phase equilibria giản đồ pha

hydro-The Chao-Seader correlation7tion for the vapor phase, the regular solution model for liquid-mix-ture non-ideality, and a pure-liquid property correlation for effects uses the Redl

and pressure and a weaker function of composition The conver-gence pressure method recognizes composition effects in

pre-dicting K-data The convergence pressure technique can be

used in hand calculations, and it is still available as computer

correlations for K-data prediction

value correlations in modern process simulators, has made the previous GPA convergence pressure charts outdated Complete sets of these charts are available from GPA as a Technical Pub-lication, TP-22

Availability of computers, coupled with the more refined K-Data for N2-CH4 and N2-C2H6 show that the K-values in these system have strong compositional dependence The com-ponent volatility sequence is N2-CH4-C2H6 and the K-values are functions of the amount of methane in the liquid phase For example, at –123°C and 2070 kPa (abs), the K-values depend-ing upon composition vary from:

N 2 CH 4 C 2 H 6

erence 5 for the data on this ternary

where * indicates the limiting infinite dilution K-value See ref- The charts retained in this edition represent roughly 12% of the charts included in previous editions These charts are a compro-mise set for gas processing as follows:

a hydrocarbons — 3000 psia Pk [20 700 kPa (abs)]

b nitrogen — 2000 psia Pk [13 800 kPa (abs)]

c hydrogen sulfide — 3000 psia Pk [20 700 kPa (abs)]The pressures in a through c above refer to convergence pressure, Pk, of the charts from the Tenth Edition of this data book They should not be used for design work or related activi-ties Again, they are in this edition for illustration and approxi-mation purposes only; however, they can be very useful in such

a role The critical locus chart used in the convergence pressure method has also been retained (Fig 25-8)

tems of interest to gas processors Detailed results are given in the annual proceedings and in various research reports and technical publications, which are listed in Section 1

∑ Ki Ni = 1.0 (bubble point) Eq 25-8

and

These are often helpful for preliminary calculations where the phase condition of a system at a given pressure and tem-perature is in doubt If ∑K iN i and ∑N i/K i are both greater than 1.0, the system is in the two phase region If ∑K iN i is less than 1.0, the system is all liquid If ∑N i/K i is less than 1.0, the system

is all vapor

Example 25-2 — A typical high pressure separator gas is used

for feed to a natural gas liquefaction plant, and a preliminary step in the process involves cooling to –30°C at 4140 kPa (abs)

peratures where these components would freeze out as solids

to liquefy heavier hydrocarbons prior to cooling to lower tem-Solution Steps

The feed gas composition is shown in Fig 25-3 The flash equation 25 -5 is solved for three estimated values of L as shown

lated ∑x i, the correct value of L where ∑x i = 1.00 is L = 0.030, whose solution is shown in columns 6 and 7 The gas composi-tion is then calculated using y i = K ix i in column 8 This “correct” value is used for purposes of illustration It is not a completely converged solution, for x i = 1.00049 and y i = 0.99998, columns 7 and 8 of Fig 25-3 This error may be too large for some applica-tions

Example 25-3 — Dew Point Calculation

A gas stream at 40°C and 5500 kPa (abs) is being cooled in a heat exchanger Find the temperature at which the gas starts to condense

Solution Steps

ilar to the previous example The equation for dew point condi-tion (∑N i/K i = 1.0) is solved for two estimated dew point tem-peratures as shown in Fig 25-4 By interpolation, the temperature at which ∑N i/K i = 1.0 is estimated at –41.4°C Note that the heaviest component is quite important in dew point calculations For more complex mixtures, the character-

and methane at typical operat-is carried to the point of producing high purity methane.Fig 25-5 depicts the phase diagram for the methane-CO 2 binary system.21 The pure component lines for methane and

CO 2 vapor-liquid equilibrium form the left and right boundaries

of the phase envelope Each curve terminates at its critical point; methane at –83°C, 4604 kPa (abs) and CO 2 at 31°C, 7382 kPa (abs) The unshaded area is the vapor-liquid region The shaded area represents the vapor-CO 2 solid region which ex-tends to a pressure of 4860 kPa (abs)

Because the solid region extends to a pressure above the methane critical pressure, it is not possible to fractionate pure methane from a CO 2-methane system without entering the solid formation region It is possible to perform a limited separation

FIG 25-2 Sources of K-Value Charts

Component

Charts available from sources as indicatedConvergence pressures, kPa (abs) [psia]

and methane if the desired methane can contain signifi-cant quantities of CO 2

At an operating pressure above 4860 kPa (abs), the methane

purity is limited by the CO 2-methane critical locus (Fig 25-6)

For example, operating at 4930 kPa (abs), it is theoretically

possible to avoid solid CO 2 formation (Fig 25-7 and 16-36) The

The separation of CO 2 and ethane by distillation is limited

FIG 25-3 Flash Calculation at 4140 kPa and –30°C

Component

Column

Feed Gas Composition 4140 kPa 30°C

Trial values of L Final L = 0.030

tropic composition of approximately 67% CO 2, 33% ethane is formed at virtually any pressure.24

by the azeotrope formation between these components An azeo-Fig 25-7 shows the CO 2-ethane system at two different pressures The binary is a minimum boiling azeotrope at both pressures with a composition of about two-thirds CO 2 and one-third ethane Thus, an attempt to separate CO 2 and ethane to nearly pure components by distillation cannot be achieved by traditional methods, and extractive distillation is required.26 (See Section 16, Hydrocarbon Recovery)

FIG 25-5

Phase Diagram CH 4 -Ch 2 Binary 21

FIG 25-6 Isothermal Dew Point and Frost Point Data for Methane-Carbon Dioxide 32

PHASE EQUILIBRIA METHODS

Numerous procedures have been devised to predict phase

tures with relatively low concentrations of non-polar or slightly polar fluids

They typically are applied only to hydrocarbon mix-Recent advancements have made cubic EOS able for handling high concentrations of CO2, H2S, and

suit-N2

● ponents (VLE) and mixtures (VLE and VLLE) and for prediction of all thermodynamic properties for vapor and liquid phases

Applicable for prediction of phase equilibria for pure com-Originally developed for handling of pure nents, but inclusion and use of various mixing rules, which incorporate binary interaction parameters, have allowed the extension of use to binary and multicompo-nent mixtures

compo-sure, including subcritical, supercritical, and retro-grade regions

Useful over wide ranges of temperature and pres-● nary data can be used to “tune” binary interaction pa-rameters, usually by regression of experimental data

Require minimal pure component data Experimental bi-● Major EOS types include cubic, virial, corresponding states, and multi-parameter Descriptions of the more commonly used cubic and virial types are included below:Cubic EOS (e.g., van der Waal, Redlich-Kwong, Soave-Redlich-Kwong, Peng Robinson)

ture (T) and volume (V) They have separate terms

Explicit in pressure (P) with respect to tempera-to correct ideal gas predictions for attraction and repulsion forces between the molecules (correcting the real vapor pressure and volume predictions, re-spectively) When considering the pressure and temperature fixed, the EOS can be algebraically re-arranged to give a relationship for V that is a cubic (3rd order) polynomial

cific to each chemical species that are generally de-termined from the critical properties, Pc and Tc, for the chemical species Additional temperature-de-pendent functions can be added to more accurately match pure component behavior (i.e., a tempera-ture dependent function correlated to the accentric factor (w) is normally used to better match a pure component’s vapor pressure versus temperature be-havior)

These EOS will include other parameters, spe-Multicomponent mixtures are treated with the same EOS parameters that are determined for the pure components present in the mixture The equa-tions used to blend the pure component values are referred to as “mixing rules”, which often include

ideal interactions between pairs of unlike mole-cules

“binary interaction parameters” to account for non-The EOSs are generally not “tuned” to pure component liquid density data, so they give poor representations of liquid molar volume/liquid den-

FIG 25-7 Vapor-Liquid Equilibria CO 2 -C 2 H 6 21

Because of the larger number of parameters

that can be tuned to pure component data, these

EOS can be more accurate than cubic EOS when

calculating liquid densities

For pure components, these EOS can give a

more accurate representation than cubic EOS for

Computerized corresponding states methods

may be based on virial EOS for reference fluids

The SAFT (Statistical Associate Fluid The-ory) family of EOS are based on Wertheims

perturbation theory and can be applied to a

Typically apply only to utility systems

within a facility, not to the main processing

and separation trains

Examples include NBS Steam Tables, Span and Wagner EOS (CO2), Wagner and Pruss EOS (Water), and heat transfer fluid models

Historical Development of EOS for Phase Equilibria

— Two popular state equations for K-value predictions are the Benedict-Webb-Rubin (BWR) equation and the Redlich-Kwong equation

The original BWR equation17 uses eight parameters for each component in a mixture plus a tabular temperature dependence for one of the parameters to improve the fit of vapor-pressure data This original equation is reasonably accurate for light paraffin mixtures at reduced temperatures of 0.6 and above.8 The equation has difficulty with low temperatures, non-hydro-carbons, non-paraffins, and heavy paraffins

perature dependence, parameters for additional compounds, and generalized forms of the parameters

Improvements to the BWR include additional terms for tem-Starling20pendence in a modified BWR equation that is capable of pre-dicting light paraffin K-values at cryogenic temperatures.The Redlich-Kwong equation has the advantage of a simple analytical form which permits direct solution for density at spec-ified pressure and temperature The equation uses two parame-ters for each mixture component, which in principle permits pa-rameter values to be determined from critical properties.However, as with the BWR equation, the Redlich-Kwong equation has been made useful for K-value predictions by em-pirical variation of the parameters with temperature and with acentric factor11, 18, 19 and by modification of the parameter-com-bination rules.15, 19 Considering the simplicity of the Redlich-Kwong equation form, the various modified versions predict K-values remarkably well

has included explicit parameter temperature de-Interaction parameters for non-hydrocarbons with carbon components are necessary in the Redlich-Kwong equa-tion to predict the K-values accurately when high concentra- tions of non-hydrocarbon components are present They are especially important in CO2 fractionation processes, and in con-ventional fractionation plants to predict sulfur compound dis-tribution

hydro-The Chao-Seader correlation7tion for the vapor phase, the regular solution model for liquid-mix-ture non-ideality, and a pure-liquid property correlation for effects

uses the Redlich-Kwong equa-of component identity, pressure, and temperature in the liquid phase The correlation has been applied to a broad spectrum of compositions at temperatures from –50°F to 300°F and pressures

to 2000 psia The original (P,T) limitations have been reviewed.12Prausnitz and Chueh have developed16 a procedure for high-pressure systems employing a modified Redlich-Kwong equa-tion for the vapor phase and for liquid-phase compressibility together with a modified Wohl-equation model for liquid phase activity coefficients Complete computer program listings are given in their book Parameters are given for most natural gas components Adler et al also use the Redlich-Kwong equation for the vapor and the Wohl equation form for the liquid phase.6The corresponding states principle10 is used in all the proce-dures discussed above The principle assumes that the behavior

of all substances follows the same equation forms and equation parameters are correlated versus reduced properties and acen-tric factor An alternate corresponding states approach is to re-fer the behavior of all substances to the properties of a reference

substance, these properties being given by tabular data or a

ture dependent term It is expressed as a function of the acen-tric factor The SRK correlation has improved accuracy in

predicting the saturation conditions of both pure substances

and mixtures It can also predict phase behavior in the critical

region, although at times the calculations become unstable

around the critical point Less accuracy has been obtained when

applying the correlation to hydrogen-containing mixtures

Peng and Robinson14 similarly developed a two-constant

equation of state in 1976 In this correlation, the attractive

pressure term of the semi-empirical van der Waals equation

even for the same correlation This can be attributed to differ-ent pure componeven for the same correlation This can be attributed to differ-ent and binary parameters, iteration

tech-niques, convergence criteria, and initial estimation values,

applicability of an EOS extended further beyond the

available experimental data; however, more mental data is required to allow for a proper fit of the mixing equation

experi-Application of more complex mixing rules can make EOS methods adequate for polar/non-ideal systems.Specifically, Activity Coefficient methods have been used directly in some mixing rules to more ac-curately predict binary interactions of mixtures with polar and non-polar components at high pres-sure, despite the Activity Coefficient method only being fit to available low pressure experimental data (i.e., Wong-Sandler)

● Enhanced binary interaction parametersGroup contribution methods have been developed to estimate binary interactions (e.g Predictive SRK) and greatly improve predictions especially for mixtures with polar and non-polar components

Interaction parameters are typically fitted to perimental data for each specific EOS and mixing rule combination In turn, more quality experimental data

ex-in the pressure, temperature, and compositional region

of a particular application of interest allows for hanced binary interaction parameters and improved EOS predictions However, fitting interaction parame-ters to different sets of data will result in inconsistent predictions from one tool to another

en-Binary interaction parameters are often ture dependent, and may be fit by differing tempera-ture dependency forms, for which proper choice can impact EOS performance The ability for a user to spec-ify binary interaction parameters is included in many

tempera-of commercially available simulation products A tool that allows for non-constant specification (e.g., includes temperature dependence) will result in improved re-sults

● Additional equation termsAddition of extended or advanced ‘alpha’ functions (intermolecular attraction) to improve fitting of vapor pressure, which can improve the ability of the EOS to handle polar/non-ideal systems Addition of volume translation parameters allow for better prediction of liquid densities for the EOS

● Liquid phase property handlingModification of the handling of the term describing real volume of molecules/intermolecular repulsion al-low for better prediction of liquid densities for the EOS

● Solids handling (e.g., ice, hydrate, solid CO2carbon)

, solid hydro-While EOS are used to represent the fugacity of components in a fluid phase (vapor and liquid), they can be combined with models representing the fugacity

tion titled “Equations of State and the Solid Phase” be-low for more detailed discussion

in the solid phase to model VSE and LSE See the sec-There are a number of multi-parameter equations (i.e., GERG35), that currently exist and are able to model systems to within experimental error However, due to the complexity and computing power required for these, they are not often used in

Other Phase Equilibria Methods

Activity Coefficient Models — Another common method

used for the purpose of phase equilibria and thermodynamic property prediction is the use of Activity Coefficient models The following is a brief summary of the basic capabilities and describes the applicability for some of the more commonly used Activity Coefficient methods

● sentation of highly non-ideal and/or polar systems (i.e., aqueous systems, amines, NH3, caustic, CO2, H2S) and are therefore typically used in the chemicals industry

Activity coefficient models are the best method for repre-● diction of phase equilibria for binary and multicompo-nent mixtures (VLE and LLE), they are not for phase equilibria of pure components However, they do require high quality pure component property predictions (e.g., vapor pressure) Depending on the specific Activity Coef-ficient method, it may not always allow for LLE predic-tion because tuning the models to VLE specific data or LLE specific data may result in drastically different pa-rameters For this reason, VLLE predictions must also be used with caution

While these models are generally only applicable to pre-● Applicable for prediction of thermodynamic properties for the liquid phase only Vapor properties are unreliable and must be calculated using another method; histori-cally this has been done using ideal gas assumptions for the vapor phase, but commonly includes more advanced EOS methods, as described in the ‘Mixed Models’ section below

● Limited to systems within the pressure and temperature ranges of the experimental data it is correlated against.These models are only suitable for low to moderate pressure systems, typical in the chemicals industry, be-cause activity coefficients depend on temperature, but are independent of pressure, while mutual solubilities are in fact dependant on pressure in high pressure LLE systems

At typical operating pressures, the use of a vapor pressure is not appropriate for light gases above the critical point and instead these light gases are treated

as Henry’s components, where Henry’s law coefficients are derived from experimental gas solubility data

Complex Systems to Model —

● Operating conditions that cause divergence from ideal

Absorption (i.e., CO2 and H2S adsorption in physical

or chemical solvents) Overall, it is important to understand the capabilities and limitation of each method of representing phase equilibria and prediction of thermodynamic properties, and each method’s specific applicability to the gas processing industry for proper choice and use However, it should be noted that tuning of a method to quality experimental data in the region of operation

or interest is perhaps more important than the method choice itself, specifically, the choice of mixing rules and quality of bi-nary interaction parameters, which can typically be readily modified in commercial software

ods can be found in Goodwin et al36 and Kontogeorgis and Fo-las.34

More specific information relative to phase equilibria meth-Dew Point Calculation — A thermodynamic dew point is

defined as that point where liquid first appears from the gas phase An EOS model actually calculates this point with ex-actly zero liquid dropout In reality, for natural gas this point cannot directly be measured from experimental methods, but can be estimated from PVT data taken very near the dew point envelope by extrapolating liquid dropout data to 0.0 volume percent liquid

In pipeline operations, one can consider a practical dew point that represents a small volume of liquid condensation which does not impact pipeline performance, usually represent-ing a trace of liquid on the pipe wall This practical dew point is what is actually measured by the Bureau of Mines chilled mir-ror device

In recent work for the GPA by Bullin, et al., (RR-213), the practical dew point was defined as 0.00027 m3 liquid per 1000

m3 gas As a natural gas gets leaner, the difference between the EOS predicted dew point of 0.0 volume percent liquid and the practical dew point of 0.00027 m3 liquid per 1000 m3 gas can increase to a much as 5.6°C The practical dew point can be represented by the temperature in a Bureau of Mines chilled mirror device where droplets begin to form Thus, when EOS models are used, both the thermodynamic dew point of 0.0 vol-ume percent liquid and the practical dew point of 0.00027 m3 liquid per 1000 m3 gas should be considered when adjusting the EOS parameters to match the experimental values, and also to better determine the conditions that impact plant/pipeline per-formance For lean gases where there is more than a 2.2 to 5°C difference in the two values, it may be necessary to only fit to the practical dew point value to evaluate plant/pipeline perfor-mance

This also points to the fact that when fitting an EOS model

to an experimentally obtained dew point value, it should not be assumed that the reported dew point (experimental) represents the thermodynamic dew point of 0.0 volume percent liquid, un-less of course it has been confirmed to be extrapolated from multiple experimental points within the two phase envelope

transfer limited, absorption/desorption systems This combina-tion of system attributes presents challenges for predicting

equilibrium and thermodynamic properties accurately All

thermodynamic phase equilibrium models depend on

(CO2 or H2S, but not both) and unless a modified approach

is used, to primary and secondary amines The model

be found for each by regressing the models to experimental data The primary limitation is not the models themselves, but the highly variable, and sometimes unknown quality of the ex-perimental data Because the experimental data is often the limitation and not the model, this may allow any of the activity coefficient models to be just as reliable as the others for a given application

Sour Water — Stripping H2S, CO2, and ammonia, from sour water is performed in many sour natural gas treating plants Common applications include condensed water (H2S and CO2), sulfur plant tail gas quench tower blowdown (H2S ,CO2, and caustic or ammonia) and to a more limited extent, stripping of sour produced water (brine, including NaCl and many other salts, with H2S, and CO2) Much of the literature describes de-sign and operation of refinery sour water strippers, which handle (H2S CO2, ammonia, cyanides, phenols, and organic acids) Guidelines specific to gas treating are more limited

Sour water serves as a good example of the strong effect of pH

nificant, effect of dissolved salt concentrations on gas solubility

on ionic dissociation, and of the smaller, though sometimes sig-A principal ionization equilibrium for H2tion,

tal H2S is close to 1 for a pH of less than 5, about 0.33 at a pH of 7.0, and less than 0.01 at a pH of 9.043 Since the vapor pressure

is greatly affected by pH The un-dissociated fraction of the to-of H2ping tower has a great effect on the stripping efficiency As H2S gas is stripped from solution, the dissociated ions re-combine to provide more un-dissociated H2S —which revives the partial pressure above the solution It should be noted that the pH of the solution changes as CO2, is stripped from the water In some services, with H2S, CO2, NH3, and low salts, the pH must be controlled to (typically to 7-8) to insure that both components can be stripped Stripping is, of course, enhanced by higher temperatures

S is produced by its un-dissociated fraction, pH in a strip-mon in produced waters, reduces the solubility of H2S and thus enhances stripping — but this is a smaller influence than tem-perature, and much smaller than pH The pH of produced water

Salt concentration of tens of thousands of ppm, as is com-is typically above neutral to start, even with the dissolved salts, because of the natural buffers in the water The pH is further elevated, as the CO2 is stripped from the brine, sometimes re-sulting in fouling of the mass transfer medium within the strip-per Therefore, acid is sometimes added in front of the stripper

to lower the pH and prevent fouling

A common method to calculate equilibrium of sour water systems is the Wilson-API-Sour method, and variants, which use a modification of Van Krevelen’s approach to account for the ionization of H2S, CO2 and NH3 in the aqueous water phase (See API Publication 95544

and GPA RR-5245

) This type of mod-el is valid up to about 50 psig, with limited other ionic (salt) species present To extend the range of the sour equilibrium prediction, mixed models using a combination of the API-Sour model, and an EOS (e.g., Peng Robinson) have been developed Alternate approaches which account for the influence of other ionic salts present in the solution are electrolytic and mixed electrolytic/EOS models

1, single component 3, V, L, and S 0 Unique “Triple Point”

2, two components 3, V, L, and S 1 Triple point locus line

3, three components 3, V, L, and S 2 No locus line; much

In the above diagram, the continuous line marked with tri-H2S) in detail

The other two lines coming in from top right are lines for isenthalpic blowdowns The dotted line marked with X’s is the result of a simulation without the benefit of any program exten-sion to allow solids prediction (see later discussion of such ex-tensions) This simulation predicted the blowdown would inter-cept the triple point locus but then go straight through (since the simulator had no knowledge of the locus) into a region to the left, which is thermodynamically impossible Thus, the simula-tor predicted (a) no solids and (b) falsely low temperatures Knowledge of the triple point locus allows a simple manual cor-rection to the simulated path, by forcing the blowdown to follow the triple point locus – as it must, so long as the three phases co-exist

The dashed line marked with circles shows a second, and smaller, correction that is discussed by Walter et al48 and mer-its only brief mention here; very accurate vapor-liquid equilib-rium data allowed a manual correction of the simulator’s isen-thalpic predictions, by adjustment of the vapor/liquid percentages along the path ahead of the interception of the tri-ple point locus line

cus line, precipitation of solid CO2 progressively enriches the L/V two-phase mixture with H2S It is not intuitively obvious that a single triple point locus line correctly shows all such P/T pairs on the graph, regardless of the starting mixture composi-tion, but that is the case For clarification of this point, refer to Sobocinski and Kurata25

As pressure reduction and cooling takes place along the lo-This method of using the triple point locus line to check on a process simulation could be applied to a few other industrially-important two-component systems, e.g., methane/CO2, and methane/benzene However, any significant presence of a third component negates the use of this tool, as discussed next

Multi-Component (3 or More) Triple Points

Once a third component is added in significant quantity, the

number of degrees of freedom increases to 2 or more That

means there are no locus lines that can be drawn on a P-T

engineer whether they are within solids forming conditions

Such predictions are usually reported by indicating at what

5 perature Data from Rice University for Vapor-Liquid and P-V-T Behavior,” April (1974)

Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- 6 Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- Adler, Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- S Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- B., Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- Ozkardesh, Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- H., Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- Schreiner, Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- W Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- C., Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- Hydrocarbon Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem- Proc., Chappelear, Patsy, GPA Technical Publication TP-4, “Low Tem-

47 (4) 145 (1968)

7 Chao, K C., Seader, J D., AIChEJ, 7, 598 (1961)

8 Barner, H E., Schreiner, W C., Hydrocarbon Proc., 45 (6) 161 (1966)

9 lecular Shape Factors in Vapor-Liquid Equilibrium Calculations with the Corresponding States Principle,” AIChEJ 14, 568-576 (1968)

Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- 10 Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- Leland, Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- T Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- W., Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- Jr., Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- and Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- Chappelear, Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- P Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- S., Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- “The Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- Corresponding Leach, J W., Chappelear, P S., and Leland, T W., “Use of Mo- States Principle — A Review of Current Theory and Practice,” Ind Eng Chem 60, 15-43 (July 1968); K C Chao (Chairman),

“Applied Thermodynamics,” ACS Publications, Washington, D.C., 1968, p 83

11 Barner, H E., Pigford, R L., Schreiner, W C., Proc Am Pet Inst (Div Ref.) 46 244 (1966)

12 Lenoir, J M., Koppany, C R., Hydrocarbon Proc 46, 249 (1967)

13 Kwong equation of state,” Chem Eng Sci 27, 1197-1203 (1972)

Soave, Giorgio, “Equilibrium constants from a modified Redlich- 14 Soave, Giorgio, “Equilibrium constants from a modified Redlich- Soave, Giorgio, “Equilibrium constants from a modified Redlich- Peng, Soave, Giorgio, “Equilibrium constants from a modified Redlich- D Soave, Giorgio, “Equilibrium constants from a modified Redlich- Y., Soave, Giorgio, “Equilibrium constants from a modified Redlich- Robinson, Soave, Giorgio, “Equilibrium constants from a modified Redlich- D Soave, Giorgio, “Equilibrium constants from a modified Redlich- B., Soave, Giorgio, “Equilibrium constants from a modified Redlich- Ind Soave, Giorgio, “Equilibrium constants from a modified Redlich- Eng Soave, Giorgio, “Equilibrium constants from a modified Redlich- Chem Soave, Giorgio, “Equilibrium constants from a modified Redlich- Fundamentals Soave, Giorgio, “Equilibrium constants from a modified Redlich- 15 Soave, Giorgio, “Equilibrium constants from a modified Redlich- (1976)

15 Spear, R R., Robinson, R L., Chao, K C., IEC Fund., 8 (1) 2 (1969)

16 Pressure Vapor-Liquid Equilibrium, Prentice-Hall (1968)

Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- 22 Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- Hwang, Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- S Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- C., Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- Lin, Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- H Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- M., Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- Chappelear, Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- P Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- S., Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- and Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- Kobayashi, Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro- R., Holmes, A S., Ryan, J M., Price, B C., and Stying, R E., Pro-

“Dew Point Values for the Methane Carbon Dioxide System,” G.P.A Research Report RR-21 (1976)

23 Price, B C., “Looking at CO2 recovery,” Oil & Gas J., p 48-53 (Dec 24, 1984)

24 Nagahana, K., Kobishi, H., Hoshino, D., and Hirata, M., “Binary Vapor-Liquid Equilibria of Carbon Dioxide-Light Hydrocarbons

at Low Temperature,” J Chem Eng Japan 7, No 5, p 323 (1974)

25 Sobocinski, D P., Kurata, F., “Heterogeneous Phase Equilibria of the Hydrogen Sulfide-Carbon Dioxide System,” AIChEJ 5, No 4,

p 545 (1959)

26 Ryan, J M and Holmes, A S., “Distillation Separation of Carbon Dioxide from Hydrogen Sulfide,” U.S Patent No 4,383,841 (1983)

27 Denton, R D., Rule, D D., “Combined Cryogenic Processing of Natural Gas,” Energy Prog 5, 40-44 (1985)

28 Redlich, O., Kwong, J N S., Chem Rev 44, 233 (1949)

Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- 44 Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- API Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- Publication Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- 955, Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- “A Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- New Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- Correlation Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- of Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- NH3, Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- CO2, Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- and Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- H2S Betz Handbook of Industrial Water Conditioning, Inc Betz Labo- Volatility Data from Aqueous Sour Water Systems,” (1978).

45 Owens, J L., Cunningham, J R., Wilson, G M., “Vapor-Liquid Equilibria for Sour Water Systems with Inert Gases Present,” GPA RR-52 (1982)

46 ping”, Brimstone Sulfur Symposia, Vail, CO, September 2008

Stevens, D K., Mosher, A., “Fundamentals of Sour Water Strip- 47 Stevens, D K., Mosher, A., “Fundamentals of Sour Water Strip- Stevens, D K., Mosher, A., “Fundamentals of Sour Water Strip- Beychok Stevens, D K., Mosher, A., “Fundamentals of Sour Water Strip- M., Stevens, D K., Mosher, A., “Fundamentals of Sour Water Strip- “Aqueous Stevens, D K., Mosher, A., “Fundamentals of Sour Water Strip- Wastes Stevens, D K., Mosher, A., “Fundamentals of Sour Water Strip- from Stevens, D K., Mosher, A., “Fundamentals of Sour Water Strip- Petroleum Stevens, D K., Mosher, A., “Fundamentals of Sour Water Strip- and Stevens, D K., Mosher, A., “Fundamentals of Sour Water Strip- chemical Plants”, John Wiley and Sons, New York and London (1967)

Petro- 48.Petro- Petro- Walter,Petro- F.Petro- B.,Petro- Miller,Petro- T.Petro- Anderson,Petro- S.,Petro- “PredictionPetro- ofPetro- LiquidsPetro- andPetro- Solids Formation for High Pressure Acid Gas Blowdown,” 90th Annual GPA Convention (2010)

Additional References

search Reports (RR) Note that RR-64, RR-77, and RR-84 provide exten-sive evaluated references for binary, ternary, and multicomponent sys-tems Also as a part of GPA/GPSA Project 806, a computer data bank is available through the GPA Tulsa office

See listing in Section 1 for GPA Technical Publications (TP) and Re-Extensive tabulation of references only is available from Elsevier Publishers of Amsterdam for the work of E Hala and I Wichterle of the Institute of Chemical Process Fundamentals, Czechoslovak Academy of Sciences, Prague-Suchdol, Czechoslovakia

Hiza, M J., Kidnay, A J., and Miller, R C., Equilibrium Properties

of Fluid Mixtures Volumes I and II, IFI/Plenum, New York, 1975 See Fluid Phase Equilibria for various symposia

K-DATA CHARTS FOLLOW

AS LISTED BELOW

Methane-Ethane BinaryNitrogen Pk 2000 psia (13 800 kPa)Methane through Decane Pk 3000 psia (20 700 kPa)Hydrogen Sulfide Pk 3000 psia (20 700 kPa)

FIG 25-8 Critical Locus as Developed for Convergence Pressure (Formerly used for Convergence Pressure for Hydrocarbons)

25-15