P)) {
if (P <= 23.5) {
return r3l_PT_v(P, T);
}
return r3g_PT_v(P, T);
}
else if (T <= b3ef_P_T(P)) {
if (P <= 23.0) {
if (T <= b3mn_P_T(P)) {
return r3m_PT_v(P, T);
}
else {
return r3n_PT_v(P, T);
}
}
return r3h_PT_v(P, T);
}
else if (T <= b3ij_P_T(P)) {
if (P <= 23.0) {
if (T <= b3op_P_T(P)) {
return r3o_PT_v(P, T);
}
else {
return r3p_PT_v(P, T);
}
}
return r3i_PT_v(P, T);
}
else if (T <= b3jk_P_T(P)) {
return r3j_PT_v(P, T);
}
else {
return r3k_PT_v(P, T);
}
}
else if (21.04336732 < P && P <= 22.5) {
if (T <= b3cd) {
return r3c_PT_v(P, T);
}
else if (T <= b3qu_P_T(P)) {
return r3q_PT_v(P, T);
}
else if (T <= b3rx_P_T(P)) {
//critical region
if (P <= 22.064) {
//Subcritical pressure region
if (T <= Tsat) {
if (P <= 21.93161551) {
return r3u_PT_v(P, T);
}
else {
if (T <= b3uv_P_T(P)) {
return r3u_PT_v(P, T);
}
else {
return r3y_PT_v(P, T);
}
}
}
else {
if (P <= 21.90096265) {
return r3x_PT_v(P, T);
}
else {
if (T <= b3wx_P_T(P)) {
return r3z_PT_v(P, T);
}
else {
return r3x_PT_v(P, T);
}
}
}
}
else {
//Supercritical pressure region
if (T <= b3uv_P_T(P)) {
return r3u_PT_v(P, T);
}
else if (T <= b3ef_P_T(P)) {
if (P <= 22.11) {
return r3y_PT_v(P, T);
}
else {
return r3v_PT_v(P, T);
}
}
else if (T <= b3wx_P_T(P)) {
if (P <= 22.11) {
return r3z_PT_v(P, T);
}
else {
return r3w_PT_v(P, T);
}
}
else {
return r3x_PT_v(P, T);
}
}
}
else if (T <= b3jk_P_T(P)) {
return r3r_PT_v(P, T);
}
else {
return r3k_PT_v(P, T);
}
}
else if (20.5 < P && P <= 21.04336732) {
if (T <= b3cd) {
return r3c_PT_v(P, T);
}
else if (T <= Tsat) {
return r3s_PT_v(P, T);
}
else if (T <= b3jk_P_T(P)) {
return r3r_PT_v(P, T);
}
else {
return r3k_PT_v(P, T);
}
}
else if (19.00881189173929 < P && P <= 20.5) {
if (T <= b3cd) {
return r3c_PT_v(P, T);
}
else if (T <= Tsat) {
return r3s_PT_v(P, T);
}
else {
return r3t_PT_v(P, T);
}
}
else if (16.52916427498 < P && P <= 19.00881189173929) {
if (T <= Tsat) {
return r3c_PT_v(P, T);
}
else {
return r3t_PT_v(P, T);
}
}
// Else specific volume cannot be calculated and set to -ve
return -1.0;
}
// Subregion Boundary equations for Region 3
// From pp. 9 of Supplementary Release on Backward Equations for Specific Volume as a Function of Pressure and Temperature v(p,T)
// Exported for testing
function b3ab_P_T(P) {
var B3ab_PT_I = [0, 1, 2, -1, -2], B3ab_PT_N = [1.54793642129415E3, -1.87661219490113E2, 2.13144632222113E1, -1.91887498864292E3, 9.18419702359447E2], T = 0;
P = Math.log(P);
for (var i = 0; i < 5; i++) {
T += B3ab_PT_N[i] * Math.pow(P, B3ab_PT_I[i]);
}
return T;
}
exports.b3ab_P_T = b3ab_P_T;
// Exported for testing
function b3op_P_T(P) {
var B3op_PT_I = [0, 1, 2, -1, -2], B3op_PT_N = [9.69461372400213E2, -3.32500170441278E2, 6.4285959846667E1, 7.73845935768222E2, -1.52313732937084E3], T = 0;
P = Math.log(P);
for (var i = 0; i < 5; i++) {
T += B3op_PT_N[i] * Math.pow(P, B3op_PT_I[i]);
}
return T;
}
exports.b3op_P_T = b3op_P_T;
// Exported for testing
function b3ef_P_T(P) {
return 3.727888004 * (P - 22.064) + 647.096;
}
exports.b3ef_P_T = b3ef_P_T;
// Exported for testing
function b3cd_P_T(P) {
var B3cd_PT_I = [0, 1, 2, 3], B3cd_PT_N = [5.85276966696349E2, 2.78233532206915, -1.27283549295878E-2, 1.59090746562729E-4], T = 0;
for (var i = 0; i < 4; i++) {
T += B3cd_PT_N[i] * Math.pow(P, B3cd_PT_I[i]);
}
return T;
}
exports.b3cd_P_T = b3cd_P_T;
// Exported for testing
function b3gh_P_T(P) {
var B3gh_PT_I = [0, 1, 2, 3, 4], B3gh_PT_N = [-2.49284240900418E4, 4.28143584791546E3, -2.6902917314013E2, 7.51608051114157, -7.87105249910383E-2], T = 0;
for (var i = 0; i < 5; i++) {
T += B3gh_PT_N[i] * Math.pow(P, B3gh_PT_I[i]);
}
return T;
}
exports.b3gh_P_T = b3gh_P_T;
// Exported for testing
function b3ij_P_T(P) {
var B3ij_PT_I = [0, 1, 2, 3, 4], B3ij_PT_N = [5.84814781649163E2, -6.16179320924617E-1, 2.60763050899562E-1, -5.87071076864459E-3, 5.15308185433082E-5], T = 0;
for (var i = 0; i < 5; i++) {
T += B3ij_PT_N[i] * Math.pow(P, B3ij_PT_I[i]);
}
return T;
}
exports.b3ij_P_T = b3ij_P_T;
// Export for testing
function b3jk_P_T(P) {
var B3jk_PT_I = [0, 1, 2, 3, 4], B3jk_PT_N = [6.17229772068439E2, -7.70600270141675, 6.97072596851896E-1, -1.57391839848015E-2, 1.37897492684194E-4], T = 0;
for (var i = 0; i < 5; i++) {
T += B3jk_PT_N[i] * Math.pow(P, B3jk_PT_I[i]);
}
return T;
}
exports.b3jk_P_T = b3jk_P_T;
// Exported for testing
function b3mn_P_T(P) {
var B3mn_PT_I = [0, 1, 2, 3], B3mn_PT_N = [5.35339483742384E2, 7.61978122720128, -1.58365725441648E-1, 1.92871054508108E-3], T = 0;
for (var i = 0; i < 4; i++) {
T += B3mn_PT_N[i] * Math.pow(P, B3mn_PT_I[i]);
}
return T;
}
exports.b3mn_P_T = b3mn_P_T;
// Exported for testing
function b3qu_P_T(P) {
var B3qu_PT_I = [0, 1, 2, 3], B3qu_PT_N = [5.65603648239126E2, 5.29062258221222, -1.02020639611016E-1, 1.22240301070145E-3], T = 0;
for (var i = 0; i < 4; i++) {
T += B3qu_PT_N[i] * Math.pow(P, B3qu_PT_I[i]);
}
return T;
}
exports.b3qu_P_T = b3qu_P_T;
// Exported for testing
function b3rx_P_T(P) {
var B3rx_PT_I = [0, 1, 2, 3], B3rx_PT_N = [5.84561202520006E2, -1.02961025163669, 2.43293362700452E-1, -2.94905044740799E-3], T = 0;
for (var i = 0; i < 4; i++) {
T += B3rx_PT_N[i] * Math.pow(P, B3rx_PT_I[i]);
}
return T;
}
exports.b3rx_P_T = b3rx_P_T;
function r3a_PT_v(P, T) {
var pi = P / 100, sig = T / 760, v = 0, R3a_PT_I = [-12, -12, -12, -10, -10, -10, -8, -8, -8, -6, -5, -5, -5, -4, -3, -3, -3, -3, -2, -2, -2, -1, -1, -1, 0, 0, 1, 1, 2, 2], R3a_PT_J = [5, 10, 12, 5, 10, 12, 5, 8, 10, 1, 1, 5, 10, 8, 0, 1, 3, 6, 0, 2, 3, 0, 1, 2, 0, 1, 0, 2, 0, 2], R3a_PT_N = [1.10879558823853E-3, 5.72616740810616E2, -7.67051948380852E4, -2.53321069529674E-2, 6.28008049345689E3, 2.34105654131876E5, 2.16867826045856E-1, -1.56237904341963E2, -2.69893956176612E4, -1.80407100085505E-4, 1.16732227668261E-3, 2.6698704085604E1, 2.82776617243286E4, -2.42431520029523E3, 4.35217323022733E-4, -1.22494831387441E-2, 1.79357604019989, 4.42729521058314E1, -5.93223489018342E-3, 4.53186261685774E-1, 1.3582570312914, 4.08748415856745E-2, 4.74686397863312E-1, 1.18646814997915, 5.46987265727549E-1, 1.95266770452643E-1, -5.02268790869663E-2, -3.69645308193377E-1, 6.3382803752842E-3, 7.97441793901017E-2];
for (var i = 0; i < 30; i++) {
var N = R3a_PT_N[i], I = R3a_PT_I[i], J = R3a_PT_J[i];
v += N * Math.pow(pi - 0.085, I) * Math.pow(sig - 0.817, J);
}
return 0.0024 * v;
}
function r3b_PT_v(P, T) {
var pi = P / 100, sig = T / 860, v = 0, R3b_PT_I = [-12, -12, -10, -10, -8, -6, -6, -6, -5, -5, -5, -4, -4, -4, -3, -3, -3, -3, -3, -2, -2, -2, -1, -1, 0, 0, 1, 1, 2, 3, 4, 4], R3b_PT_J = [10, 12, 8, 14, 8, 5, 6, 8, 5, 8, 10, 2, 4, 5, 0, 1, 2, 3, 5, 0, 2, 5, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1], R3b_PT_N = [-8.27670470003621E-2, 4.16887126010565E1, 4.83651982197059E-2, -2.91032084950276E4, -1.11422582236948E2, -2.02300083904014E-2, 2.94002509338515E2, 1.40244997609658E2, -3.44384158811459E2, 3.61182452612149E2, -1.40699677420738E3, -2.02023902676481E-3, 1.71346792457471E2, -4.25597804058632, 6.91346085000334E-6, 1.51140509678925E-3, -4.16375290166236E-2, -4.13754957011042E1, -5.06673295721637E1, -5.72212965569023E-4, 6.08817368401785, 2.39600660256161E1, 1.22261479925384E-2, 2.16356057692938, 3.98198903368642E-1, -1.16892827834085E-1, -1.02845919373532E-1, -4.92676637589284E-1, 6.5554045640679E-2, -2.4046253507853E-1, -2.69798180310075E-2, 1.28369435967012E-1];
for (var i = 0; i < 32; i++) {
var N = R3b_PT_N[i], I = R3b_PT_I[i], J = R3b_PT_J[i];
v += N * Math.pow(pi - 0.280, I) * Math.pow(sig - 0.779, J);
}
return 0.0041 * v;
}
function r3c_PT_v(P, T) {
var pi = P / 40, sig = T / 690, v = 0, R3c_PT_I = [-12, -12, -12, -10, -10, -10, -8, -8, -8, -6, -5, -5, -5, -4, -4, -3, -3, -2, -2, -2, -1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 8], R3c_PT_J = [6, 8, 10, 6, 8, 10, 5, 6, 7, 8, 1, 4, 7, 2, 8, 0, 3, 0, 4, 5, 0, 1, 2, 0, 1, 2, 0, 2, 0, 1, 3, 7, 0, 7, 1], R3c_PT_N = [3.1196778876303, 2.76713458847564E4, 3.22583103403269E7, -3.42416065095363E2, -8.99732529907377E5, -7.93892049821251E7, 9.53193003217388E1, 2.29784742345072E3, 1.75336675322499E5, 7.91214365222792E6, 3.19933345844209E-5, -6.59508863555767E1, -8.33426563212851E5, 6.45734680583292E-2, -3.82031020570813E6, 4.06398848470079E-5, 3.10327498492008E1, -8.92996718483724E-4, 2.34604891591616E2, 3.77515668966951E3, 1.58646812591361E-2, 7.07906336241843E-1, 1.2601622514657E1, 7.36143655772152E-1, 6.76544268999101E-1, -1.78100588189137E1, -1.56531975531713E-1, 1.17707430048158E1, 8.40143653860447E-2, -1.86442467471949E-1, -4.40170203949645E1, 1.23290423502494E6, -2.40650039730845E-2, -1.07077716660869E6, 4.38319858566475E-2];
for (var i = 0; i < 35; i++) {
var N = R3c_PT_N[i], I = R3c_PT_I[i], J = R3c_PT_J[i];
v += N * Math.pow(pi - 0.259, I) * Math.pow(sig - 0.903, J);
}
return 0.0022 * v;
}
function r3d_PT_v(P, T) {
var pi = P / 40, sig = T / 690, v = 0, R3d_PT_I = [-12, -12, -12, -12, -12, -12, -10, -10, -10, -10, -10, -10, -10, -8, -8, -8, -8, -6, -6, -5, -5, -5, -5, -4, -4, -4, -3, -3, -2, -2, -1, -1, -1, 0, 0, 1, 1, 3], R3d_PT_J = [4, 6, 7, 10, 12, 16, 0, 2, 4, 6, 8, 10, 14, 3, 7, 8, 10, 6, 8, 1, 2, 5, 7, 0, 1, 7, 2, 4, 0, 1, 0, 1, 5, 0, 2, 0, 6, 0], R3d_PT_N = [-4.52484847171645E-10, 3.15210389538801E-5, -2.14991352047545E-3, 5.08058874808345E2, -1.27123036845932E7, 1.15371133120497E12, -1.97805728776273E-16, 2.41554806033972E-11, -1.56481703640525E-6, 2.772113468366250E-3, -2.03578994462286E1, 1.44369489909053E6, -4.11254217946539E10, 6.23449786243773E-6, -2.21774281146038E1, -6.89315087933158E4, -1.95419525060713E7, 3.16373510564015E3, 2.24040754426988E6, -4.36701347922356E-6, -4.04213852833996E-4, -3.48153203414663E2, -3.85294213555289E5, 1.35203700099403E-7, 1.34648383271089E-4, 1.25031835351736E5, 9.68123678455841E-2, 2.25660517512438E2, -1.90102435341872E-4, -2.99628410819229E-2, 5.00833915372121E-3, 3.87842482998411E-1, -1.38535367777182E3, 8.70745245971773E-1, 1.71946252068742, -3.26650121426383E-2, 4.98044171727877E3, 5.51478022765087E-3];
for (var i = 0; i < 38; i++) {
var N = R3d_PT_N[i], I = R3d_PT_I[i], J = R3d_PT_J[i];
v += N * Math.pow(pi - 0.559, I) * Math.pow(sig - 0.939, J);
}
return 0.0029 * Math.pow(v, 4);
}
function r3e_PT_v(P, T) {
var pi = P / 40, sig = T / 710, v = 0, R3e_PT_I = [-12, -12, -10, -10, -10, -10, -10, -8, -8, -8, -6, -5, -4, -4, -3, -3, -3, -2, -2, -2, -2, -1, 0, 0, 1, 1, 1, 2, 2], R3e_PT_J = [14, 16, 3, 6, 10, 14, 16, 7, 8, 10, 6, 6, 2, 4, 2, 6, 7, 0, 1, 3, 4, 0, 0, 1, 0, 4, 6, 0, 2], R3e_PT_N = [7.15815808404721E8, -1.14328360753449E11, 3.7653100201572E-12, -9.03983668691157E-5, 6.65695908836252E5, 5.35364174960127E9, 7.94977402335603E10, 9.22230563421437E1, -1.42586073991215E5, -1.11796381424162E6, 8.9612162964076E3, -6.69989239070491E3, 4.51242538486834E-3, -3.39731325977713E1, -1.20523111552278, 4.75992667717124E4, -2.66627750390341E5, -1.53314954386524E-4, 3.05638404828265E-1, 1.23654999499486E2, -1.04390794213011E3, -1.57496516174308E-2, 6.85331118940253E-1, 1.78373462873903, -5.4467412487891E-1, 2.04529931318843E3, -2.28342359328752E4, 4.13197481515899E-1, -3.41931835910405E1];
for (var i = 0; i < 29; i++) {
var N = R3e_PT_N[i], I = R3e_PT_I[i], J = R3e_PT_J[i];
v += N * Math.pow(pi - 0.587, I) * Math.pow(sig - 0.918, J);
}
return 0.0032 * v;
}
function r3f_PT_v(P, T) {
var pi = P / 40, sig = T / 730, v = 0, R3f_PT_I = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 6, 7, 7, 10, 12, 12, 12, 14, 14, 14, 14, 14, 16, 16, 18, 18, 20, 20, 20, 22, 24, 24, 28, 32], R3f_PT_J = [-3, -2, -1, 0, 1, 2, -1, 1, 2, 3, 0, 1, -5, -2, 0, -3, -8, 1, -6, -4, 1, -6, -10, -8, -4, -12, -10, -8, -6, -4, -10, -8, -12, -10, -12, -10, -6, -12, -12, -4, -12, -12], R3f_PT_N = [-2.51756547792325E-8, 6.01307193668763E-6, -1.00615977450049E-3, 9.99969140252192E-1, 2.14107759236486, -1.65175571959086E1, -1.41987303638727E-3, 2.69251915156554, 3.49741815858722E1, -3.00208695771783E1, -1.31546288252539, -8.39091277286169, 1.81545608337015E-10, -5.91099206478909E-4, 1.52115067087106, 2.52956470663225E-5, 1.00726265203786E-15, -1.4977453386065, -7.93940970562969E-10, -1.50290891264717E-4, 1.51205531275133, 4.70942606221652E-6, 1.95049710391712E-13, -9.11627886266077E-9, 6.04374640201265E-4, -2.25132933900136E-16, 6.10916973582981E-12, -3.03063908043404E-7, -1.37796070798409E-5, -9.19296736666106E-4, 6.39288223132545E-10, 7.53259479898699E-7, -4.00321478682929E-13, 7.56140294351614E-9, -9.12082054034891E-12, -2.37612381140539E-08, 2.69586010591874E-5, -7.32828135157839E-11, 2.4199557830666E-10, -4.05735532730322E-4, 1.89424143498011E-10, -4.86632965074563E-10];
for (var i = 0; i < 42; i++) {
var N = R3f_PT_N[i], I = R3f_PT_I[i], J = R3f_PT_J[i];
v += N * Math.pow(pi - 0.587, 0.5 * I) * Math.pow(sig - 0.891, J);
}
return 0.0064 * Math.pow(v, 4);
}
function r3g_PT_v(P, T) {
var pi = P / 25, sig = T / 660, v = 0, R3g_PT_I = [-12, -12, -12, -12, -12, -12, -10, -10, -10, -8, -8, -8, -8, -6, -6, -5, -5, -4, -3, -2, -2, -2, -2, -1, -1, -1, 0, 0, 0, 1, 1, 1, 3, 5, 6, 8, 10, 10], R3g_PT_J = [7, 12, 14, 18, 22, 24, 14, 20, 24, 7, 8, 10, 12, 8, 22, 7, 20, 22, 7, 3, 5, 14, 24, 2, 8, 18, 0, 1, 2, 0, 1, 3, 24, 22, 12, 3, 0, 6], R3g_PT_N = [4.12209020652996E-5, -1.14987238280587E6, 9.4818088503208E9, -1.95788865718971E17, 4.962507048713E24, -1.05549884548496E28, -7.58642165988278E11, -9.22172769596101E22, 7.25379072059348E29, -6.17718249205859E1, 1.07555033344858E4, -3.79545802336487E7, 2.28646846221831E11, -4.99741093010619E6, -2.80214310054101E30, 1.04915406769586E6, 6.13754229168619E27, 8.02056715528378E31, -2.98617819828065E7, -9.10782540134681E1, 1.35033227281565E5, -7.12949383408211E18, -1.04578785289542E36, 3.04331584444093E1, 5.93250797959445E9, -3.64174062110798E27, 9.21791403532461E-1, -3.37693609657471E-1, -7.24644143758508E1, -1.10480239272601E-1, 5.36516031875059, -2.91441872156205E3, 6.16338176535305E39, -1.2088917586118E38, 8.18396024524612E22, 9.40781944835829E8, -3.67279669545448E4, -8.37513931798655E15];
for (var i = 0; i < 38; i++) {
var N = R3g_PT_N[i], I = R3g_PT_I[i], J = R3g_PT_J[i];
v += N * Math.pow(pi - 0.872, I) * Math.pow(sig - 0.971, J);
}
return 0.0027 * Math.pow(v, 4);
}
function r3h_PT_v(P, T) {
var pi = P / 25, sig = T / 660, v = 0, R3h_PT_I = [-12, -12, -10, -10, -10, -10, -10, -10, -8, -8, -8, -8, -8, -6, -6, -6, -5, -5, -5, -4, -4, -3, -3, -2, -1, -1, 0, 1, 1], R3h_PT_J = [8, 12, 4, 6, 8, 10, 14, 16, 0, 1, 6, 7, 8, 4, 6, 8, 2, 3, 4, 2, 4, 1, 2, 0, 0, 2, 0, 0, 2], R3h_PT_N = [5.61379678887577E-2, 7.74135421587083E9, 1.11482975877938E-9, -1.43987128208183E-3, 1.9369655876492E3, -6.05971823585005E8, 1.71951568124337E13, -1.85461154985145E16, 3.8785116807801E-17, -3.95464327846105E-14, -1.70875935679023E2, -2.1201062070122E3, 1.77683337348191E7, 1.10177443629575E1, -2.34396091693313E5, -6.56174421999594E6, 1.56362212977396E-5, -2.129462570214, 1.35249306374858E1, 1.77189164145813E-1, 1.39499167345464E3, -7.03670932036388E-3, -1.52011044389648E-1, 9.81916922991113E-5, 1.47199658618076E-3, 2.02618487025578E1, 8.9934551894424E-1, -2.11346402240858E-1, 2.49971752957491E1];
for (var i = 0; i < 29; i++) {
var N = R3h_PT_N[i], I = R3h_PT_I[i], J = R3h_PT_J[i];
v += N * Math.pow(pi - 0.898, I) * Math.pow(sig - 0.983, J);
}
return 0.0032 * Math.pow(v, 4);
}
function r3i_PT_v(P, T) {
var pi = P / 25, sig = T / 660, v = 0, R3i_PT_I = [0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 7, 7, 8, 8, 10, 12, 12, 12, 14, 14, 14, 14, 18, 18, 18, 18, 18, 20, 20, 22, 24, 24, 32, 32, 36, 36], R3i_PT_J = [0, 1, 10, -4, -2, -1, 0, 0, -5, 0, -3, -2, -1, -6, -1, 12, -4, -3, -6, 10, -8, -12, -6, -4, -10, -8, -4, 5, -12, -10, -8, -6, 2, -12, -10, -12, -12, -8, -10, -5, -10, -8], R3i_PT_N = [1.06905684359136, -1.48620857922333, 2.59862256980408E14, -4.46352055678749E-12, -5.66620757170032E-7, -2.35302885736849E-3, -2.69226321968839E-1, 9.22024992944392, 3.57633505503772E-12, -1.73942565562222E1, 7.00681785556229E-6, -2.67050351075768E-4, -2.31779669675624, -7.53533046979752E-13, 4.81337131452891, -2.23286270422356E21, -1.18746004987383E-5, 6.46412934136496E-3, -4.10588536330937E-10, 4.22739537057241E19, 3.13698180473812E-13, 1.6439533434504E-24, -3.39823323754373E-6, -1.35268639905021E-2, -7.232525142116250E-15, 1.84386437538366E-9, -4.63959533752385E-2, -9.9226310037675E13, 6.88169154439335E-17, -2.22620998452197E-11, -5.40843018624083E-8, 3.45570606200257E-3, 4.22275800304086E10, -1.26974478770487E-15, 9.27237985153679E-10, 6.126708120164890E-14, -7.22693924063497E-12, -3.83669502636822E-4, 3.74684572410204E-4, -9.31976897511086E4, -2.47690616026922E-2, 6.58110546759474E1];
for (var i = 0; i < 42; i++) {
var N = R3i_PT_N[i], I = R3i_PT_I[i], J = R3i_PT_J[i];
v += N * Math.pow(pi - 0.910, 0.5 * I) * Math.pow(sig - 0.984, J);
}
return 0.0041 * Math.pow(v, 4);
}
function r3j_PT_v(P, T) {
var pi = P / 25, sig = T / 670, v = 0, R3j_PT_I = [0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 10, 12, 12, 14, 14, 14, 16, 18, 20, 20, 24, 24, 28, 28], R3j_PT_J = [-1, 0, 1, -2, -1, 1, -1, 1, -2, -2, 2, -3, -2, 0, 3, -6, -8, -3, -10, -8, -5, -10, -12, -12, -10, -12, -6, -12, -5], R3j_PT_N = [-1.1137131739554E-4, 1.00342892423685, 5.30615581928979, 1.79058760078792E-6, -7.28541958464774E-4, -1.87576133371704E1, 1.99060874071849E-3, 2.4357475537729E1, -1.77040785499444E-4, -2.5968038522713E-3, -1.98704578406823E2, 7.38627790224287E-5, -2.36264692844138E-3, -1.61023121314333, 6.22322971786473E3, -9.60754116701669E-9, -5.10572269720488E-11, 7.67373781404211E-3, 6.63855469485254E-15, -7.17590735526745E-10, 1.46564542926508E-5, 3.09029474277013E-12, -4.64216300971708E-16, -3.90499637961161E-14, -2.36716126781431E-10, 4.54652854268717E-12, -4.22271787482497E-3, 2.83911742354706E-11, 2.70929002720228];
for (var i = 0; i < 29; i++) {
var N = R3j_PT_N[i], I = R3j_PT_I[i], J = R3j_PT_J[i];
v += N * Math.pow(pi - 0.875, 0.5 * I) * Math.pow(sig - 0.964, J);
}
return 0.0054 * Math.pow(v, 4);
}
function r3k_PT_v(P, T) {
var pi = P / 25, sig = T / 680, v = 0, R3k_PT_I = [-2, -2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 5, 5, 5, 6, 6, 6, 6, 8, 10, 12], R3k_PT_J = [10, 12, -5, 6, -12, -6, -2, -1, 0, 1, 2, 3, 14, -3, -2, 0, 1, 2, -8, -6, -3, -2, 0, 4, -12, -6, -3, -12, -10, -8, -5, -12, -12, -10], R3k_PT_N = [-4.01215699576099E8, 4.84501478318406E10, 3.94721471363678E-15, 3.72629967374147E4, -3.69794374168666E-30, -3.80436407012452E-15, 4.75361629970233E-7, -8.79148916140706E-4, 8.44317863844331E-1, 1.224331626566E1, -1.04529634830279E2, 5.89702771277429E2, -2.91026851164444E13, 1.7034307284185E-6, -2.77617606975748E-4, -3.44709605486686, 2.21333862447095E1, -1.94646110037079E2, 8.08354639772825E-16, -1.8084520914547E-11, -6.96664158132412E-6, -1.81057560300994E-3, 2.55830298579027, 3.28913873658481E3, -1.73270241249904E-19, -6.61876792558034E-7, -3.9568892342125E-3, 6.04203299819132E-18, -4.00879935920517E-14, 1.60751107464958E-9, 3.83719409025556E-5, -6.49565446702457E-15, -1.49095328506E-12, 5.41449377329581E-9];
for (var i = 0; i < 34; i++) {
var N = R3k_PT_N[i], I = R3k_PT_I[i], J = R3k_PT_J[i];
v += N * Math.pow(pi - 0.802, I) * Math.pow(sig - 0.935, J);
}
return 0.0077 * v;
}
function r3l_PT_v(P, T) {
var pi = P / 24, sig = T / 650, v = 0, R3l_PT_I = [-12, -12, -12, -12, -12, -10, -10, -8, -8, -8, -8, -8, -8, -8, -6, -5, -5, -4, -4, -3, -3, -3, -3, -2, -2, -2, -1, -1, -1, 0, 0, 0, 0, 1, 1, 2, 4, 5, 5, 6, 10, 10, 14], R3l_PT_J = [14, 16, 18, 20, 22, 14, 24, 6, 10, 12, 14, 18, 24, 36, 8, 4, 5, 7, 16, 1, 3, 18, 20, 2, 3, 10, 0, 1, 3, 0, 1, 2, 12, 0, 16, 1, 0, 0, 1, 14, 4, 12, 10], R3l_PT_N = [2.60702058647537E9, -1.88277213604704E14, 5.54923870289667E18, -7.58966946387758E22, 4.13865186848908E26, -8.1503800073806E11, -3.81458260489955E32, -1.23239564600519E-2, 2.26095631437174E7, -4.9501780950672E11, 5.29482996422863E15, -4.44359478746295E22, 5.21635864527315E34, -4.87095672740742E54, -7.14430209937547E5, 1.27868634615495E-1, -1.00752127917598E1, 7.7745143796099E6, -1.08105480796471E24, -3.57578581169659E-6, -2.12857169423484, 2.70706111085238E29, -6.95953622348829E32, 1.1060902747228E-1, 7.21559163361354E1, -3.06367307532219E14, 2.6583961888553E-5, 2.53392392889754E-2, -2.14443041836579E2, 9.37846601489667E-1, 2.231840431017, 3.38401222509191E1, 4.94237237179718E20, -1.98068404154428E-1, -1.4141534988114E30, -9.93862421613651E1, 1.25070534142731E2, -9.96473529004439E2, 4.73137909872765E4, 1.16662121219322E32, -3.15874976271533E15, -4.45703369196945E32, 6.42794932373694E32];
for (var i = 0; i < 43; i++) {
var N = R3l_PT_N[i], I = R3l_PT_I[i], J = R3l_PT_J[i];
v += N * Math.pow(pi - 0.908, I) * Math.pow(sig - 0.989, J);
}
return 0.0026 * Math.pow(v, 4);
}
function r3m_PT_v(P, T) {
var pi = P / 23, sig = T / 650, v = 0, R3m_PT_I = [0, 3, 8, 20, 1, 3, 4, 5, 1, 6, 2, 4, 14, 2, 5, 3, 0, 1, 1, 1, 28, 2, 16, 0, 5, 0, 3, 4, 12, 16, 1, 8, 14, 0, 2, 3, 4, 8, 14, 24], R3m_PT_J = [0, 0, 0, 2, 5, 5, 5, 5, 6, 6, 7, 8, 8, 10, 10, 12, 14, 14, 18, 20, 20, 22, 22, 24, 24, 28, 28, 28, 28, 28, 32, 32, 32, 36, 36, 36, 36, 36, 36, 36], R3m_PT_N = [8.11384363481847E-1, -5.68199310990094E3, -1.78657198172556E10, 7.95537657613427E31, -8.14568209346872E4, -6.59774567602874E7, -1.52861148659302E10, -5.60165667510446E11, 4.58384828593949E5, -3.85754000383848E13, 4.53735800004273E7, 9.39454935735563E11, 2.66572856432938E27, -5.47578313899097E9, 2.00725701112386E14, 1.85007245563239E12, 1.85135446828337E8, -1.70451090076385E11, 1.57890366037614E14, -2.02530509748774E15, 3.6819392618357E59, 1.70215539458936E17, 6.39234909918741E41, -8.21698160721956E14, -7.95260241872306E23, 2.3341586947851E17, -6.00079934586803E22, 5.94584382273384E24, 1.89461279349492E39, -8.10093428842645E45, 1.88813911076809E21, 1.11052244098768E35, 2.91133958602503E45, -3.2942192395146E21, -1.37570282536696E25, 1.81508996303902E27, -3.46865122768353E29, -2.1196114877426E37, -1.28617899887675E48, 4.79817895699239E64];
for (var i = 0; i < 40; i++) {
var N = R3m_PT_N[i], I = R3m_PT_I[i], J = R3m_PT_J[i];
v += N * Math.pow(pi - 1, I) * Math.pow(sig - 0.997, 0.25 * J);
}
return 0.0028 * v;
}
function r3n_PT_v(P, T) {
var pi = P / 23, sig = T / 650, v = 0, R3n_PT_I = [0, 3, 4, 6, 7, 10, 12, 14, 18, 0, 3, 5, 6, 8, 12, 0, 3, 7, 12, 2, 3, 4, 2, 4, 7, 4, 3, 5, 6, 0, 0, 3, 1, 0, 1, 0, 1, 0, 1], R3n_PT_J = [-12, -12, -12, -12, -12, -12, -12, -12, -12, -10, -10, -10, -10, -10, -10, -8, -8, -8, -8, -6, -6, -6, -5, -5, -5, -4, -3, -3, -3, -2, -1, -1, 0, 1, 1, 2, 4, 5, 6], R3n_PT_N = [2.80967799943151E-39, 6.14869006573609E-31, 5.82238667048942E-28, 3.90628369238462E-23, 8.21445758255119E-21, 4.02137961842776E-15, 6.51718171878301E-13, -2.11773355803058E-8, 2.64953354380072E-3, -1.35031446451331E-32, -6.07246643970893E-24, -4.02352115234494E-19, -7.44938506925544E-17, 1.89917206526237E-13, 3.64975183508473E-6, 1.77274872361946E-26, -3.34952758812999E-19, -4.21537726098389E-9, -3.91048167929649E-2, 5.41276911564176E-14, 7.05412100773699E-12, 2.58585887897486E-9, -4.93111362030162E-11, -1.58649699894543E-6, -5.250374278861E-1, 2.20019901729615E-3, -6.43064132636925E-3, 6.29154149015048E1, 1.35147318617061E2, 2.40560808321713E-7, -8.90763306701305E-4, -4.40209599407714E3, -3.02807107747776E2, 1.59158748314599E3, 2.32534272709876E5, -7.926812071326E5, -8.69871364662769E10, 3.54542769185671E11, 4.00849240129329E14];
for (var i = 0; i < 39; i++) {
var N = R3n_PT_N[i], I = R3n_PT_I[i], J = R3n_PT_J[i];
v += N * Math.pow(pi - 0.976, I) * Math.pow(sig - 0.997, J);
}
return 0.0031 * Math.exp(v);
}
function r3o_PT_v(P, T) {
var pi = P / 23, sig = T / 650, v = 0, R3o_PT_I = [0, 0, 0, 2, 3, 4, 4, 4, 4, 4, 5, 5, 6, 7, 8, 8, 8, 10, 10, 14, 14, 20, 20, 24], R3o_PT_J = [-12, -4, -1, -1, -10, -12, -8, -5, -4, -1, -4, -3, -8, -12, -10, -8, -4, -12, -8, -12, -8, -12, -10, -12], R3o_PT_N = [1.28746023979718E-35, -7.35234770382342E-12, 2.8907869214915E-3, 2.44482731907223E-1, 1.41733492030985E-24, -3.54533853059476E-29, -5.94539202901431E-18, -5.85188401782779E-9, 2.01377325411803E-6, 1.38647388209306, -1.73959365084772E-5, 1.37680878349369E-3, 8.14897605805513E-15, 4.25596631351839E-26, -3.87449113787755E-18, 1.3981474793024E-13, -1.71849638951521E-3, 6.41890529513296E-22, 1.18960578072018E-11, -1.55282762571611E-18, 2.33907907347507E-8, -1.74093247766213E-13, 3.77682649089149E-9, -5.16720236575302E-11];
for (var i = 0; i < 24; i++) {
var N = R3o_PT_N[i], I = R3o_PT_I[i], J = R3o_PT_J[i];
v += N * Math.pow(pi - 0.974, 0.5 * I) * Math.pow(sig - 0.996, J);
}
return 0.0034 * v;
}
function r3p_PT_v(P, T) {
var pi = P / 23, sig = T / 650, v = 0, R3p_PT_I = [0, 0, 0, 0, 1, 2, 3, 3, 4, 6, 7, 7, 8, 10, 12, 12, 12, 14, 14, 14, 16, 18, 20, 22, 24, 24, 36], R3p_PT_J = [-1, 0, 1, 2, 1, -1, -3, 0, -2, -2, -5, -4, -2, -3, -12, -6, -5, -10, -8, -3, -8, -8, -10, -10, -12, -8, -12], R3p_PT_N = [-9.82825342010366E-5, 1.05145700850612, 1.16033094095084E2, 3.24664750281543E3, -1.23592348610137E3, -5.61403450013495E-2, 8.56677401640869E-8, 2.36313425393924E2, 9.72503292350109E-3, -1.03001994531927, -1.49653706199162E-9, -2.15743778861592E-5, -8.34452198291445, 5.86602660564988E-1, 3.43480022104968E-26, 8.16256095947021E-6, 2.94985697916798E-3, 7.11730466276584E-17, 4.00954763806941E-10, 1.07766027032853E1, -4.09449599138182E-7, -7.29121307758902E-6, 6.77107970938909E-9, 6.02745973022975E-8, -3.82323011855257E-11, 1.79946628317437E-3, -3.45042834640005E-4];
for (var i = 0; i < 27; i++) {
var N = R3p_PT_N[i], I = R3p_PT_I[i], J = R3p_PT_J[i];
v += N * Math.pow(pi - 0.972, 0.5 * I) * Math.pow(sig - 0.997, J);
}
return 0.0041 * v;
}
function r3q_PT_v(P, T) {
var pi = P / 23, sig = T / 650, v = 0, R3q_PT_I = [-12, -12, -10, -10, -10, -10, -8, -6, -5, -5, -4, -4, -3, -2, -2, -2, -2, -1, -1, -1, 0, 1, 1, 1], R3q_PT_J = [10, 12, 6, 7, 8, 10, 8, 6, 2, 5, 3, 4, 3, 0, 1, 2, 4, 0, 1, 2, 0, 0, 1, 3], R3q_PT_N = [-8.2043384325995E4, 4.73271518461586E10, -8.05950021005413E-2, 3.2860002543598E1, -3.5661702998249E3, -1.72985781433335E9, 3.51769232729192E7, -7.75489259985144E5, 7.10346691966018E-5, 9.93499883820274E4, -6.4209417190457E-1, -6.12842816820083E3, 2.32808472983776E2, -1.42808220416837E-5, -6.43596060678456E-3, -4.28577227475614, 2.25689939161918E3, 1.0035565172151E-3, 3.33491455143516E-1, 1.09697576888873, 9.61917379376452E-1, -8.38165632204598E-2, 2.47795908411492, -3.19114969006533E3];
for (var i = 0; i < 24; i++) {
var N = R3q_PT_N[i], I = R3q_PT_I[i], J = R3q_PT_J[i];
v += N * Math.pow(pi - 0.848, I) * Math.pow(sig - 0.983, J);
}
return 0.0022 * Math.pow(v, 4);
}
function r3r_PT_v(P, T) {
var pi = P / 23, sig = T / 650, v = 0, R3r_PT_I = [-8, -8, -3, -3, -3, -3, -3, 0, 0, 0, 0, 3, 3, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 12, 14], R3r_PT_J = [6, 14, -3, 3, 4, 5, 8, -1, 0, 1, 5, -6, -2, -12, -10, -8, -5, -12, -10, -8, -6, -5, -4, -3, -2, -12, -12], R3r_PT_N = [1.44165955660863E-3, -7.01438599628258E12, -8.30946716459219E-17, 2.61975135368109E-1, 3.93097214706245E2, -1.04334030654021E4, 4.90112654154211E8, -1.47104222772069E-4, 1.03602748043408, 3.05308890065089, -3.99745276971264E6, 5.6923371959375E-12, -4.64923504407778E-2, -5.35400396512906E-18, 3.99988795693162E-13, -5.36479560201811E-07, 1.59536722411202E-2, 2.70303248860217E-15, 2.44247453858506E-8, -9.83430636716454E-6, 6.63513144224454E-2, -9.93456957845006, 5.46491323528491E2, -1.43365406393758E4, 1.50764974125511E5, -3.37209709340105E-10, 3.77501980025469E-9];
for (var i = 0; i < 27; i++) {
var N = R3r_PT_N[i], I = R3r_PT_I[i], J = R3r_PT_J[i];
v += N * Math.pow(pi - 0.874, I) * Math.pow(sig - 0.982, J);
}
return 0.0054 * v;
}
function r3s_PT_v(P, T) {
var pi = P / 21, sig = T / 640, v = 0, R3s_PT_I = [-12, -12, -10, -8, -6, -5, -5, -4, -4, -3, -3, -2, -1, -1, -1, 0, 0, 0, 0, 1, 1, 3, 3, 3, 4, 4, 4, 5, 14], R3s_PT_J = [20, 24, 22, 14, 36, 8, 16, 6, 32, 3, 8, 4, 1, 2, 3, 0, 1, 4, 28, 0, 32, 0, 1, 2, 3, 18, 24, 4, 24], R3s_PT_N = [-5.32466612140254E22, 1.00415480000824E31, -1.91540001821367E29, 1.05618377808847E16, 2.02281884477061E58, 8.84585472596134E7, 1.66540181638363E22, -3.13563197669111E5, -1.85662327545324E53, -6.24942093918942E-2, -5.0416072413259E9, 1.87514491833092E4, 1.21399979993217E-3, 1.88317043049455, -1.6707350396206E3, 9.65961650599775E-1, 2.94885696802488, -6.53915627346115E4, 6.04012200163444E49, -1.98339358557937E-1, -1.75984090163501E57, 3.56314881403987, -5.75991255144384E2, 4.56213415338071E4, -1.09174044987829E7, 4.37796099975134E33, -6.16552611135792E45, 1.93568768917797E9, 9.50898170425042E53];
for (var i = 0; i < 29; i++) {
var N = R3s_PT_N[i], I = R3s_PT_I[i], J = R3s_PT_J[i];
v += N * Math.pow(pi - 0.886, I) * Math.pow(sig - 0.990, J);
}
return 0.0022 * Math.pow(v, 4);
}
function r3t_PT_v(P, T) {
var pi = P / 20, sig = T / 650, v = 0, R3t_PT_I = [0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 7, 7, 7, 7, 7, 10, 10, 10, 10, 10, 18, 20, 22, 22, 24, 28, 32, 32, 32, 36], R3t_PT_J = [0, 1, 4, 12, 0, 10, 0, 6, 14, 3, 8, 0, 10, 3, 4, 7, 20, 36, 10, 12, 14, 16, 22, 18, 32, 22, 36, 24, 28, 22, 32, 36, 36], R3t_PT_N = [1.55287249586268, 6.64235115009031, -2.8936623672721E3, -3.85923202309848E12, -2.91002915783761, -8.29088246858083E11, 1.76814899675218, -5.34686695713469E8, 1.60464608687834E17, 1.96435366560186E5, 1.56637427541729E12, -1.78154560260006, -2.29746237623692E15, 3.85659001648006E7, 1.10554446790543E9, -6.77073830687349E13, -3.27910592086523E30, -3.41552040860644E50, -5.27251339709047E20, 2.45375640937055E23, -1.68776617209269E26, 3.58958955867578E28, -6.56475280339411E35, 3.55286045512301E38, 5.6902145441327E57, -7.00584546433113E47, -7.05772623326374E64, 1.66861176200148E52, -3.00475129680486E60, -6.68481295196808E50, 4.28432338620678E68, -4.44227367758304E71, -2.81396013562745E76];
for (var i = 0; i < 33; i++) {
var N = R3t_PT_N[i], I = R3t_PT_I[i], J = R3t_PT_J[i];
v += N * Math.pow(pi - 0.803, I) * Math.pow(sig - 1.02, J);
}
return 0.0088 * v;
}
// Auxillary Equations for the region very close to the critical point
// T3uv ( p) approximates the isochore v = 0.00264 m3 kg-1 from 2.193161551x10^1 MPa to 22.5 MPa.
// Exported for testing
function b3uv_P_T(P) {
var B3uv_PT_I = [0, 1, 2, 3], B3uv_PT_N = [5.28199646263062E2, 8.90579602135307, -0.222814134903755, 0.286791682263697E-2], T = 0;
for (var i = 0; i < 4; i++) {
T += B3uv_PT_N[i] * Math.pow(P, B3uv_PT_I[i]);
}
return T;
}
exports.b3uv_P_T = b3uv_P_T;
//T3wx ( p) approximates the isochore v = 0.00385 m3 kg-1 from 2.190096265x10 MPa to 22.5 MPa
// Exported for testing
function b3wx_P_T(P) {
var B3wx_PT_I = [0, 1, 2, -1, -2], B3wx_PT_N = [7.2805260914538, 9.73505869861952E1, 1.47370491183191E1, 0.329196213998375E3, 8.73371668682417E2], T = 0;
P = Math.log(P);
for (var i = 0; i < 5; i++) {
T += B3wx_PT_N[i] * Math.pow(P, B3wx_PT_I[i]);
}
return T;
}
exports.b3wx_P_T = b3wx_P_T;
function r3u_PT_v(P, T) {
var pi = P / 23, sig = T / 650, v = 0, R3u_PT_I = [-12, -10, -10, -10, -8, -8, -8, -6, -6, -5, -5, -5, -3, -1, -1, -1, -1, 0, 0, 1, 2, 2, 3, 5, 5, 5, 6, 6, 8, 8, 10, 12, 12, 12, 14, 14, 14, 14], R3u_PT_J = [14, 10, 12, 14, 10, 12, 14, 8, 12, 4, 8, 12, 2, -1, 1, 12, 14, -3, 1, -2, 5, 10, -5, -4, 2, 3, -5, 2, -8, 8, -4, -12, -4, 4, -12, -10, -6, 6], R3u_PT_N = [1.22088349258355E17, 1.04216468608488E9, -8.82666931564652E15, 2.59929510849499E19, 2.22612779142211E14, -8.78473585050085E17, -3.14432577551552E21, -2.16934916996285E12, 1.59079648196849E20, -3.39567617303423E2, 8.84387651337836E12, -8.43405926846418E20, 1.14178193518022E1, -1.22708229235641E-4, -1.06201671767107E2, 9.03443213959313E24, -6.93996270370852E27, 6.48916718965575E-9, 7.18957567127851E3, 1.05581745346187E-3, -6.51903203602581E14, -1.60116813274676E24, -5.10254294237837E-9, -1.52355388953402E-1, 6.77143292290144E11, 2.7637843837893E14, 1.16862983141686E-2, -3.01426947980171E13, 1.6971981388484E-8, 1.04674840020929E26, -1.0801690456014E4, -9.90623601934295E-13, 5.36116483602738E6, 2.26145963747881E21, -4.8873156577621E-10, 1.5100154888067E-05, -2.2770046464392E04, -7.81754507698846E27];
for (var i = 0; i < 38; i++) {
var N = R3u_PT_N[i], I = R3u_PT_I[i], J = R3u_PT_J[i];
v += N * Math.pow(pi - 0.902, I) * Math.pow(sig - 0.988, J);
}
return 0.0026 * v;
}
function r3v_PT_v(P, T) {
var pi = P / 23, sig = T / 650, v = 0, R3v_PT_I = [-10, -8, -6, -6, -6, -6, -6, -6, -5, -5, -5, -5, -5, -5, -4, -4, -4, -4, -3, -3, -3, -2, -2, -1, -1, 0, 0, 0, 1, 1, 3, 4, 4, 4, 5, 8, 10, 12, 14], R3v_PT_J = [-8, -12, -12, -3, 5, 6, 8, 10, 1, 2, 6, 8, 10, 14, -12, -10, -6, 10, -3, 10, 12, 2, 4, -2, 0, -2, 6, 10, -12, -10, 3, -6, 3, 10, 2, -12, -2, -3, 1], R3v_PT_N = [-4.15652812061591E-55, 1.77441742924043E-61, -3.57078668203377E-55, 3.59252213604114E-26, -2.59123736380269E1, 5.9461976619346E4, -6.24184007103158E10, 3.13080299915944E16, 1.05006446192036E-9, -1.92824336984852E-6, 6.54144373749937E5, 5.13117462865044E12, -6.97595750347391E18, -1.03977184454767E28, 1.19563135540666E-48, -4.36677034051655E-42, 9.26990036530639E-30, 5.87793105620748E20, 2.80375725094731E-18, -1.92359972440634E22, 7.42705723302738E26, -5.17429682450605E1, 8.20612048645469E6, -1.88214882341448E-9, 1.84587261114837E-2, -1.35830407782663E-6, -7.23681885626348E16, -2.23449194054124E26, -1.11526741826431E-35, 2.76032601145151E-29, 1.34856491567853E14, 6.5244029334586E-10, 5.1065511977436E16, -4.68138358908732E31, -7.60667491183279E15, -4.17247986986821E-19, 3.12545677756104E13, -1.00375333864186E14, 2.47761392329058E26];
for (var i = 0; i < 39; i++) {
var N = R3v_PT_N[i], I = R3v_PT_I[i], J = R3v_PT_J[i];
v += N * Math.pow(pi - 0.960, I) * Math.pow(sig - 0.995, J);
}
return 0.0031 * v;
}
function r3w_PT_v(P, T) {
var pi = P / 23, sig = T / 650, v = 0, R3w_PT_I = [-12, -12, -10, -10, -8, -8, -8, -6, -6, -6, -6, -5, -4, -4, -3, -3, -2, -2, -1, -1, -1, 0, 0, 1, 2, 2, 3, 3, 5, 5, 5, 8, 8, 10, 10], R3w_PT_J = [8, 14, -1, 8, 6, 8, 14, -4, -3, 2, 8, -10, -1, 3, -10, 3, 1, 2, -8, -4, 1, -12, 1, -1, -1, 2, -12, -5, -10, -8, -6, -12, -10, -12, -8], R3w_PT_N = [-5.86219133817016E-8, -8.94460355005526E10, 5.31168037519774E-31, 1.09892402329239E-1, -5.75368389425212E-2, 2.28276853990249E4, -1.58548609655002E18, 3.29865748576503E-28, -6.34987981190669E-25, 6.15762068640611E-9, -9.61109240985747E7, -4.06274286652625E-45, -4.71103725498077E-13, 7.25937724828145E-1, 1.87768525763682E-39, -1.03308436323771E3, -6.62552816342168E-2, 5.7951404176571E2, 2.37416732616644E-27, 2.71700235739893E-15, -9.0788621348360E1, -1.71242509570207E-37, 1.56792067854621E2, 9.2326135790147E-1, -5.97865988422577, 3.21988767636389E6, -3.99441390042203E-30, 4.93429086046981E-08, 8.12036983370565E-20, -2.07610284654137E-12, -3.40821291419719E-07, 5.42000573372233E-18, -8.56711586510214E-13, 2.66170454405981E-14, 8.58133791857099E-6];
for (var i = 0; i < 35; i++) {
var N = R3w_PT_N[i], I = R3w_PT_I[i], J = R3w_PT_J[i];
v += N * Math.pow(pi - 0.959, I) * Math.pow(sig - 0.995, J);
}
return 0.0039 * Math.pow(v, 4);
}
function r3x_PT_v(P, T) {
var pi = P / 23, sig = T / 650, v = 0, R3x_PT_I = [-8, -6, -5, -4, -4, -4, -3, -3, -1, 0, 0, 0, 1, 1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 8, 8, 8, 8, 10, 12, 12, 12, 12, 14, 14, 14, 14], R3x_PT_J = [14, 10, 10, 1, 2, 14, -2, 12, 5, 0, 4, 10, -10, -1, 6, -12, 0, 8, 3, -6, -2, 1, 1, -6, -3, 1, 8, -8, -10, -8, -5, -4, -12, -10, -8, -6], R3x_PT_N = [3.77373741298151E18, -5.07100883722913E12, -1.0336322559886E15, 1.84790814320773E-6, -9.24729378390945E-4, -4.25999562292738E23, -4.62307771873973E-13, 1.07319065855767E21, 6.48662492280682E10, 2.44200600688281, -8.51535733484258E9, 1.69894481433592E21, 2.1578022250902E-27, -3.20850551367334E-1, -3.826424