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getEOS.js
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getEOS.js
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import { R } from '../data/constants.js';
import { EOSParameters } from './eosParameters';
import { getPhasefromPhi } from './phase.js';
/**
* Based on a MolecularFluid, temperature, and pressure or volume and
* the choice of equation of state (EOS) return the thermodynamic properties
* of the system
*
* @export
* @param {MolecularFluid} molecularFluid instance of the MolecularFluid class
* @param {Number} temperature in Kelvin
* @param {Object} [options={}]
* @param {Number} options.pressure in bar
* @param {Number} options.volume in L
* @param {String} otpions.eos Type of the equation of states (EOS). Available options: pr (Peng-Robinson), vdw (Van der Waals), rk (Redlich–Kwong), rks (Redlich–Kwong-Soave). Defaults to pr.
* @returns {Object}
*/
export function getProperties(molecularFluid, temperature, options = {}) {
let { pressure = 1, volume = null, eos = 'pr' } = options;
validateInput(pressure, volume);
let eosParameters = new EOSParameters(molecularFluid, temperature, {
eos: eos,
});
eosParameters.relativeTemperature =
temperature / molecularFluid.criticalTemperature;
if (Number.isFinite(volume) & !Number.isFinite(pressure)) {
pressure = getPressure(eosParameters, temperature, volume);
}
updateEOSParameters(eosParameters, pressure, temperature);
let zList = solveZ(eosParameters);
let phaseProperties = getThermodynamicProperties(
zList,
eosParameters,
eos,
molecularFluid,
pressure,
temperature,
);
let phis = [];
phaseProperties.forEach((properties) => {
phis.push(properties.fugacityCoefficient);
});
return {
temperature: temperature,
pressure: pressure,
phaseProperties: phaseProperties,
zList: zList,
inPhase: getPhasefromPhi(phis),
};
}
function validateInput(volume, pressure) {
if (Number.isFinite(volume) & Number.isFinite(pressure)) {
throw new Error('You need to specify pressure OR volume, not both!');
}
if (!Number.isFinite(volume) & !Number.isFinite(pressure)) {
throw new Error('You need to specify pressure or volume!');
}
}
function getPressure(eosParameters, temperature, volume) {
return (
(R * temperature) / (volume - eosParameters.b) -
eosParameters.a /
(volume ** 2 +
eosParameters.u * eosParameters.b * volume +
eosParameters.w * eosParameters.b ** 2)
);
}
function updateEOSParameters(eosParameters, pressure, temperature) {
eosParameters.A =
(eosParameters.a * eosParameters.k * pressure) / R ** 2 / temperature ** 2;
eosParameters.B = (eosParameters.b * pressure) / R / temperature;
eosParameters.alpha =
-1 - eosParameters.B + eosParameters.u * eosParameters.B;
eosParameters.beta =
eosParameters.A +
eosParameters.w * eosParameters.B ** 2 -
eosParameters.u * eosParameters.B -
eosParameters.u * eosParameters.B ** 2;
eosParameters.gamma =
-eosParameters.A * eosParameters.B -
eosParameters.w * eosParameters.B ** 2 -
eosParameters.w * eosParameters.B ** 3;
eosParameters.p = eosParameters.beta - eosParameters.alpha ** 2 / 3;
eosParameters.q =
(2 * eosParameters.alpha ** 3) / 27 -
(eosParameters.alpha * eosParameters.beta) / 3 +
eosParameters.gamma;
eosParameters.Delta = eosParameters.q ** 2 / 4 + eosParameters.p ** 3 / 27;
}
/**
*Some background here https://pubs.acs.org/doi/pdf/10.1021/ie2023004
*
*/
function solveZ(eosParameters) {
// Cardano solution formula
let zList = [];
if (eosParameters.Delta > 0) {
zList = solveCardano(eosParameters);
} else {
zList = solveTrigonometric(eosParameters);
}
return zList;
}
function solveCardano(eosParameters) {
let xSol;
let zList = [];
xSol =
Math.cbrt(-eosParameters.q / 2 + Math.sqrt(eosParameters.Delta)) +
Math.cbrt(-eosParameters.q / 2 - Math.sqrt(eosParameters.Delta));
zList = [xSol - eosParameters.alpha / 3];
return zList;
}
function solveTrigonometric(eosParameters) {
let xSol;
let zList = [];
let subeq = Math.acos(
((3 * eosParameters.q) / 2 / eosParameters.p) *
Math.sqrt(-3 / eosParameters.p),
);
for (let offset = 0; offset < 3; offset++) {
xSol =
2 *
Math.sqrt(-eosParameters.p / 3) *
Math.cos(subeq / 3 - (2 * Math.PI * offset) / 3);
zList.push(xSol - eosParameters.alpha / 3);
}
zList.sort(); // [ z_liq, z_meaningless, z_vap ]
//remove the meaningless value
zList.splice(1, 1);
return zList;
}
function getThermodynamicProperties(
zList,
eosParameters,
eos,
molecularFluid,
pressure,
temperature,
) {
let phaseProperties = [];
switch (eos) {
case 'pr':
zList.forEach((z) => {
phaseProperties.push(
getThermodynamicPropertiesPR(
z,
eosParameters,
molecularFluid,
pressure,
temperature,
),
);
});
break;
default:
throw new Error('Only supported EOS are VDW and PR.');
}
return phaseProperties;
}
function getThermodynamicPropertiesPR(
z,
eosParameters,
molecularFluid,
pressure,
temperature,
) {
const ecap =
eosParameters.S *
Math.sqrt(eosParameters.relativeTemperature / eosParameters.k);
const subeq1 = eosParameters.A / 2 / Math.sqrt(2) / eosParameters.B;
const subeq2 = Math.log(
(z + eosParameters.B * (1 + Math.sqrt(2))) /
(z + eosParameters.B * (1 - Math.sqrt(2))),
);
const residualEnthalpy = z - 1 - subeq1 * (1 + ecap) * subeq2;
const residualEntropy =
Math.log(z - eosParameters.B) - subeq1 * ecap * subeq2;
const { gibbs, fugacityCoefficient } = computeGibbsFugacity(
residualEnthalpy,
residualEntropy,
);
const molarDensity = computeMolarDensity(pressure, temperature, z);
return {
fugacityCoefficient: fugacityCoefficient,
fugacity: fugacityCoefficient * pressure,
residualEnthalpy: residualEnthalpy,
residualEntropy: residualEntropy,
residualGibbsEnergy: gibbs,
compressibilityFactor: z,
molarDensity: molarDensity,
density: computeDensity(molarDensity, molecularFluid),
};
}
function computeGibbsFugacity(enthalpy, entropy) {
const gibbs = enthalpy - entropy;
const fugacityCoefficient = Math.exp(gibbs);
return { gibbs, fugacityCoefficient };
}
function computeMolarDensity(pressure, temperature, compressibilityFactor) {
return pressure / (R * 1000 * temperature * compressibilityFactor);
}
function computeDensity(molarDensity, molecularFluid) {
return (molarDensity * molecularFluid.molarMass) / 1000;
}