Joule-Thomson Inversion Curve Research Articles

Predictions of the Joule-Thomson Inversion Curve for Water and Methanol from the LJ-SAFT EOS

In this work, we have calculated the Joule-Thomson inversion curve of two important associating fluids, namely water and methanol, from the SAFT equation of state. Comparisons with the available experimental data, for water and methanol indicate that this molecular based equation of state gives good prediction of the low temperature branch; but, unfortunately, due to lack of isenthalpic data for high-pressure-high- temperature gas condensate for water and methanol, the reliability of model predictions could not be completely verified. We have also reported the influence of the molecular dipole moment and the segment number on the Joule-Thomson inversion curve.

New Attraction Term for the Soave‐Redlich‐Kwong Equation of State

AbstractA new 3‐parameter attraction term for the Soave‐Redlich‐Kwong equation of state, that ensures a correct physical behaviour, is proposed to improve its predictive capabilities, particularly in the supercritical region and in the gas phase. Vapour pressure and second virial coefficient data for a set of eight pure fluids with a low acentric factor ω (Ar, Ne, Kr, O2, N2, C‐H4, CO and C2‐H6) are used to determine the equation's adjustable parameters. When only vapour pressure data are considered the supercritical region is poorly described. An extension of the data base by including for instance the second virial coefficient data leads to a significant improvement in the description of the sub and supercritical regions of the considered fluids and particularly in the prediction of the Joule‐Thomson inversion curves. The new attraction term is shown to be suitable for other pratical fluids like hydrocarbons as well as their mixtures.

Predictions of the Joule–Thomson inversion curves for polar and non-polar fluids from the SAFT-CP equation of state

In this work, we calculate the Joule–Thomson inversion curves of some non-polar fluids, including argon, nitrogen, oxygen, carbon dioxide, n-alkanes (C 1–C 4), ethene, acetylene, benzene and toluene and some polar fluids, including hydrogen sulfide, ammonia, acetone and ethyl ether from the SAFT-CP equation of state. Comparisons with correlated experimental data and reference equation of state indicate that this molecular based equation of state gives good prediction for non-polar fluids. For polar fluids, the predictions of the low-temperature branch are satisfied; but, unfortunately, due to lack of isenthalpic data for high-pressure–high-temperature gas condensate, the reliability of model predictions could not be completely verified. In this work, the performance of some cubic equations of state in predicting the Joule–Thomson inversion curves is also compared with SAFT-CP equation of state.

A new equation of state derived by the statistical mechanical perturbation theory

We have derived an analytical equation of state (EOS) based on the soft-core statistical mechanical perturbation theory for fluids, using the Weeks–Chandler–Andersen (WCA) theory recently developed by Ben–Amotz–Stell (BAS) for the choice of the hard-sphere diameter, but with a new algorithm for calculation of the pair and many-body interactions. We have used Carnahan–Starling expression with the Boltzmann factor criterion (BFC) as an effective hard-sphere diameter for the reference system, and also decomposed the perturbed pair potential to symmetric and asymmetric terms. The former term is due to the many-body interactions at high densities as was used in the linear isotherm regularity known as LIR EOS, and the latter term supports the interaction of two isolated particles that is dominating at low densities. The resulting EOS is obtained as Z = Z cs + αρ + Aρ 3 + Bρ 5, in which Z cs is the Carnahan–Starling expression for the compressibility factor of the reference system which contains the effective van der Waals co-volume, and α is due to the asymmetric interaction term, or the attraction contribution of the second virial coefficient. The A and B parameters are the attractive and repulsive contributions of symmetric term, respectively. The temperature-dependencies of all parameters of the EOS are obtained. We select some different fluids, namely Ar, N 2, CH 4, Ne, CO 2, C 2H 6, C 3H 8, NH 3 and H 2O which are spherical, roughly spherical, non-spherical, polar and associated fluids, due to their abundance of P– V– T experimental data. We have found that, except for the critical region, 0.8 < ρ r ≤ 1.5, 1 ≤ T r ≤ 1.5, the new EOS is accurate for all temperatures and densities available in the literatures, in such a way that the average percent deviation of density for Ar, Ne, N 2, CH 4, CO 2, C 2H 6, C 3H 8, and NH 3 is less than 2.81%. Then some thermodynamic properties including vapor–pressure curve, Joule–Thomson inversion curve, P– T isochors curves, and the second virial coefficient have been applied to check the accuracy of the new EOS. Results for some isochors of argon show that the new EOS gives a small negative curvature for all isochors. The new EOS prediction of the inversion Joule–Thomson curve is reasonable, and its prediction of Clausius–Clapeyron diagram for neon and argon is very accurate, but small deviation for methane and nitrogen can be seen.

Joule–Thomson inversion curve prediction by using equation of state

In this paper five equations of state are tested for checking their ability to predict the Joule–Thomson inversion curve. These five equations of state are: Mohsennia–Modarres–Mansoori (MMM), Ji-Lemp (JL), modified Soave–Redlich–Kwang (SRK) equation of state by Graboski (MSRK1), modified SRK equation of state by Peneloux and Rauzy (MSRK2), and modified Peng–Robinson (PR) equation of state by Rauzy (PRmr). The investigated equations of state give good prediction of the low-temperature branch of the inversion curve, except for MMM equation of state. The high-temperature branch and the peak of the inversion curve have been observed, in general, to be sensitive to the applied equation of state. The values of the maximum inversion temperature and maximum inversion pressure are calculated for each component used in this work.

Joule–Thomson inversion curves of mixtures by molecular simulation in comparison to advanced equations of state: Natural gas as an example

Molecular modelling and simulation as well as four equations of state (EOS) are applied to natural gas mixtures regarding Joule–Thomson (JT) inversion. JT inversion curves are determined by molecular simulation for six different natural gas mixtures consisting of methane, nitrogen, carbon dioxide and ethane. These components are also regarded as pure fluids, leading to a total of 10 studied systems. The results are compared to four advanced mixture EOS: DDMIX, SUPERTRAPP, BACKONE and the recent GERG-2004 Wide-Range Reference EOS. It is found that molecular simulation is competitive with state-of-the-art EOS in predicting JT inversion curves. The molecular based approaches (simulation and BACKONE) are superior to DDMIX and SUPERTRAPP.

PARAMETRIC GENERATION OF SINGLE-PHASE PROPERTIES (P-T CURVES) FOR MOST CUBIC EQUATIONS OF STATE AND ANY MIXING RULES

A simple method is proposed for the calculation of any type of P-T curve for the most general case of two-parameter equations of state in the single-phase area. For each component parameter, temperature dependency can be expressed on the basis of any analytical function; for the mixture, any mixing rule can be considered for any parameter. For the construction of these curves, the numerical algorithm is completely described. This method is illustrated for the Joule-Thomson inversion and Boyle curves.

REMOVED: Calculation of Joule–Thomson inversion curves from equation of state

REMOVED: Calculation of Joule–Thomson inversion curves from equation of state

Deriving Analytical Expressions for the Ideal Curves and Using the Curves to Obtain the Temperature Dependence of Equation-of-State Parameters

Different equations of state (EOSs) have been used to obtain analytical expressions for the ideal curves, namely, the Joule–Thomson inversion curve (JTIC), Boyle curve (BC), and Joule inversion curve (JIC). The selected EOSs are the Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), Deiters, linear isotherm regularity (LIR), modified LIR (MLIR), dense system equation of state (DSEOS), and van der Waals (vdW). Analytical expressions have been obtained for the JTIC and BC only by using the LIR, MLIR, and vdW equations of state. The expression obtained using the LIR is the simplest. The experimental data for the JTIC and the calculated points from the empirical EOSs for the BC are well fitted into the derived expression from the LIR, in such a way that the fitting on this expression is better than those on the empirical expressions given by Gunn et al. and Miller. No experimental data have been reported for the BC and JIC; therefore, the calculated curves from different EOSs have been compared with those calculated from the empirical equations. On the basis of the JTIC, an approach is given for obtaining the temperature dependence of an EOS parameter(s). Such an approach has been used to determine the temperature dependences of A 2 of the LIR, a and b parameters of the vdW, and the cohesion function of the RK. Such temperature dependences, obtained on the basis of the JTIC, have been found to be appropriate for other ideal curves as well.

Calculation of Joule–Thomson inversion curves for two-phase mixtures

The Joule–Thomson inversion curve (JTIC), defined as the locus in the p– T plane where the adiabatic Joule–Thomson (JT) coefficient is zero, separates regions for which heating and cooling occur upon an isenthalpic expansion. JTIC calculation for mixtures is a clear matter for single-phase conditions. For two-phase mixtures, an apparent JT coefficient can be defined, which incorporates: (i) JT effects and (ii) phase distribution changes effects. Three different ways for calculating the apparent JTIC are presented: a volumetric approach, an approach based on enthalpy departure variation, and an approach based on isenthalpic flashes. Cubic equations of state are used in this work, but any thermodynamic model can be used. Several examples show that for mixtures, the locus separating heating/cooling regions may have two or three distinct branches, and that at phase boundaries there are discontinuities in the JT coefficient corresponding to angular points of enthalpy variations.

A Combined Pressure-controlled Scanning Calorimetry and Monte Carlo Determination of the Joule−Thomson Inversion Curve. Application to Methane

A combination of a pressure-controlled scanning calorimetry (PCSC) and Monte Carlo simulations (MCS) is presented for an unequivocal determination of the Joule-Thomson inversion curve (JTIC) with high accuracy over wide ranges of pressure and temperature. The MCS performed with the fluctuation method are fast and easy to operate, but the results can vary significantly depend on the set of primary molecular data needed for the calculations. The PCSC is an experimental and more laborious technique, but supplies data of high quality. Thus, it can be used to check the MCS data and to verify the molecular parameters used for the calculations. Such a combined procedure was used in the present study for determination of the JTIC for methane, for which a correlation equation was established valid from 302.9 to 586.5 K. A combination of a direct experimental technique with molecular simulations permits also to better understand the complex behavior of the Joule-Thomson inversion phenomenon over wide ranges of pressure and temperature.

A novel EOS that combines van der Waals and Dieterici potentials

AbstractA novel approach is proposed for solving the problem of the overestimation of the liquid–liquid equilibrium (LLE) range in mixtures typically associated with the use of equations of state (EOS) of the van der Waals type. This approach modifies the internal EOS structure by combining the van der Waals and the Dieterici forms. It advantageously uses the drawback of the Dieterici form, which strongly underestimates the LLE range. Thus, the new EOS is capable of generating an appropriate balance for the representation of vapor–liquid equilibria (VLE) and LLE critical data and therefore represents a major improvement in comparison with typical van der Waals–type EOSs. In addition, it gives accurate representation of the Joule–Thomson inversion curve and predicts critical data for nonpolar mixtures without any binary parameters. For polar systems, the novel EOS predicts critical data for complete homologous series of mixtures using a pair of binary parameters evaluated from a single system. © 2005 American Institute of Chemical Engineers AIChE J, 2005

Evaluation of the parameters of the Bender equation of state for low acentric factor fluids and carbon dioxide

Volumetric properties of several low acentric factor fluids (Ar, CH 4, C 2H 6, Kr, N 2, Ne, O 2, Xe) as well as CO 2 are modeled using the Bender equation of state. This equation is a linear function of 19 adjustable parameters, which are evaluated from properties data, using a linear numerical procedure. The validity of the EOS is tested by calculating the Joule–Thomson inversion curve. A simple model is in particular used to correlate the inversion properties predicted by the Bender equation, expressed in term of reduced pressure as a function of reduced temperatures ranging from 0.8 to 6. The simple correlation reproduces accurately the used data. We employ data on state behaviour ρ ( P , T ) of homogeneous fluid phases, vapour–liquid equilibrium, second virial coefficient and the coordinates of the critical point.

Molecular simulation of the Joule–Thomson inversion curve of hydrogen sulphide

The complete Joule–Thomson inversion curve for hydrogen sulphide is determined via molecular simulations in adiabatic ensembles. In addition to NpH Monte Carlo simulations, two new versions of the density-of-states simulations are applied for smoothly scanning relevant thermodynamic ranges. With the use of realistic site–site intermolecular potential models the calculations yield good agreement with the accessible experimental data.

Prediction of Joule–Thomson inversion curves for pure fluids and one mixture by molecular simulation

The predictive power of a set of molecular models, which have been adjusted to vapor–liquid equilibria only, is validated. For that purpose, Joule–Thomson inversion curves were determined by molecular simulation for 15 pure fluids, i.e. argon, methane, oxygen, nitrogen, carbon dioxide, ethylene, carbon monoxide, R11, R23, R41, R124, R125, R134a, R143a, R152a, and for air. Comparison of the simulation results with reference equations of state shows an excellent agreement.

Direct molecular-level Monte Carlo simulation of Joule—Thomson processes

We present an application of the recently developed constant enthalpy-constant pressure Monte Carlo method [SMITH, W. R., and LÍSAL, M., 2002, Phys. Rev. E, 66, 01114] for the direct simulation of Joule-Thomson expansion processes using a molecular-level system model. For the alternative refrigerant HFC-32 (CH2F 2), we perform direct simulations of the isenthalpic integral Joule-Thomson effect (temperature drop) resulting from Joule-Thomson expansion from an initial pressure to the representative final pressure of 1 bar. We consider representative expansions from single-phase states yielding final states in both single-phase and two-phase regions. We also predict the dependence of T(P, h) and of the Joule-Thomson coefficient, μ (P, h), on pressure along several representative isenthalps, as well as points on the Joule-Thomson inversion curve. HFC-32 is modelled using a five-site potential taken from the literature, with parameters derived from ab initio calculations and vapour-liquid equilibrium data. The simulated results show excellent agreement with those calculated from an international standard equation of state.

Accurate CO 2 Joule–Thomson inversion curve by molecular simulations

We present simulation of the Joule–Thomson inversion curve (JTIC) for carbon dioxide using two different approaches based on Monte Carlo (MC) simulations in the isothermal–isobaric ensemble. We model carbon dioxide using a two-center Lennard–Jones (LJ) plus point quadrupole moment (2CLJQ) potential. We show that a precision of four significant figures in ensemble averages of thermodynamic quantities of interest is needed to obtain accurately the JTIC. The agreement between the experimental data, Wagner equation of state (EOS) and our simulations results indicates that the 2CLJQ potential represents an excellent balance between simplicity and accuracy in modeling of carbon dioxide. Additionally, we calculate the JTIC using the BACKONE EOS (that uses the same intermolecular potential as in our simulations) and show that the BACKONE EOS performs very well in predicting the JTIC for carbon dioxide.

Simulation of Isoenthalps and Joule-Thomson Inversion Curves of Pure Fluids and Mixtures

This paper examines the molecular simulation of expansion and compression processes of fluids under common non-isothermal conditions. It is shown that accurate isoenthalps can be traced if simulated configurational properties obtained from the particular molecular force-field adopted are complemented by experimentally-based data for the ideal-gas contributions to the heat capacity. The simulation of inversion curves is also analyzed and found to be particularly challenging as conventional extrapolation techniques have limited applicability. Several approaches were investigated to overcome such difficulties including (1) simulation of several isobars and isoenthalps, (2) thermodynamic integration, and (3) histogram reweighting techniques. Contrary to the results of a recent study, our calculations show that the Johnson et al, equation of state does provide a good description of the inversion curve for the Lennard-Jones fluid. Isoenthalps and the inversion curve for a model gas condensate mixture were also simulated; calculations of this sort could be used to identify conditions at which isoenthalpic decompression leads to heating of hydrocarbon reservoir fluids.

Calculation of the Joule–Thomson inversion curves from cubic equations of state

In this paper the Joule–Thomson (JT) inversion curve has been used to test the predictive capabilities of some recent cubic equations of state. The three and two parameter cubic equations of state included modified Patel–Teja (MPT), modified Peng–Robinson (MPR) by Melhem–Saini–Goodwin, Iwai–Margerum–Lu (IML), modified Redlich–Kwong (MRK) by Souahi–Sator–Albane–Kies–Chitoure and the four parameter Trebble–Bishnoi (TB) equation of state were chosen for our study. All of the equations studied here except MRK have been given good prediction of the low-temperature branch of the JT inversion curve. In the high-temperature region and the peak of the curves depend on components the MPR, MPT and TB equations provided relatively fair agreement with experimental data and Gunn, Chueh and Prausnitz (GCP) correlated inversion curve. We considered the effect of the constants in α function of the MPT equation of state, in its ability of the prediction of the JT inversion curve. The consequence of volumetric parameter on the high pressure and relatively high temperature region has been shown. Isenthalp calculation has also been included.

Molecular simulation of the Joule–Thomson inversion curve of carbon dioxide

The complete Joule–Thomson (JT) inversion curve for carbon dioxide is calculated using molecular simulations. A two center Lennard–Jones model with an embedded point quadrupole is used to model the fluid–fluid interactions. The simulation results agree quantitatively with all available experimental data. Comparison with commonly used equations of state provides only a modest agreement, with the highest discrepancies being observed at the high temperature branch of the inversion curve.