- Thermodynamic Methods PROIII offers numerous methods for calculating thermodynamic properties such as K-values, enthalpies, entropies, densities, gas and solid solubilities in liquids, and vapor fugacities. These methods include: = Generalized correlations, such as the Chao-Seader K-value method, and the API liquid density method,

Equations of state, such as the Soave-Redlich-Kwong method for calculating K-values, enthalpies, entropies, and densities, m Liquid activity coefficient methods, such as the Non-Random Iwo-liquid (NRTL) method for calculating K-values, = Vapor fugacity methods, such as the Hayden-O'Connell Method for dimerizing species, = Special methods for calculating the properties of specific systems of components such as alcohols, amines, glycols, and sour water systems. This section, 1.2, Thermodynamic Methods, contains the following subsections:

Basic Principles Application Guidelines Generalized Correlation Methods Equations of State Free Water Decant Liquid Activitv Coefficient Methods Vapor Phase Fuqacities Special Packaqes Electrolvte Mathematical Model Electrolvte Thermodynamic Equations Solid-Liquid Equilibria - -

Transport properties

Also See: TABLE OF CONTENTS

Related Topics

Thermodynamic Main Window

- Phase Equilibria

When two or more phases are brought into contact, material is transferred from one to another until the phases reach equilibrium, and the compositions in each phase become constant. At equilibrium for a multicomponent system, the temperature, pressure, and chemical potential of component i is the same in every phase, i.e.:

where: T = system temperature P = system pressure p = the chemical potential a, p, ..., .rr represent the phases

The fugacity of a substance is then defined as:

where: fi = fugacity of component i D

fi = standard state fugacity of component i at T, P 0

= standard state chemical potential of component i at T, P It follows from (3) and (4) that the fugacities in each phase must also be equal:

The fugacity of a substance can be visualized as a "corrected partial pressure" such that the fugacity of a component in an ideal-gas mixture is equal to the component partial pressure. For vapor-liquid equilibrium calculations, the ratio of the mole fraction of a component in the vapor phase to that in the liquid phase is defined as the K-value:

where: = K-value, or equilibrium ratio

Yi = mole fraction in the vapor phase

Xi = mole fraction in the liquid phase For liquid-liquid equilibria, a corresponding equilibrium ratio or distribution coefficient is defined:

I. I.. &.EX j / x j

where:

P$ = liquid-liquid distribution coefficient I, II represent the two liquid phases

F The vapor-phase fugacity coefficient of a component, $' i is defined as the ratio of its fugacity to its partial pressure, i.e.:

where: V (9 = vapor-phase fugacity coefficient of component i

If a liquid activity coefficient method is used in the liquid phase calculation, then the activity coefficient of the liquid phase can be related to the liquid fugacity by the following relationship:

where:

k = liquid-phase activity coefficient [IL

fi = standard state fugacity of pure liquid i With this definition of liquid fugacity, yiL+ 1 as xi + 1. The standard state fugacity is as follows:

where:

Pi xd = saturated vapor pressure of component i at T R = gas constant

4 = liquid molar volume of component i at T and P 'i = fugacity coefficient of pure component i at T and Pisat

Equation (10) provides two correction factors for the pure liquid fugacity. The fugacity coefficient, ' y , corrects for deviations of the saturated vapor from ideal-gas behavior. The exponential correction factor, known as the Poynting correction factor, corrects for the effect of pressure on the liquid fugacity. The Poynting correction factor is usually negligible for low and moderate pressures. Combining equations (6), (9, and (9) yields:

Combining equations (7) and (9) yields:

If an equation of state is applied to both vapor and liquid phases, the vapor-liquid K-values can be written as:

The liquid-liquid equilibria can be written as:

Equations (1 I ) , (12), (13), and (14) are used to calculate the distribution of components between phases. For vapor-liquid equilibria, equation-of-state methods may be used to calculate the fugacity coefficients for both liquid and vapor phases using equation (13). One important limitation of equation-of-state methods is that they have to be applicable over a wide range of densities, from near-zero density for gases to high liquid densities, using constants obtained from pure-component data. Equations of state are not very accurate for nonideal systems unless combined with component mixing rules and alpha formulations (see Section 1.2.4, Equations of State) appropriate for those components.

Equation (1 1) may be solved by using equation-of-state methods to calculate vapor fugacities

combined with liquid activity methods to compute liquid activity coefficients (see Section 1.2.6, Liquid Activity Methods). Liquid activity methods are most often used to describe the behavior of strongly nonideal mixtures.

References 1. Prausnitz, J. M., Lichtenthaler, R. N., and Gomes de Azevedo, E., 1986, Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd Ed., Prentice-Hall, N.Y.

2. Sandier, S. I., 1989, Chemical and Engineering Thermodynamics, 2nd ed., John Wiley & Sons, New York.

3. Smith, J. M. and Van Ness, H. C., 1987, Introduction to Chemical Engineering Thermodynamics, 4th ed., McGraw-Hill, New York.

4. Van Ness, H. C. and Abbott, M. M., 1982, Classical Thermodynamics of Nonelectrolyte Solutions: With Applications to Phase Equilibria, McGraw-Hill, New York.

Also See: Basic Principles

Enthalpy

The enthalpy of a system, H, is defined in terms of the energy of the system, U as follows:

where: H = enthalpy of the system of nT moles U = internal energy of the system of nT moles V = total volume of the system

At constant temperature and pressure, the internal energy of the system is related to the volume by:

The enthalpy of the system is then given by:

where:

H* = mixture ideal gas enthalpy = zi ?lhp

4' = molar enthalpy of ideal gas i at temperature T z = compressibility factor = PVInTRT

PROIII provides two distinct approaches to the calculation of enthalpy. For the majority of thermodynamic systems of methods, enthalpy is calculated as a departure from the ideal-gas enthalpy of the mixture. Enthalpy departure functions for both vapor and liquid phases are calculated by an equation of state or corresponding states model. For liquid activity coefficient thermodynamic systems, however, PROIII, by default, invokes the LIBRARY thermodynamic method for vapor and liquid enthalpy calculations. The LIBRARY method consists of two correlations. The first correlates saturated-liquid enthalpy as a function of temperature and the second correlates latent heat of vaporization, also as a function of temperature. At temperatures below the critical, vapor enthalpy is calculated by adding the latent heat to the saturated liquid enthalpy at the system temperature. In other words, the vapor enthalpy is the saturated vapor enthalpy at the system temperature. For both phases, the pressure is implicitly the saturated vapor pressure at the system temperature. No other pressure correction term is applied. For almost all library components, the correlations in use for liquid enthalpy can be used safely up to a reduced temperature, Tnc, of approximately 0.9. Tc is the temperature at the critical point, beyond which vapor and liquid become indistinguishable. Note: The normal boiling point of a library component typically occurs when Tr is approximately

equal to 0.7 In general, the use of liquid activity coefficient models is not recommended for system pressures above 1000 kPA. Below these conditions, the use of LIBRARY enthalpy methods will not introduce significant errors provided that the system temperature is below the critical temperatures of all components present in significant quantities. Quite often, however, we would like to use a liquid activity coefficient model when permanent gases are present in the mixture. As the system temperature is usually above the critical temperature of these gases, there is no standard-state liquid fugacity at system conditions, so we replace that term by the Henry's Law constant. However, the problem of adding the supercritical components' contribution to the liquid enthalpies remains. For the liquid phase contribution, PROIII extrapolates the component's saturated liquid enthalpy curve linearly from the critical temperature. Above the critical this extrapolation uses the slope of the library enthalpy tangent to the liquid saturation curve at the normal boiling point. At temperatures above the critical, there is no distinction between vapor and liquid phases and the vapor enthalpy is set equal to the extrapolated liquid enthalpy. The point at which the slope for linear extrapolation is obtained is chosen quite arbitrarily; as mentioned, we use the normal boiling point temperature. Note: At temperatures near Tc, the enthalpy of the saturated vapor for a pure component exhibits a decrease with temperature. This can lead to the computation of a negative value of the constant-pressure heat capacity Cp when using the LIBRARY method for vapor enthalpies. This is entirely an artifact of the fact that the saturation curve is not a constant-pressure path. The printout of a negative heat capacity is therefore a sign that the temperature is too high to be using LIBRARY vapor enthalpies, and the user should switch to another method. For low pressure and temperatures well below the lowest critical, LIBRARY enthalpies are often satisfactory. For high pressures or temperatures above the critical of a component, it will usually be better to use an equation of state for vapor and, possibly, liquid enthalpies. Beware, however, if a liquid activity coefficient method was selected for K-value; in such systems the traditional cubic equation of state may not be capable of describing the liquid phase nonideality, and it is therefore unlikely that the equation of state will predict the correct liquid phase enthalpy. In this situation, one of the more advanced cubic equations using an alpha formulation, which correctly predicts pure component vapor pressures, is a better choice. As the contribution to the liquid enthalpy of dissolved supercritical components is usually small, the LIBRARY method can usually safely be used for liquid enthalpies. Ideal-gas based enthalpies and saturation enthalpies can be used in combination for vapor and liquid, respectively, for defined components because the ideal-gas enthalpy datum has been fixed relative to the saturated-liquid enthalpy datum (HL = 0 at T = 273.1 5 K). For components that are sub-critical at 273.15 K, the SRK vapor enthalpy departure function, which applied to the ideal gas enthalpy, gives the equivalent results as adding the latent heat to zero-liquid enthalpy. For components that are supercritical at 273.15 K, using an alpha formulation will give consistent results between departure-based and library enthalpies.

Also See: Basic Principles

General Information

Choosing an appropriate thermodynamic method for a specific application is an important step in obtaining an accurate process simulation. Normally, there may be any number of thermodynamic methods suitable for a given application. The user is left to use his or her best judgement, experience, and knowledge of the available thermodynamic methods to choose the best method. It is important to note that for most thermodynamic methods, the PRO111 databanks contain adjustable binary parameters obtained from fitting published experimental and/or plant data. The thermodynamic method chosen should ideally be used only in the temperature and pressure ranges at which the parameters were regressed. Ideally, for each simulation, actual experimental or plant data should be regressed in order to obtain the best interaction parameters for the application. There are several places where the user can find information and guidelines on using the thermodynamic methods available in PROIII. These are: = PROAI Casebooks LJ PRO/// Application Briefs Manual

These show how PROIII is used to simulate many refinery, chemical, and petrochemical processing applications using the thermodynamic methods appropriate to each system.

Also See: Application Guidelines

General Information

Hydrocarbon streams may be defined in terms of laboratory assay data. Typically, such an assay would consist of distillation data (TBP, ASTM D86, ASTM D l 160, or ASTM D2887), gravity data (an average gravity and possibly a gravity curve), and perhaps data for molecular weight, lightends components, and special refining properties such as pour point and sulfur content. This information is used by PROIII to produce one or more sets of discrete pseudocomponents which are then used to represent the composition of each assay stream.The process by which assay data are converted to pseudocomponents can be analyzed in terms of several distinct steps. Before each of these is examined in detail, it will be useful to list briefly each step of the process in order:

The user defines one or more sets of TBP cutpoints (or accepts the default set of cutpoints that PROIII provides). These cutpoints define the (atmospheric) boiling ranges that will ultimately correspond to each pseudocomponent. Multiple cutpoint sets (also known as blends) may also be defined to better model different sections of a process. = Each set of user-supplied distillation data is converted to a TBP (True.Boilina Point) % basis at one atmosphere (760 mm Hg) pressure. = The resulting TBP data are fitted to a continuous curve and then the program 'E' each curve to determine what percentage of each assay goes into each -

pseudocomponent as defined by the appropriate cutpoint set. Gravity and molecular weight data are similarly processed so that each cut has a normal boiling point, specific gravity, and molecular weight. During this step, the lowest-boiling cuts may be eliminated or modified to account for any lightends components input by the user.

Within each cutpoint set, all assay streams using that set (unless they are explicitly excluded from the blending -this is described later) are combined to get an average normal boiling point, gravity, and molecular weight for each of the pseudocomponents generated from that cutpoint set. These properties are then used to generate all other properties (critical properties, enthalpy data, etc.) for that pseudocomponent. Note: Special refinery properties such as cloud point and sulfur content may also be defined within assays. The distribution of these properties into pseudocomponents and their subsequent processing by the simulator is outside the scope of this chapter but will be covered in a later document.

Also See: Assav Processing

- Cutpoint Sets (Blends)

Defining Cutpoints

In any simulation, there is always a "primary" cutpoint set, which defaults as shown in Table 1.1.3-1.

Table 1 . I .3-1: Primary TBP Cutpoint Set Number of Width per

TBP Range, F Components cut, F

The primary cutpoints shown in Table 1 .I .3-1 may be overridden by supplying a new set for which no name is assigned. In addition, "secondary" sets of cutpoints may be supplied by supplying a set and giving it a name. The blend with no name (primary cutpoint set) always exists (even if only named blends are specifically given); there is no limit to the number of named blends (secondary cutpoint sets) that may be defined. The user may designate one cutpoint set as the "default"; if no default is explicitly specified, the primary cutpoint set will be the default. Each cutpoint set (if it is actually used by one or more streams) will produce its own set of pseudocomponents for use in the flowsheet.

Association of Streams With Blends Each assay stream is associated with a particular blend. By default, an assay stream is assigned to the default cutpoint set. A stream may be associated with a specific secondary cutpoint set by explicitly specifying the name of that cutpoint set (blend) in association with the stream. If the assay stream is associated with a blend name not given for any cutpoint set previously defined, a new blend with that name is created using the same cutpoints as the primary cutpoint set. The user may also specify that a stream use a certain set of cutpoints but not contribute to the blended properties of the pseudocomponents generated from that set (this might be appropriate if an estimate were being supplied for a recycle stream, for example). This is done by selecting the XBLEND option, which excludes the stream in question from the blending. The default is for the stream to be included in the blending for the purposes of pseudocomponent property generation; this is called the BLEND option. It is not allowed for the XBLEND option to be used on all streams associated with a blend, since at least one stream must be blended in to define the pseudocomponent properties. The blending logic is best illustrated by an example: Suppose that two secondary cutpoint sets A1 and A2 were defined, and that A1 was designated as the default. This means that three sets actually exist, since the primary cutpoint set supplied by PROIII still exists (though it is no longer the set with which streams will be associated by default). Now, suppose the following streams (where extraneous information like the initial conditions is not shown) are given:

Table 1 . I .3-2: Blending Example Stream Blend Option Blend Name

S1 none given none given (defaulted to BLEND) (defaulted to A l )

XBLEND none given (defaulted to A l )

S3 XBLEND A1

S4 BLEND A2 55 BLEND B1

XBLEND

BLEND

Streams S1 and S2 will use the pseudocomponents defined by secondary cutpoint set A l , since it is the default. S3 will also use Al 's pseudocomponents since it is specified directly. The pseudocomponents in blend A1 will have properties determined only by the cuts from stream S1, since the XBLEND option was used for S2 and S3. Stream S4 will use the pseudocomponents defined by cutpoint set A2. Streams S5 and S6 will go into a new blend B1 which will use the cutpoints of the primary cutpoint set. Since XBLEND is used for stream S6, only stream S5's cuts will be used to determine the properties of the pseudocomponents in blend B1. Finally, stream S7 will use another new blend, B2, also with the cutpoints from the primary cutpoint set. Since it is a different blend, however, the pseudocomponents from blend B2 will be completely distinct (even though they will use the same cutpoint ranges) from those of blend B1.

Application Considerations The selection of cutpoints is an important consideration in the simulation of hydrocarbon processing systems. Too few cuts can result in poor representation of yields and stream properties when distillation operations are simulated; moreover, desired separations may not be possible because of component distributions. On the other hand, the indiscriminate use of cuts not needed for a simulation serves only to increase the CPU time unnecessarily. It is wise to examine the cut definition for each problem in light of simulation goals and requirements. The default primary cutpoint set in PROlll represents, in our experience, a good selection for a wide rarrge of refinery applications. In some circumstances, it may be desirable to use more than one cutpoint set in a given problem. This "multiple blends" functionality is useful when different portions of a flowsheet are best represented by different TBP cuts; for example, one part of the process may have streams that are much heavier than another and for which more cutpoints at higher temperatures would be desirable. It is also useful when hydrocarbon feeds to a flowsheet differ in character; for example, different blends might be used to represent an aromatic stream (producing pseudocomponents with properties characteristic of aromatics) and a paraffinic stream feeding into the same flowsheet. The extra detail and accuracy possible with this feature must be balanced against the increase in CPU time caused by the increased number of pseudocomponents.

-

Also See: Assav Processing

5

- Interconversion of Distillation Curves

Types of Distillation Curves Assays of hydrocarbon streams are represented by distillation curves. A distillation curve represents the amount of a fluid sample that is vaporized as the temperature of the sample is raised. The temperature where the first vaporization takes place is referred to as the initial point (IP), and the temperature at which the last liquid vaporizes is called the end point (EP). Each data point represents a cumulative portion (usually represented as volume percent) of the sample vaporized when a certain temperature is reached.Estimation of thermophysical properties for the pseudocomponents requires (among other things) a distillation curve that represents the true boiling point (TBP) of each cut in the distillation. However, rigorous TBP distillations are difficult and not well standardized so it is common to perform some other well-defined distillation procedure; standard methods are defined by the American Society for Testing and Materials (ASTM). The ASTM procedures most commonly used for hydrocarbons are D86, D l 160, and D2887. ASTM D86 distillation is typically used for light and medium petroleum products and is carried out at atmospheric pressure. D l 160 distillation is used for heavier petroleum products and is often carried out under vacuum, sometimes at absolute pressures as low as 1 mm Hg. The D2887 method uses gas chromatography to produce a simulated distillation curve; it is applicable to a wide range of petroleum systems. D2887 results are always reported by weight percent; other distillations are almost always reported on a volume percent basis. More details on these distillation procedures may be found in the API Technical Data Book; complete specifications are given in volume 5 (Petroleum Products and Lubricants) of the Annual Book of ASTM Standards.

Conversion of Dl160 Curves PROIII converts D l 160 curves to TBP curves at 760 mm Hg using the three-step procedure recommended in the API Technical Data Book: LJ Convert to D l 160 at 10 mm Hg using API procedure 3A4.1 (which in turn references procedure 5A1.13). This procedure is expressed as a way to estimate a vapor pressure at any temperature given the normal boiling point, but the same equations may be solved to yield a normal boiling temperature given the boiling temperature at another pressure. The equations used are as follows:

3000,538X- 6.76 156 (1) loglOP* = for X> 0.0 0 22 (P* < 2 mm Hg) 43X- 0,987672

(2S 3% 760 mm Hg)

2770m085X-6'412631 forX< 0,0013 (P* >760mmHg) (3) logloP* = 3 U - 0,989679

where: P* = vapor pressure in mm Hg at temperature T (in degrees Rankine)

The parameter X is defined by:

where: Tb = boiling point (in degrees Rankine) at a pressure of 760 mm Hg

For conversions where neither pressure is 760 mm Hg, the conversion may be made by applying the above equations twice in succession, using 760 mm Hg as an intermediate point:

= Convert to TBP at 10 mm Hg using API Figure 3A2.1 (which has been converted to equation form by SimSci).

Convert to TBP at 760 mm Hg using API procedure 3A4.1.

Conversion of D2887 Curves PROIII converts D2887 simulated distillation data to TBP curves at 760 mm Hg using the two-step procedure recommended in the API Technical Data Book: = Convert to D86 at 760 mm Hg using API procedure 3A3.1. This procedure converts D2887 Simulated Distillation (SD) points (in weight percent) to D86 points (in volume percent) using the following equation:

where:

D86 and SD = the ASTM D86 and ASTM D2887 temperatures in degrees Rankine at each volume percent (for D86) and the corresponding weight percent (for SD), and a, b, and c are constants varying with percent distilled according to Table 1 . I .3-3.

Table 1.1.3-3: Values of Constants a, b, c Percent Distilled

0

10

30

50

70

90

95

The parameter F in equation (5) is calculated by the following equation:

where: SD10% and SD50% = D2887 temperatures in degrees Rankine at the 10% and 50% points, respectively

= Convert to TBP at 760 mm Hg using API procedure 3A1 . I , which is described in the section Conversion of D86 Curves with New (1987) API Method below.

Conversion of D86 Curves PROIII has three options for the conversion of D86 curves to TBP curves at 760 mm Hg. These are the currently recommended (1987) API method, the older (1963) API method, and the Edmister-Okamoto correlation, In addition, a correction for cracking may be applied to D86 data; this correction was recommended bv the API for use with their older conversion ~rocedure. but is

- not recommenaed tor use with the current (1987) method. he conversion of D86 curves takes place in the following steps: = If a cracking correction is desired, correct the temperatures above 475 F as

follows:

where:

Gh = the corrected and observed temperatures, respectively, in degrees Fahrenheit. 'If necessary, convert the D86 curve at pressure P to D86 at 760 mm Hg with the standard ASTM correction factor:

where: TP = D86 temperature in Fahrenheit at pressure P T760 = D86 temperature in Fahrenheit at 760 mm Hg

= Convert from D86 at 760 mm Hg to TBP at 760 mm Hg using one of the three procedures below.

a) Conversion of D86 Curves with New (1987) API Method By default, PROIII converts ASTM D86 distillation curves to TBP curves at 760 mm Hg using procedure 3A1 .I (developed by Riazi and Daubert in 1986) recommended in the 5th edition of the API Technical Data Book. The equation for this procedure is as follows:

where a and b are constants varying with percent of liquid sample distilled as given in Table 1 .I .3-4:

Table 1 .I .3-4: Values of Constants a, b Percent Distilled a b

0 0.9167 1.001 9

10 0.5277 1.0900

30 0.7429 1.0425

b) Conversion of D86 Curves with Old (1963) API Method This method, while no longer the default, is still available for users whose flowsheets may be tuned to the results using the old method. This method was recommended (and shown in graphical form) in older editions of the API Technical Data Book. The graphical correlation has been converted to equation form by SimSci.

C) Conversion of D86 Curves with Edmister-Okamoto Method Edmister and Okamoto (1969) developed a method which is still widely used for converting ASTM D86 curves to TBP curves. If the Edmister-Okamoto method is specified as the conversion method, their procedure (converted from the original graphical form to equations by SimSci) is used for conversion of D86 to TBP curves.

Also See: Assav Processinq

- Cutting TBP Curves

Fitting of Distillation Curves

Before a curve is cut into pseudocomponents, the distillation data must be fitted to a continuous curve. This is necessary because the supplied data points will not in general correspond to the desired cutpoints. PROIII offers three methods for fitting distillation curves.

The default is the cubic spline method (known as the SPLINE option). A cubic spline function is used to fit all given volume percents between the first and last points. Beyond those bounds, points 1 and 2 and points N and N-I are used to define a normal distribution function to extrapolate to the 0.01 % and 99.99% points, respectively. If only two points are supplied, the entire curve is defined by the distribution function fit. This extrapolation feature is particularly valuable when extrapolating heavy ends distillations which often terminate well below 50 volume percent. This method in general results in an excellent curve fit. The only exception is when the distillation data contain a significant stepunction (such a step is often the unphysical result of an error in obtaining or reporting the data); in that case, the step creates an instability that tends to propagate throughout the entire length of the curve. Should this happen, the input data should be checked for validity.

The quadratic fit method (known as the QUADRATIC option) provides a successive quadratic approximation to the shape of the input assay curve. This method is recommended in the rare case (see above) where a cubic spline fit is unstable.

The Probability Density Function (PDF) method (known as the PDF option) is different in that it does not necessarily pass through all the points input by the user. Instead, it fits a probability density function to all points supplied. The resulting curve will maintain the probability-curve shape characteristic of petroleum distillations, while minimizing the sum of the squares of the differences between the curve and the input data. If desired, the curve may be constrained to pass through either or both of the initial point and end point. The PDF method is recommended whenever it is suspected that the distillation data are "noisy," containing significant random errors.

It is worth noting that the choice of curve-fitting procedure will also have a slight impact on the distillation interconversions described in the previous section. That is because most of the conversion procedures work by doing the conversion at a fixed set of volume percents, which must be obtained by interpolation and sometimes extrapolation, using some curve-fitting procedure.

Division into Pseudocomponents Once a smooth distillation curve is obtained, the volume percent distilled at* each cutpoint is determined, The differences between values at adjacent --

cutpoints define the percent of the stream's volume that is assigned to the pseudocomponent defined by the interval between two adiacent c u t p o w o r example, using the default set of cutpoints shown in Table 1 .I .3-1, the first pseudocomponent would contain all material boilirlg between 100 F and 125 F, the second would contain the material boiling between 125 F and 150 F,

and so forth. Material boiling above the last cutpoint (,I 600 F) would be combined with the last (1 500-1 600) cut, while (with the exception of lightends as discussed below) material boiling below 100 F would be combined with the first cut. If the distillation data do not extend into all of the cut ranges (in this example, if the initial point were higher than 125 F or if the end point were lower than 1500 F), the unused cuts are omitted from the simulation,

The normal boilirrg point (NBP) of each cut is determined as a volume-fraction . b y average (or, in rare cases where TBP, D86, or D l 160 distillations are entered

\ on a welght bass, as a weight-fraction average) by integrating across the cut range. For small cut ranges, this will closely approach other types of average boiling points. These averaQe boiling points are used (possibly after blending with cuts from other assav streams in the flowsheet) as correlating parameters

-when calculating other thermophysical properties for each pseudocomponent.

These procedures are demonstrated in Figure 1 .I .3-1 for a fictitious assay with an IP of 90 F being cut according to the default cutpoint set (Table 1 . I .3-1); for simplicity only the first ten percent of the curve is shown. In addition to its range, the first cut picks up the portion boiling below 100 F, and its average boiling point (about 110 F in this case) is determined by integrating the curve from the IP to the 125 F point. The second cut is assigned the material boiling from 125 F to 150 F, which is integrated to get a NBP of approxirnateljl 138 F. The third and subsequent cuts are generated in a similar manner.

FIGURE 1.1.3-1: CUTTING TBP CURVES

Volume % Dlstllled

Gravity Data /

PROIII requires the user to enter an average gravity (either as a Specific Gravity, API Gravity, or Watson K-factor) for each assay. If a Watson K is given, it is converted to a gravity using the TBP data for the curve. Entry of a gravity curve is recommended but not required.

If a user-supplied gravity curve does not extend to the 95% point, quadratic extrapolation is used to generate an estimate for the gravity at the 100% point. A gravity for each cut is determined at its mid-point, and an average gravity for the stream is computed. If this average does not agree with the specified average, the program will either normalize the gravity curve (if data are given up to 95%) or adjust the estimated 100% point gravity value to force agreement. Since the latter could in some cases result in unreasonable gravity values for the last few cuts, the user should consider providing an estimate of the 100h point gravity value and letting the program normalize the curve, particularly when gravity data are available to 80% or beyond.

If no gravity curve is given, the pragram will qenerate one from the specified average gravity. The default method for doing this is referred to as the WATSONK method. For a pure component, the Watson K-factor is defined by the following equation:

where: NBP = normal boiling point in degrees Rankine SG = specific gravity at 60 F relative to H20 at 60 F

For a mixture (such as a petroleum cut), the NBP is traditionally replaced by a more complicated quantitv called the mean average boiling point (MeABP). For this purpose, however, it is sufficient to simply use the volume-averaged boiling point computed from the distillation curve. The aravitv curve is , generatedby assuming a constant value of the Watson K, applying equation (1 0) to each cut to get a gravity, averaging these values, and then adjusting the assumed value of the Watson K until the resultina average gravity agrees with the average gravity input by the user.

Another method (known as the PRE301 option) is available primarily for compatibility,with older versions. It is similar to the preferred method described above, except that the average Watson K is estimated from the 10, 30, 50, 70, and 90 percent points on a D86 curve (which can be obtained from the TBP curve by reversing one of the procedures in the previous section) and then applied to the NBP of each TBP cut to generate a gravity curve. This curve is then normalized to produce the specified average gravity.

The'preferred method (constant Watson K applied to TBP curve) is justified by the observation that, for many petroleum crude streams, the Watson K of various petroleum cuts above light naphtha tends to remain fairly constant. For other types of petroleum streams, however, this assumption is often incorrect. Hence, for truly accurate simulation work, the user is advised to supply gravity curves whenever possible.

- Molecular Weight Data

In addition to the NBP and specific gravity, simulation with assays requires the molecular weight of each cut. These may be omitted completely by the user, in which case they are estimated by the program.

The user may supply a molecular weight curve, which is quadratically interpolated and extrapolated to cover the entire range of pseudocomponents. Optionally, the user may also supply an average molecular weight. In that case, the molecular weight value for the last cut is adjusted so that the curve matches the given average, or if the 100% value is provided, the entire molecular weight curve is normalized to match the given average.

If no molecular-weight data are supplied, the molecular weights are estimated; the default method is a proprietary modification (known as the SlMSCl method) of the method.developed by Twu (1984). This method is a perturbation expansion with the normal alkanes as a reference fluid. Twu's method was originally developed to be an improvement over Figure 2B2.1 in older editions of the API Technical Data Book. That figure relates molecular weight to NBP and API gravity for NBPs greater than 300 F. The SlMSCl method matches that data between normal boiling points of 300 F and 800 F, and better extrapolates outside that temperature range.

The unaltered old API method is (AP163) is also available. A newer API method, called the extended API method (known as the EXTAPI option), is also available. This is API procedure 2B2.1, and it is an extension of the earlier API method which better matches known pure-component data below 300 F. The equation is as follows:

where: SG = specific gravity of the pseudocomponent Tb = normal boiling point in de'grees Rankine

Lightends Data Hydrocarbon streams often contain significant amounts of light hydrocarbons (while there is no universal definition of "light," C6 is a common upper limit). Simulation of such systems is more accurate if these components are considered explicitly rather than being lumped into pseudocomponents. If the distillation curve is reported on a lightends-free basis, the light components can be fed to the fldwsheet in a separate stream and handled in a straightforward manner. Typically, however, the lightends make up the initial part of the reported distillation curve, and adjustment of the cut-up curves is required to avoid double-counting the lightends components.

By default, the program "matches" user-supplied lightends data to the TBP curve. The user-specified rates for all lightends components are adjusted up

or down, all in the same proportion, until the NBP of the highest-boiling lightends component exactly intersects the TBP curve. All of the cuts from the TBP curve falling into the region covered by the lightends are then discarded and the lightends components are used in subsequent calculations. This procedure is illustrated in Figure 1 .I .3-2, where lightend component flows are adjusted until the highest-boiling lightend (nC5 in this example) has a mid-volume percent (point "a") that exactly coincides with the point on the TBP curve where the temperature is equal to the NBP of nC5. The cumulative volume percent of lightends is represented by point "b," and the cuts below point b (and the low-boiling portion of the cut encompassing that point) are discarded.

FIGURE 1.1.3-2: MATCHING LIGHTENDS TO TBP CURVE

Yo lurne % blsil l led Alternatively, the lightends may be specified as a fraction or percent (on a weight or liquid-volume basis) of the total assay or as a fixed lightends flowrate. In these cases, the input numbers for the lightends components can be normalized to determine the individual component flowrates. A final alternative is to specify the flowrate of each lightends component individually.

Also See: Assav Processing

Generating Pseudocomponent Properties

Once each curve is cut, the program processes each blend to produce average properties for the pseudocomponents from each cutpoint interval in that blend., All the streams in a given blend (except for those for which the XBLEND option was used) are totaled to get the weights, volumes, and moles for each cutpoint : ~nterval. Using the above totals, the average molecular weight and gravity are calculated for each cut range. Finally, the normal boiling point for each_

- pseudocomponent is calculated by weight averaging the individual values from, the contributing streams.Once the normal boiling point, gravity, and molecular weight are known for each pseudocomponent, all other properties (critical properties, enthalpies, etc.) are determined according to the characterization method selected by the user (or defaulted by the program). These methods are described in Section 1.1.2, Petroleum Components.

Also See: Assav Processing

-

Vapor Pressure Calculations

While not a part of the program's actual processing of assay streams, many problems involving hydrocarbon systems will involve a specification on some vapor pressure measurement. The two most common of these are the True Vapor Pressure (TVP) and the Reid Vapor Pressure (RVP). PROIII allows specification of these quantities from several unit operations, and they may be reported in output in the HeatingICooling Curve (HCURVE) utility or as part of a user-defined stream report.True Vapor Pressure (TVP) Calculations.

True Vapor Pressure The TVP of a stream is defined as the bubble-point pressure at a given reference temperature. By default, that reference temperature is 100 F, but this may be overridden by the user. The user may specify a specific thermodynamic system to be used in performing all TVP calculations in the flowsheet; by default, the calculation fora stream is performed using the thermodynamic system used to generate that stream.

Reid Vapor Pressure (RVP) Calculations The RVP laboratory procedure provides an inexpensive and reproducible measurement correlating to the vapor pressure of a fluid. The measured RVP is usually within 1 psi of the TVP of a stream. It is always reported as "psi," although the ASTM test procedures (except for D5191 which, as mentioned below, uses an evacuated sample bomb) actually read gauge pressure. Since the air in the bomb accounts for approximately 1 atm, the measured gauge pressure is a rough measure of the true vapor pressure. Six different calculation methods are available. Within each calculation method, the answer will depend somewhat on the thermodynamic system used. As with the TVP, the thermodynamic system for RVP calculations may be specified explicitly or, by default, the thermodynamic system used to generate the stream will be used.

The APIIVAPHTHA method calculates the RVP from Figure 5B1 .I in the API Technical Data Book, which represents the RVP as a function of the TVP and the slope of the D86 curve at the 10% point. The graphical data have been converted to equation form by Simsci. This method is the default for PROIll's RVP calculations. It is useful for many gasolines and other finished petroleum products, but it should not be used for oxygenated gasoline blends. The APICRUDE method calculates the RVP from Figure 5B1.2 in the API Technical Data Book, which represents the RVP as a function of the TVP and the slope of the D86 curve at the 10% point. The graphical data have been converted to equation form by SimSci. It is primarily intended for crude oils. The ASTM D323-82 method (known as the D323 method) simulates a standard ASTM procedure for RVP measurement. The liquid hydrocarbon portion of the sample is saturated with air at 33 F and 1 atm pressure. This liquid is then mixed at 100 F with air in a 4:l volume ratio. Since the test chamber is not dried in this procedure, a small amount of water is also added to simulate this mixture. The mixture is flashed at 100 F at a constant volume (corresponding to the experiment in a sealed bomb), and the gauge pressure of the resulting vapor-liquid mixture is reported as the RVP. Both air and water should be in the component list for proper use of this method.

The obsolete ASTIW D323-73 method (known as the P323 method) is available for compatibility with earlier versions of the program.

The ASTM D4953-91 method (known as the D4953 method) was developed by the ASTM primarily for oxygenated gasolines. The experimental method is identical to the D323 method, except that the system is kept completely free of water. The algorithm for simulating this method is identical to that for D323, except that no water is added to the mixture. Air should be in the component list for proper use of this method.

The ASTM D5 l9 l -91 method (known as the D5 l9 l method) was developed as an alternative to the D4953 method for gasolines and gasoline-oxygenate blends. In this method, the air-saturated sample is placed in an evacuated bomb with five times the volume of the sample, and then the total pressure of the sample is measured. In the simulator, this is accomplished by flashing, at constant volume, a mixture of 1 part sample (at 33 F and 1 atm) and 4 parts air (at the near-vacuum conditions of 0.01 psia and 100 F). The resulting total pressure is then converted to a dry vapor pressure equivalent (DVPE) using the following equation:

DYPE= 0.965X- A (12) where:

X = the measured total pressure A = 0.548 psi (3.78 kPa)

This number is then reported as the RVP. Air should be in the component list for proper use of this method.

Comments on RVP and TVP Methods Because of the sensitivity of the RVP (and the TVP) to the light components of the mixture, these components should be modeled as exactly as possible if precise values of RVP or TVP are important. This might mean treating more light hydrocarbons as defined components rather than as pseudocomponents; oxygenated compounds blended into gasolines should also be represented as defined components rather than as part of an assay. It is also important to apply a thermodynamic method that is appropriate for the stream in question (see Section 1.2.2, ADDlication Guidelines). The thermodynamics becomes particularly important for oxygenated systems, which are not well-modeled by traditional hydrocarbon methods such as Grayson-Streed. These systems are probably best modeled by an equation of state such as SRK with the SimSci alpha formulation and one of the advanced mixing rules (see Section 1.2.4, Equations of State). It is important to have binary interaction parameters between the oxygenates and the hydrocarbon components of the system. PROIll's databanks contain many such parameters, but others may have to be regressed to experimental data or estimated.

One should not be too surprised if calculated values for RVP differ from an experimental measurement by as much as one psi. Part of this is due to the uncertainty in the experimental procedure, and part is due to the fact that the lightends composition inside the simulation may not be identical to that of the experimental sample.

One of the less appreciated effects in experimental measurements is the presence of water, not only in the sample vessel, but also in the air in the form

of humidity. The difference between the D323 (a "wet" method) RVP and the D4953 (a "dry" method) RVP will be approximately the vapor pressure of water at 100 F (about 0.9 psi), with the D323 RVP being higher. Both of these calculations assume that dry air is used in the procedure. The presence of humidity in the air mixed with the sample can alter the D323 results, lowering the measured RVP because of the decreased driving force for vaporization of the liquid water. In the extreme case of 100% humidity, the D323 results will be nearly identical with the D4953 results. Therefore, a "wet" test performed with air that was not dry would be expected to give results intermediate between PRO/llts D323 and D4953 calculations. The results from the D5191 method (both in terms of the experimental and calculated numbers) should in general be very close to D4953 results.

The primary application guideline for which RVP calculational model to use is, of course, to choose the one that corresponds to the experimental procedure applied to that stream. Secondary considerations include limitations of the individual methods. The APINAPHTHA and APICRUDE methods are good only for hydrocarbon naphtha and crude streams, respectively. The D323 method (and its obsolete predecessor, P323) is intended for hydrocarbon streams; the presence of water makes it less well-suited for use with streams containing oxygenated compounds. The D4953 and D5191 methods are both better suited for oxygenated systems, and calculations with these methods should give similar results.

References 1. American Petroleum Institute, 1988, Technical Data Book -

Petroleum Refining, 5th edition (also previous editions), American Petroleum Institute, Washington, DC. 2. American Society for Testing of Materials, Annual Book of ASTM

Standards, section 5 (Petroleum Products, Lubricants, and Fossil Fuels), ASTM, Philadelphia, PA (issued annually). 3. Edmister, W.C., and Okamoto, K.K., 1959, Applied Hydrocarbon

Thermodynamics, Part 12: Equilibrium Flash Vaporization Calculations for Petroleum Fractions, Petroleum Refiner, 38(8), 11 7. 4. Twu, C.H., 1984, An Internally Consistent Correlation for Predicting

the Critical Properties and Molecular Weights of Petroleum and Coal-tar Liquids, Fluid Phase Equil., 16, 137-1 50.

Also See: Assay Processing

Refinery and Gas Processes

These processes may be subdivided into the following: = Low pressure crude systems (vacuum towers and atmospheric stills) = High pressure crude systems (including FCCU main fractionators, and coker fractionators) = Reformers and hydrofiners LJ Lube oil and solvent de-asphalting units

Low Pressure Crude Units Low pressure crude units generally contain less than 3 volume % light ends. Moreover, the petroleum fractions present in the feed exhibit nearly ideal behavior. For these units, the characterization of the petroleum fractions is far more important than the thermodynamic method used. The user should try different assay and characterization methods first if the simulation results do not match the plant data. Since these units contain a small amount of light ends, the Braun K10 (BKIO) method should be used quickly as a first attempt, and will likely give acceptable answers. The BKIO method does, however, provide only gross estimates for the K-values for H2, and is not recommended for streams containing H2. For such systems, and for other systems where the BKI 0 results are not satisfactory, the Grayson-Streed (GS), Grayson-Streed Erbar (GSE), or Improved Grayson-Streed (IGS) methods should be chosen. These methods contain special coefficients for hydrogen and methane, and as such, provide better predictions for streams containing small amounts of H2 at low pressures. It is important to note that the pre-defined thermodynamic systems GS, GSE, and IGS use the Curl-Pitzer (CP) method for calculating enthalpies. For systems containing heavy ends such as vacuum towers, however, the saturated vapor is often at reduced temperatures of less than 0.6. This is the lower limit of the Curl-Pitzer enthalpy method. For these units, therefore, substituting the Lee-Kesler (LK) method for Curl-Pitzer enthalpies may improve the results. In addition, the top of many of these low pressure units often contain significant amounts of light components such as methane. Under these conditions, an equation of state method such as Soave-Redlich-Kwong (SRK) or Peng-Robinson (PR) will provide better answers than the BKIO or Grayson-Streed methods.

Table 1.2.2-1 Methods Recommdded for Low Pressure Crude Systems

BKIO GSIGSEIIGS

SRWPR

Gives fast and acceptable answers. Generally more accurate than BKI 0 especially for streams containing HZ. Use LK enthalpies instead of CP enthalpies for vacuum towers. Provides better results when light ends dominate.

High Pressure Crude Units High pressure crude units generally contain greater amounts of light ends than low pressure units. Still, for these units, as for the low pressure crude units, the characterization of the petroleum fractions remains far more important than the thermodynamic method used. The user should again try different assay and characterization methods first if the simulation results do not match the plant data. Since these units contain larger amounts of light ends, the GS, GSE, IGS, SRK or PR methods should be used, and will likely give acceptable answers. For FCCU main fractionators, the petroleum fractions are much more hydrogen deficient than are crude fractions. Since most characterization correlations are derived from crude petroleum

- data, it is expected that the results will be less accurate than for crude fractions.

Table 1.2.2-2 Methods Recommended for High Pressure Crude Systems

GSIGSEIIGS Quicker but generally less accurate than SRK or PR, especially for streams containing light ends. Use LK enthalpies instead of CP enthalpies for vacuum towers.

SRWPR Provides better results when light ends dominate.

Reformers and Hydrofiners These units contain streams with a high hydrogen content. The Grayson-Streed method, which contains special liquid activity curves for methane and hydrogen, may be used to provide adequate answers. For the SRK and PR methods, the PROIII databanks contain extensive binary interaction parameter data for component pairs involving hydrogen.

Table 1.2.2-3 Methods Recommended for Reformers and Hydrofiners

GSIGSEIIGS Quicker but generally less accurate than SRK or PR, especially for predicting the hydrogen content of the liquid phase.

SRWPR Provides better results than GS methods. SRKMIPRM Provides better results than SRWPR when predicting the

hydrogen content of the liquid phase.

These methods provide results comparable or better than the GS methods. Moreover, these methods are more accurate than GS methods in predicting the hydrogen solubility in the liquid phase. If the user wishes to obtain the most accurate prediction of hydrogen solubility in the hydrocarbon liquid phase, helshe should use the SimSci modified SRK or PR methods, SRKM or PRM.

Lube Oil and Solvent De-asphalting Units These units contain streams with nonideal components such as H2S and mercaptans. The SimSci modified SRK or PR methods, SRKM or PRM, are recommended, but only if user-supplied binary interaction data are available. If no binary interaction data specifically regressed for the system are available, then the data in the PROIII databanks can be used, and the SRK or PR methods are recommended.

Table 1.2.2-4 Methods Recommended for Lube Oil and Solvent

De-asphalting Units SRKMIPRM Recommended when user-supplied binary interaction

data are available SRWPR Recommended when no user-supplied binary

interaction data are available

Also See: Application Guidelines

- Natural Gas Processing

Natural gas systems often contain inerts such as N2, acid or sour gases such as C02, H2S, or mercaptans, and water, along with the usual light hydrocarbon components. Natural gas streams may be treated by a number of methods, e.g., to sweeten using amines, or to dehydrate using glycol. For natural gas systems containing less than 5% N2, C02, or H2S, but no polar components, SRK, PR, or BWRS methods provide excellent answers. The SRK and PR binary interaction parameters between these lower molecular weight molecules and other components are estimated by correlations based on the molecular weight of the hydrogen molecule. For small amounts of these components, this is satisfactory. The BWRS equation of state also contains many binary interaction parameters for component pairs involving lower weight components supplied in Dechema. Unlike cubic equations of state such as SRK or PR, the BWRS equation of state does not satisfy the critical constraints, and so does not extrapolate well into the critical region. For natural gas systems containing more than 5% N2, C02, or H2S, but no polar components, equation-of-state methods such as SRK or PR are still recommended, althoughthe binary parameters estimated by molecular weight correlations may not produce the best results. The user should provide binary interaction parameters for component pairs involving these lower molecular weight components if possible. For natural gas systems containing water at low pressures, equation-of-state methods such as SRK or PR may be used, along with the default water decant option, to predict the behavior of these systems.

Table 1.2.2-5 Methods Recommended for Natural Gas Systems

SRK/PR/ BWRS Recommended for most natural gas and low pressure natural gas + water systems

SRKKD Recommended for high pressure natural gas + water systems

SRKMIPRM Recommended for natural gas + polar components ISRKS

For these systems at high pressures, where the solubility of hydrocarbon in water is significant, the default water decant option, which predicts a pure water phase, is unacceptable. In this case, equation-of-state methods containing advanced mixing rules such as SRKM, PRM or SRKS, or the Kabadi-Danner modification to SRK (SRKKD) should be used to predict the vapor-liquid-liquid behavior of these systems. These methods provide the best answers if all the relevant binary interaction parameters are available. For the SRKKD method in particular, PRO/II contains binary interaction parameters for component pairs involving N2, H2, C02, CO, and H2S. For SRKM, PRM, or SRKS methods, the user should make sure that all relevant binary interaction data are entered. For natural gas systems containing polar components such as methanol, the SRKM, PRM, or SRKS methods are recommended to predict the vapor-liquid-liquid behavior of these systems. The processes used to treat natural gas streams may be sub-divided into the following:

LA Glycol dehydration systems Sour water systems .

= Amine systems.

Glycol Dehydration Systems

- The predefined thermodynamic system GLYCOL has been specially created for these systems. This system uses the predefined system SRKM but invokes the GLYCOL databank. This databank contains binary interaction parameters for component pairs involving glycols tri-ethylene glycol (TEG) and, to a lesser extent, diethylene glycol (DEG) and ethylene glycol (EG). These data have been regressed in the temperature and pressure range normally seen in glycol dehydrators: Temperature: 80-400 OF Pressure: up to 2000 psia This method is described in more detail in Section 1.2.8, of this manual, Special Packages.

Sour Water Systems The standard version of PROIII contains two methods, SOUR and GPSWATER, for predicting the VLE behavior of sour water systems. These methods are described in more detail in Section 1.2.8, of this manual, Special Packages. The recommended temperature, pressure and composition ranges for each method is given in Table 1.2.2-6 below.

Table 1.2.2-6 Methods Recommended for Sour Water Systems

Recommended Ranges: 68 < T (F) < 300 P(psia) < 1500 wNH3 + wC02 + wH2S < 0.30

GPSWATER Recommended Ranges: 68 < T(F) < 600 P(psia) < 2000 wNH3 < 0.40 PC02 + PH2S < 1200 psia

Electrolyte Version of PROIII

Recommended when strong electrolytes such as caustic are used, or when pH control or accurate prediction of HCN or phenol phase distribution is important. Recommended Ranges: 32 < T("F) < 400 P(psia) < 3000 xdissolved gases < 0.30

Amine Systems Amine systems used to sweeten natural gas streams may be modeled in PROIII using the AMlNE special package (see Section 1.2.8, Special Packaaes). Data is provided for amines MEA, DEA, DGA, DIPA, and WIDEA. Results obtained for MEA and DEA are accurate enough for use in final design work. However, results for DIPA systems are not suitable for final design work. For MDEA or DGA systems, the results may be made to more closely fit plant data by the use of a dimensionless residence time correction. The recommended temperature, pressure, and loading ranges (gmoles sour gases per gmole amine) for each amine system available in PROIII is given in Table 1.2.2-7.

Table 1.2.2-7 Methods Recommended for Amine Systems

MEA Recommended Ranges: 25 < P(psig) < 500 T(oF) < 275 wamine - 0.15 - 0.25 0.5-0.6 gmole gaslgmole amine

DEA Recommended Ranges: 100 < P(psig) < 1000 T(oF) < 275 wamine - 0.25 - 0.35 0.45 gmole gaslgmole amine

DGA Recommended Ranges: 100 < P(psig) < 1000 T(oF) < 275 wamine - 0.55 - 0.65 0.50 gmole gaslgmole amine

MDEA Recommended Ranges: 100 < P(psig) < 1000 T(oF) < 275 wamine - 0.50 0.40 gmole gaslgmole amine

Dl PA Recommended Ranges: 100 < P(psig) < 1000 T(oF) < 275 wamine - 0.30 0.40 gmole gaslgmole amine

Also See: A~plication Guidelines

Petrochemical Applications

Common examples of these processes are the following: = Light hydrocarbon applications = Aromatic systems = Aromaticlnon-aromatic systems

Alcohol dehydration systems

Light Hydrocarbon Applications Most light hydrocarbon mixtures at low pressures may be modeled well by the SRK or PR equations of state. The BWRS equation of state, which was developed for light hydrocarbon mixtures is also recommended, but not near the critical region. At high pressures, the SRKM or SRKS equation of state should be used to best predict the water solubility in the hydrocarbon phase. The COSTALD liquid density was developed expressly for light hydrocarbon mixtures. This method is over 99.8% accurate in predicting the liquid densities of these mixtures, and should be requested by the user.

Table I .2.2-8 Methods Recommended for Light Hydrocarbons

SRKlPRl Recommended for systems of similar light BWRS hydrocarbons at low pressures SRKM ISRKS

Recommended at higher pressures

COSTALD Recommended for liquid density

Aromatic Systems Mixtures of pure aromatic components such as aniline, and nitrobenzene at low pressures less than 2 atmospheres exhibit close to ideal behavior. Ideal methods can therefore be used to predict phase behavior, and compute enthalpies, entropies, and densities. At pressures above 2 atmospheres, the Grayson-Streed, or SRK, or PR methods provide good results in the prediction of phase equilibria. The SRK or PR equations of state should provide better results, but with a small CPU penalty.

Table 1.2.2-9 Methods Recommended for Aromatics

IDEAL Recommended for systems at low pressures below 2 atm

GSI SRW PR Recommended at pressures higher than 2 atm IDEAL1 APII Recommended for liquid density. The COSTALD COSTALD method is best at high temperatures and if light

components such as CH4 are present.

AromaticlNon-aromatic Systems Systems of mixtures of aromatic and non-aromatic components are highly non-ideal. Liquid activity methods such as NRTL or UNIQUAC, or equation-of-state methods with advanced mixing rules such as SRKM or SRKS can be used to model these systems. Both types of methods can be used to successfully model aromaticlnon-aromatic mixtures, provided that all the binary interaction data for the components in the system are provided. The PROIII databanks

contain an extensive variety of interaction data for the NRTL and UNIQUAC, and SRKM methods. One advantage to using the liquid activity methods NRTL or UNIQUAC however, is that the FlLL option may be used to fill in any missing interaction parameters using UNIFAC. All library components in the PROIII databanks have UNIFAC structures already defined. PROlll also will estimate UhllFAC structures for petro components based on their Watson K and molecular weight values, and the user may supply UNIFAC structures for components not in the PROll databanks. When gases such as H2, N2, or 0 2 are present in small quantities (up to about 5 mole %), the Henry's Law option may be used to calculate the gas solubilities. Once the Henry's Law option is selected by the user, PROIII arbitrarily defines all components with critical temperatures less than 400 Kelvin as solute components, though the user may override these selections. For large amounts of supercritical gases, an equation-of-state method with an advanced mixing rule should be used to predict the phase behavior.

Table 1.2.2-1 0 Methods Recommended for AromaticlNon-aromatic Systems

SRKMl PRM Recommended at high pressures or when > 5 mole % supercritical gases are present

NRTLI Recommended with the FILL option when binary UNIQUAC interaction parameters are not available or with the

HENRY option when < 5 mole % supercritical gases are present

Alcohol Dehydration Systems The PROIII special package ALCOHOL is recommended for systems containing alcohols with water. This package uses a special databank of NRTL parameters containing interaction parameters expressly regressed under temperature and pressure conditions commonly found in dehydration systems. The NRTL method is suggested if user-supplied interaction data are to be used.

Table 1.2.2-1 1 Methods Recommended for Alcohol Systems

ALCOHOL

NRTU UNIQUAC

Also See: A~plication Guidelines

Recommended for all alcohol dehydration systems. Recommended when user-supplied data are provided.

Chemical Applications

Non-ionic Systems These systems, which typically contain oxygen, nitrogen, or halogen derivatives of hydrocarbons such as amides, esters, or ethers, are also sim~lar to non-hydrocarbon systems found in petrochemical applications. For low pressure systems, a liquid activity coefficient method is recommended. For single liquid phase systems, the WILSON, NRTL, or UNIQUAC methods are equally good, provided all interaction parameters are provided. PROIII databanks contain extensive parameters for NRTL and UNIQUAC, but the user must supply interaction data for the WILSON method. The WILSON method is the simplest, and requires the least CPU time. For systems with two liquid phases, the NRTL or ClNlQUAC methods should be used, provided that at least some interaction data is available. The FlLL option can be used to fill in any missing interaction data using the CINIFAC method. If no interaction data are available, the UNIFAC method should be used since the PROIII databanks contain a large amount of group interaction data for both VLE and LLE applications. For moderate pressure systems up to 10 atmospheres, a liquid activity method can still be used, provided that the interaction parameters used are still valid in that pressure range. For example, if the system pressure were much higher than the pressure at which the interaction parameters were regressed, the vapor phase fugacity may be taken into account in modeling the phase behavior. If the PHI option is selected, the liquid-phase Poynting correction factor is automatically selected also. It is also important to note that all the interaction parameters in the PROIII databanks, except for dimerizing components such as carboxylic acids, were regressed without including any vapor-phase nonideality. This means that the PHI option should be used for carboxylic acid systems at all pressures, but should only be used for most components at high pressures. For systems containing components such as carboxylic acids that dimerize in the vapor phase, the Hayden-O'Connell fugacity method may be used to calculate all vapor-phase properties such as fugacity, enthalpy, and density. For components such as hydrogen fluoride which forms hexamers in the vapor phase, PROIII contains an equation of state specially created for such systems, HEXAMER. This method is recommended for processes such as HF alkylation or the manufacture of refrigerants such as HFC-134a. For all other components, an equation-of-state method such as SRK or PR may be used to calculate vapor-phase fugacities. When supercritical gases are present in small quantities (generally less than 5 mole %), the Henry's Law option should be used to compute gas solubilities. For high pressure systems, greater than 10 atmospheres, or for systems with large quantities of supercritical gas, an equation-of-state method using an advanced mixing rule such as SRKM or PRIM should be used. The UNIWAALS equation-of-state method uses UNl FAC structure information to predict phase behavior. This method is useful when interaction data are not avaialable and, unlike a liquid activity method such as UNIFAC, is able to handle supercritical gases.

Table 1.2.2-1 2 Methods Recommended for Non-ionic Chemical Systems

WILSON Recommended for single liquid phase slightly nonideal mixtures. If all interaction data are not available use the FILL=UNIFAC option.

NRTLI Recommended for all nonideal mixtures. Use with the FILL UNIQUAC option when binary interaction parameters are not available or

with the HENRY option when < 5 mole % supercritical gases are present. For moderate pressures use the PHI option for vapor phase nonidealities.

SRKSISRKMI Recommended for high pressure systems or when > 5 mole % PRMI supercritical gases are present. U N IWAALS

HOCV Recommended for vapor fugacity and enthalpy and density calculations in systems containing dimerizing components such as carboxylic acids. Use with a liquid activity method .

HEXAMER Recommended for systems containing hexamerizing components such as HF.

lonic Systems A special version of PROIII expressly made for aqueous electrolytes is rec-ommended when modeling these systems. This version combines the PROIII flowsheet simulator with rigorous electrolyte thermodynamic algorithms devel-oped by OLI Systems, Inc. Chemical systems which may be modeled by this special version include amine, acid, mixed salts, sour water, caustic, and Ben-field systems. See Sections 1.2.9, Electrolyte Mathematical Model, and 1.2.1 0, Electrolvte Thermodvnamic Equations for further details.

Table 1.2.2-1 3 Methods Recommended for lonic Chemical Systems

PROIII Electrolyte Version

Environmental Applications These systems typically involve stripping dilute pollutants out of water. By themselves, liquid activity methods such as NRTL do not model these dilute systems with much accuracy. A better approach is to use a liquid activity method in combination with Henry's Law constants at the process temperature to model these dilute aqueous systems. PROIII contains Henry's Law constants for many components such as HCI, S02, and ethanediol in water. Some additional Henry's Law constants for chlorofluorocarbons (CFCs) and hydrofluorocarbons (HFCs) in water are also available in the PROIII databanks. Other sources for Henry's Law data include the U.S. Environmental Protection Agency.

Table 1.2.2-14 Methods Recommended for Environmental Applications

Liquid Activity Method + Henry's Law Option

Solid Applications Solid-liquid equilibria for most systems can be represented in PROIII by the van't Hoff (ideal) solubility method or by using user-supplied solubility data. In general, for those systems where the solute and solvent components are chemically similar and form a near-ideal solution, the van' t Hoff method is appropriate. For nonideal systems, solubility data should be supplied. For many organic crystallization systems, which are very near ideal in behavior, the van't Hoff SLE method provides good results. The VLE behavior can usually be adequately represented by IDEAL or any liquid activity methods. Precipitation of solid salts and minerals from aqueous solutions can be calculated more rigorously by using the electrolyte version of PROIII.

Table 1.2.2-1 5 Methods Recommended for Solid Applications

Ideal or Liquid Activity Recommended for most solid systems Method(VLE) + VANT HOFF involving organics. Method (SLE) PROIII Electrolyte Version Recommended for solid salt and mineral

precipitation from aqueous solutions.

Related Topics

Braun- KIO Grayson-Streed Gravson-Streed-Erbar Improved Grayson-Streed Chao-Seader Chao-Seader-Erbar ideal

Soave-Redlich-Kwong SRK-Kabadi-Danner SRK-Huron-Vidal SRK-Panaqiotopoulos-Reid SRK- Modified SRK-SimSci SRK- Hexarner Pens-Robinson

PR-Huron-Vidal PR-Panaqiotopoulos-Reid PR-Modified Benedict-Webb-Rubin-Starling U hl l WAALS GPA Sour Water Arnine Glycol Sour Water Curl-Pitzer Johnson-Grayson Lee-Kesler API -

Rackett COSTALD

Also See:

Application Guidelines Thermodvnamic Methods

ldeal (IDEAL) ldeal K-values are generally applicable to systems which exhibit behavior close to ideality in the liquid phase. Mixtures of similar fluids often exhibit nearly ideal behavior. In an ideal solution at constant temperature and pressure, the fugacity of every component is proportional to its mole fraction. For every component i, the following fundamental thermodynamic equilibrium relationship holds:

where: superscript L refers to the liquid phase superscript V refers to the vapor phase

fi = fugacity of component i In the vapor phase, the fugacity is assumed to be equal to the partial pressure:

where: yi = vapor mole fraction P = system pressure

In the liquid phase for an "ideal" liquid (ignoring correction factors that are usually small):

where: Xi = liquid mole fraction

'v = pure component i liquid fugacity pi'"f

= vapor pressure of component i at the system temperature Raoult's law thus holds:

The ideal K-value is therefore given by:

& = y i / x j = q ? v (5)

Note that there is no compositional dependency of the K-values. They are only a function of temperature (due to the dependence of Pisat on T) and pressure. ldeal vapor densities are obtained from the ideal gas law:

where: p = vapor density of mixture

Ideal-liquid densities are obtained from pure-component saturated-liquid density correlations. ldeal liquid enthalpies are obtained from pure-component liquid enthalpy correlations, and the corresponding vapor enthalpies are obtained by adding in the effect of the known latent heat of vaporization of the component. ldeal entropies are calculated from the ideal enthalpy data using the following equation:

where: 'i = ideal entropy

'pi = ideal component heat capacity

H i = ideal enthalpy

T=f = reference temperature (1 degree Rankine) T = temperature of mixture

Also See: Generalized Correlation Methods

C hao-Seader (CS) Chao and Seader calculated liquid K-values for the components of nonideal mixtures using the relationship:

Ka. fi = the standard-state fugacity of component i in the pure liquid phase yi= the activity coefficient of component i in the equilibrium liquid mixture

9% = the fugacity coefficient of component i in the equilibrium vapor mixture It was shown that yi could be calculated from molar liquid volumes and solubility parameters, using the Scatchard-Hildebrand equation, with regular liquid solution assumed. The Redlich-Kwong equation of state (see Section 1.2.4, Equations of State), was used to evaluate 4.

[IL Chao and Seader presented a generalized correlation for fi jP, the fugacity coefficient of pure liquid "I" in real and hypothetical states. In the development of their correlation for their vapor-liquid K-value correlation, Chao and Seader used the framework of Pitzer's modified form of the principle of corresponding states for the

m. pure-liquid fugacity coefficients, giving values of fi f P as a function of reduced temperature, reduced pressure, and acentric factor for both real and hypothetical liquids:

where: o = acentric factor

The first term on the right hand side of equation (9) represents the fugacity coefficient of simple fluids. The second term is a correction accounting for the departure of the properties of real fluids from those of simple fluids. Limitations of the Chao-Seader method are given below: = For all hydrocarbons (except methane); Pressure: up to 2000 psia, but not exceeding 0.8 of the critical pressure of the system. Temperature: -100 OF to 500 OF, and pseuodoreduced temperature, Tr, of the equilibrium liquid mixture less than 0.93. The pseudoreduced temperature is based on the molar average of the critical temperatures of the components. Concentration: up to 20 mole % of other dissolved gases in the liquid. = This method is not suitable for other non-hydrocarbon components such as N2, H2S, C02, etc.

Reference Chao, K. C., and Seader, J. D., 1961, A Generalized Correlation of Vapor-Liquid Equilibria in Hydrocarbon Mixtures, AlChE J., 7(4), 598-605.

Also See: Generalized Correlation Methods

Grayson-Streed (GS) Grayson and Streed modified the Chao-Seader correlation in 1963 by fitting data over a wider range of conditions and hence deriving different constants for the equations giving the fugacity coefficients of the pure liquids. Special coefficients for hydrogen and methane are supplied because typical application temperatures are far above the critical points of these two components. Grayson and Streed's modifications have extended the application range for hydrocarbon systems up to 800 OF and 3000 psia. The lower limits imposed by Chao and Seader still apply. Reference Grayson, H. G., and Streed, C. W., 1963, Vapor-Liquid Equilibria for High temperature, High Pressure Hydrocarbon-Hydrocarbon Systems, 6th World Congress, Frankfurt am Main, June 1 9-26.

Also See: Generalized Correlation Methods

Erbar Modification to Chao-Seader (CSE) and Grayson-Streed (GSE) In 1963, Erbar and Edmister developed a new set of constants for the Chao-Seader liquid fugacity coefficient specifically for N2, H2S, and C02, in order to improve the prediction of the K-values of these gases. At the same time, new solubility parameter and molar volume values were found for these components. A limitation of this modified method, however, is that the H2S correlation cannot be used in any cases where an azeotrope may exist (e.g., H2SIC3H8 mixtures), as the azeotrope will not be predicted. Reference Erbar, J. H., and Edmister, W. C., 1963, Vapor-Liquid Equilibria for High Temperature, High Pressure Hydrocarbon-Hydrocarbon Systems, 6th World Congress, Frankfurt am Main, June 19-26.

Also See: Generalized Correlation Methods

lmproved Grayson-Streed (IGS) For hydrocarbon-water mixtures, the Grayson-Streed and Erbar-modified Grayson-Streed methods accurately predict the phase behavior of the hydrocarbon-rich phase, but does not do as well in predicting the water-rich phase. A separate set of solubility parameters was used in the water-rich phase, and a new set of liquid fygacity coefficients developed for N2, H20, H2S, CO, and 02. This new method is known as the lmproved Grayson-Streed. It was found that the Grayson-Streed liquid fugacity coefficient for the "simple" fluid decreases rapidly as Tr increases above 2.5, and can in fact become negative. The liquid fugacity coefficient for the "simple" fluid was therefore replaced by that for hydrogen at reduced temperatures of 2.5 and above.

Also See: Generalized Correlation Methods

Curl-Pitzer (CP) This correlation may be used to predict both liquid and vapor enthalpies and entropies. It computes the enthalpy deviation using the principle of corresponding states, i.e. in terms of the reduced temperature, reduced pressure, and acentric factor. The critical temperature and pressure for the mixture is computed using the mixture rules of Stewart, Burkhart, and Voo. The mixture acentric factor used is the molar average value. The Curl-Pitzer method is limited to nonpolar mixtures, and may be used for Pr up to 10, and Tr from 0.35 to 4.0 for liquids, and Tr from 0.6 to 4.0 for vapors. For systems containing heavy ends, the saturated vapor is sometimes at a reduced temperature of less than 0.6. In this case, the CP correlation extrapolates reasonably, producing satisfactory results. The Curl-Pitzer method is generally useful for refinery hydrocarbons, and in oil absorption gas plants. References 1. Stewart, Burkhart, and Voo, 1959, Prediction of Pseudo-Critical Constants for Mixtures, Paper presented at AlChE Meeting, Kansas City. 2. American Petroleum Institute, 1970, Technical Data Book - Petroleum Refining, 2nd Ed., Procedure 783.7, 7-29 - 7-286. 3. American Petroleum Institute, 1970, Technical Data Book - Petroleum Refining, 2nd Ed., Procedure 7H2.1, 7-201 - 7-202.

Also See: Generalized Correlation Methods

Braun K10 (BKIO) The K-value of each component is a function of the system temperature, pressure, and the composition of the vapor and liquid phases. For natural gas systems, the convergence pressure can be used as the parameter that represents the composition of the vapor and liquid phases in equilibrium. The convergence pressure is, in general, the critical pressure of a system at a given temperature at which the K-values of all components converge to unity (when the system pressure reaches the convergence pressure). The Braun K10 charts developed by Cajander et al. in 1960 show the low pressure equilibrium ratio, arbitrarily taken at 10 psia system pressure and 5000 psi convergence pressure. For many hydrocarbon systems, no experimental data are available. For these cases, the equilibrium K-values may be predicted from vapor pressure:

where: p t

= saturated vapor pressure in psia. The relationship given in equation (10) only holds for K-values less than 2.5. For H2, the K-value is assumed to be 10 times as large as the methane value. For N2, 02, and CO, the K-values are assumed to be identical to that of methane. The K-values for C02 and H2S are assumed to be identical to that of propylene. For petroleum fractions in which the form of the vapor pressure curve is unknown, a rough K10 chart is developed from the normal boiling point of the fraction. The following method is used: = On the appropriate K10 chart, the point K10 = 14.711 0 = 1.27 is plotted at the atmospheric boiling point. = The whole K10 curve can then be sketched in by similitude to the known K10 curves for homologous hydrocarbons. The K10 charts apply to mixtures that behave ideally at low pressures, e.g., for mixtures of one molecule type such as mixtures of paraffins and olefins. For mixtures of naphthalenes mixed with olefins and paraffins, the accuracy of BKIO is slightly poorer. Large errors can be expected for mixtures of aromatics with paraffins, olefins, or naphthalenes, which cause nonidealities and form azeotropes. Reference Cajander, B. C., Hipkin, H. G., and Lenior, J. M., 1960, Prediction of Equilibrium Ratios from Nomographs of Improved Accuracy, J. Chem. Eng. Data, 5(3), 251-259. Also See: Generalized Correlation Methods

Johnson-Grayson (JG) This correlation may be used to predict both liquid and vapor enthalpies. It is essentially an ideal-enthalpy correlation, using saturated liquid at 0 C as the datum for the correlation (-200 F in versions 3.5 and earlier). Vapor phase corrections are calculated using the Curl-Pitzer. correlation. Pressure effects are not considered for the liquid phase. Johnson-Grayson is useful for systems containing heavy ends between 0 F and 1200 F. However, it can be extrapolated to higher temperatures. The correlation should not be used if the mixture is C4-C5 or lighter.

Reference Johnson, and Grayson, 1961, Enthalpy of Petroleum Fractions, Petroleum Refiner, 40(2), 123-29.

Also See: Generalized Correlation Methods

Lee-Kesler (LK) This correlation may be used to predict both liquid and vapor enthalpies, entropies, and densities. This correlation uses the three-parameter corresponding-states theory, which essentially states that all fluids having the same acentric factor must have the same properties at the same reduced temperature and pressure. Special mixing rules have been used to calculate the mixture reduced properties. For most fluids, the Lee-Kesler method is 98% accurate in predicting the gas phase compressibility factors. The method also gives reasonable results for slightly polar mixtures. This method is not recommended for highly polar mixtures, or those which form strongly associative hydrogen bonds. However, the Lee-Kesler method provides accurate results for polar fluids at low temperatures near the saturated vapor region. The Lee-Kesler method is not recommended for calculating liquid densities of hydrocarbons heavier than C8.

References 1. American Petroleum Institute, 1975, Technical Data Book, Petroleum Refining, 3rd Ed., 2-1 - 7-4. 2. Lee, B. I., and Kesler, M. G., 1975, A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States, AlChE J., 21, 510-527. 3. Kesler, M. G., and Lee, B. I., 1976, Improved Prediction of Enthalpy of Fractions, Hydrocarbon Proc., 53, 153-1 58.

Also See: Generalized Correlation Methods

General Cubic Equation of State

A general two-parameter cubic equation of state can be expressec j by the equation:

where: P = the pressure T = the absolute temperature v = the molar volume u,w = constants, typically integers

The values of u and w determine the type of cubic equation of state. Table 1.2.4-1 shows three of the best known of these. The van der Waals equation developed in 1873 is obtained by setting u=w=O. By setting u=l and w=O, the Redlich-Kwong equation (1949) is obtained. Peng and Robinson developed their equation of state in 1976 by setting u=2 and w=-I.

Table 1.2.4-1 Some Cubic Equations of State u w Equation of state 0 0 van der Waals (vdW) 1 0 Redlich-Kwong (RK) 2 -1 Peng-Robinson (PR)

The parameters a and b at the critical temperature, (ar and hc ) are found by setting the first and second derivatives of pressure with respect to volume equal to zero at the critical point. Application of these constraints at the critical point to equation (1) yields:

where:

subscript c refers to the critical point The critical constraints result in three expressions for three unknowns, Ac, Bc, and Zc. These unknowns depend on the values of u and w. Actually, Ac and Bc are the only true unknowns appearing in these equations, because PC, Tc, and Vc (and hence Zc) are properties of a substance, having numerical values independent of any equation of state. In solving these three equations, Vc is in fact treated as a third unknown. Table 1.2.4-2 lists these constants for the van der Waals, Redlich-Kwong, and Peng-Robinson equations of state.

Table 1.2.4-2 Constants for Two-Parameter Cubic Equations of State Ac Bc Zc Equation of state

0.421 88 0.1250 0.3750 van ber waals ( v d ~ ) 0.42747 0.0866403 0.3333 Redlich-Kwong (RK) 0.45724 0.0778 0.3074 Peng-Robinson (PR)

References 1. Abbott, M. M., 1973, Cubic Equations of State, AlChE J., 19(3), 596-601. 2. van der Waals, J. D., 1873, Over de Constinuiteit van den gas-en Vloeistoftoestand, Doctoral Dissertation, Leiden, Holland.

3. Redlich, O., and Kwong, N. S., 1949, On the Thermodynamics of Solutions. v: An Equation of State. Fugacities of Gaseous Solutions, Chem. Rev., 44, 233.

4. Peng, D. Y., and Robinson, D. B., 1976, A New Two-constant Equation of State for Fluids and Fluid Mixtures, Ind. Eng. Chem. Fundam., 15, 58-64.

Also See: Equations of State

Alpha Formulations

The temperature dependent parameter a(T) can be rewritten as:

In equation (5), a(T) is a temperature-dependent function which takes into account the attractive forces between molecules. The accuracy of the equation of state for pure-component vapor pressures (and therefore to a large extent for mixture phase equilibria) depends on the form of the alpha formulation, a(T), from equation (5). The real-gas behavior approaches that of the ideal gas at high temperatures, and this requires that a goes to a finite number as the temperature becomes infinite. Three basic requirements for the temperature-dependent alpha function must therefore all be satisfied:

1. The a function must be finite and positive for all temperatures, 2. The a function must equal unity at the critical point, and 3. The a function must approach a finite value as the temperature approaches infinity. For the Redlich-Kwong equation of state, which works well for the vapor phase at high temperatures, a(T) is given by:

a (T) = Ty -l/ 2

PRO/II allows the user to utilize a choice of 11 different alpha formulations for cubic equations of state (SRK, PR, modified SRK or PR, or UWIWAALS). Table 1.2.4-3 shows the 11 available alpha formulations for a(T).

Table 1.2.4-3 Alpha Formulations

Form Equation Reference

Soave (1 972)

Peng-Robinson (1980)

Soave (1 979)

Boston-Mathias (1 980)

Twu (1 988)

Twu-Bluck-Cunningham-Coon (1 991) (Recommended by SimSci)

Alternative for form (04)

Alternative for form (06) = T%? [ak- TP)]

Mathias-Copeman

a = [ l + C ( l - T ! . ) + C a ( l - 4 +C?(J.-TP.)?]' (1 983)

Melhem-Saini-Goodwin (1 989)

Some newer formulations(9) have been added for the temperature dependent alpha term. These forms do not require the user to supply values for constants (CI, C2, etc.) Instead, they perform t