2 DISTILLATION PROCESSES has long been used for the separation ... VOLUME II / REFINING AND...

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2 DISTILLATION PROCESSES

Transcript of 2 DISTILLATION PROCESSES has long been used for the separation ... VOLUME II / REFINING AND...

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DISTILLATION PROCESSES

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2.1.1 The nature of crude oil

Crude oil, or petroleum, is a very complex mixture ofthousands of different species of chemicalcomponents. The most common compounds belong tothe paraffins (alkanes), naphthenes (cycloparaffins),aromatics, or combinations such as alkyl substitutedaromatics and polycyclic compounds. The number ofcarbon atoms in the components varies from one tofour for gases, while heavy oils and waxes may havefifty or more and asphalts have hundreds. Thecomponents have atmospheric boiling ranges from�162°C to more than 500°C.

Distillation has long been used for the separationof multi-component mixtures and still represents themost common separation process in use, even thoughit is energy-intensive. The same principles that can beapplied to the separation of two components that havedifferent boiling points can be applied to theseparation of a complex mixture, such as petroleum.

Unfortunately, crude oils differ markedly incharacteristics, depending on where in the world theyare found and on the geologic history of the area.Crude oil from the Far East is generally waxy, black orbrown in colour and low in sulphur. Oil from theMiddle East is usually black, less waxy and higher insulphur. Western Australia produces crude oils that canbe light, straw-coloured liquids and North-Sea oils aretypically waxy and greenish-black in colour. TheUnited States of America produce many differentkinds of crude oil because there is a great diversity ofgeological history in the different regions of thecountry.

Although crude oil consists largely of carbon andhydrogen atoms, other elements are found. Sulphur,in the form of free sulphur, hydrogen sulphide,mercaptans and thiophenes, is common and is anextremely undesirable constituent in any fuel.

Nitrogen also occurs, and is undesirable because itwould poison catalysts, which are used indownstream reactors. Other poisons to catalysts thatare found in crude oil are arsenic, vanadium andnickel. Oxygen containing components, such asnaphthenic acids, are corrosive. Salts, such assodium chloride as well as sulphates and carbonatesof sodium, calcium and magnesium, can causecorrosion or can deposit on the surfaces ofequipment, such as heat exchangers, causing foulingand are, therefore, undesirable.

The products of the distillation of crude oil are,themselves, complex mixtures – unlike in manychemical and specialty chemical processes, wheredistillation is used to separate pure or high purityproducts from mixtures. The products from thedistillation of crude oil are usually characterized byboiling range and the yields of these products varysignificantly, depending on the source of thefeedstock. Maples (2000) describes the main refineryproducts according to atmospheric boiling range andthe approximate number of carbon atoms per molecule(Table 1).

Refinery distillation columns are usually verylarge. It is not uncommon for a single crudedistillation column to process over 250,000 barrelsof crude oil per day (about 12.5 million tons peryear). Distillation columns are used for theatmospheric and vacuum distillation of crude oil,fractionation of the gaseous effluent from catalyticand thermal cracking. The equipment consumeslarge amounts of energy, because of the need to boiland condense the material. Consequently,optimization of design and operation is veryimportant, especially as the configuration ofequipment - heat exchangers, furnaces, columns,etc. - can be very complex resulting from the desireto recover as much energy as possible.

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2.1

Fundamentals

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2.1.2 Petroleum fractioncharacterization

Gas chromatography, Nuclear Magnetic Resonance(NMR) and other techniques have allowed moreprecise identification of many individualcomponents in crude oil. However, knowledge ofthe identity and quantity of each individualcomponent is impossible and quite unnecessary formost analysis and design purposes, because thefinal products are defined as mixtures withacceptable ranges of boiling points. It is usuallysatisfactory to characterize petroleum andpetroleum fractions by parameters that are derivedfrom normal inspection tests, a laboratorydistillation curve and the specific gravity of themixture.

The Technical data book. Petroleum refining(1983) edited by API (American Petroleum Institute)describes five different boiling points and a quantitycalled the K factor, which is an index ofparaffinicity, as useful parameters for the correlationof the thermodynamic and physical properties ofpetroleum fractions. Based on our knowledge of theproperties of defined chemical components, such asethane, propane, butane, pentane, etc. in thehomologous series of normal paraffins, theproperties of any unknown fraction can be estimatedby comparison of the boiling point and specificgravity (Twu, 1984).

The five boiling points are described by thefollowing equations:• Volume Average Boiling Point (VABP):

[1] VABP �n

�i�1

xviTbi

where xvi is the volume fraction of component i and Tbiis the normal boiling point of component i.

• Molar Average Boiling Point (MABP):

[2] MAPB �n

�i�1

xiTbi

where xi is the mole fraction of component i and Tbi isthe normal boiling point of component i.• Weight Average Boiling Point (WABP):

[3] WABP �n

�i�1

xwiTbi

where xwi is the weight fraction of component i and Tbiis the normal boiling point of component i.• Cubic Average Boiling Point (CABP):

[4] CABP �n

�i�1

(xviTbi1/3)3

where xvi is the volume fraction of component i and Tbiis the normal boiling point of component i; in absolutetemperature units.• Mean Average Boiling Point (MeABP):

MABP �CABP[5] MeABP �11131121

2

MABP and CABP must be in the same absolutetemperature units.

Although the volume, mole and weight fractions arenot known for undefined mixtures the API technicaldata book provides empirical correlations for the boilingpoints based on laboratory distillations.

The characterization parameter K, sometimes alsodescribed as the KUOP factor, is defined by theequation:

(MeABP)1/3[6] K�1111121211111

specific gravity (60°F/60°F)

where MeABP must be in degrees Rankine.Paraffins have a K value close to 13 (n-hexane

12.81), mono-olefins have a lower K value, with

ENCYCLOPAEDIA OF HYDROCARBONS

DISTILLATION PROCESSES

Table 1. Principal refinery products

Product Boiling range (°C) Average molecularweight

Carbon atoms per molecule

Liquefied Petroleum Gases (LPG) �42-0 44-58 3-4

Gasoline 0-200 100-110 4-11

Kerosene, jet fuel 190-270 160-190 10-15

Diesel 270-340 245 15-20

Atmospheric gas oil 340-425 320 20-25

Atmospheric residue �425 �25

Vacuum gas oil 425-540 430 25-50

Vacuum residue �540 �800 �50

Petroleum coke �1,100 �2,500 �200

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cyclo-paraffins lower still, followed by aromatics(1-hexane 12.48; cyclohexane 10.98; benzene9.72).

Many other properties are used to characterizepetroleum fractions, such as sulphur content, metalcontent, salt content, pour point, cloud point, anilinepoint, freezing point, smoke point, octane number,cetane index, diesel index, refractive index, waxcontent and carbon content. There are literally tensof such properties, usually classified as refineryinspection properties, which are measured inlaboratories and are used to specify the quality ofthe finished products. Fortunately, these propertiesare significantly less important than volatilitymeasurements in the design or analysis of adistillation column.

ASTM (American Society for Testing ofMaterials) and TBP (True Boiling Point)analytical distillations are used to define thevolatility characteristics of crude oils andpetroleum fractions. Both are batch distillationsand differ in the degree of fractionation thatoccurs in the process. Atmospheric pressureASTM distillations are run in an Engler flask,with no packing and reflux results only from heatlosses through the neck of the flask. TBPdistillations, on the other hand, are run in multi-stage columns at high reflux ratio. Althoughmore reliable than ASTM distillations, TBPdistillations take a lot longer to run and there isno standardization of the test method. Table 2summarizes the common methods used for crudeoils and heavy fractions.

The data from ASTM D86 distillations areplotted as temperature vs. volume percent distilled;D2887 simulated distillations are plotted astemperature vs. weight percent distilled.

When carrying out ASTM distillations there maybe residue left in the flask and there well may belosses when the volume of the original charge doesnot equal the sum of the distillate collected andresidue. The loss is assumed to be volatilecomponents that did not condense and is added tothe individual measurements of percentage distilledat the reported temperature.

Heavier petroleum fractions tend to decomposebefore they boil – a process called cracking. The APItechnical data book used to recommend theapplication of a correction to ASTM D86temperatures above 475°F (246°C) to adjust forcracking. This adjustment has been dropped in themost recent edition of the technical data book.

Table 3 shows a typical ASTM D86 distillationcurve for a crude oil that might be obtained from alaboratory.

If the pressure at which the distillation is done isnot equal to atmospheric (760 mmHg, 101.325 kPa),temperature measurements should be adjusted toequivalent atmospheric pressure by the applicationof the Sidney Young equation, which for degreesFahrenheit is:

[7] T760�TP�0.00012(760�P)(460�TP)

where T760 is the temperature corrected to 760 mmHgin degrees Fahrenheit, TP is the measured temperaturein degrees Fahrenheit and P is the measured pressionin mmHg.

Although the ASTM test methods are simpler,the TBP distillation provides the best theoreticalbasis for the characterization of a sample. In theextreme case of a large number of theoreticalstages and high reflux, the TBP distillation willtend to separate each component in the sampleaccording to its boiling point. This assumes that the

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Table 2. Laboratory assays

Test Applicability

ASTM Method D86Distillation of motor gasolines, aviation gasolines, aviation turbine fuels, naphthas, kerosenes,gas oils, distillate fuel oils and similar products. Distillation is at atmospheric pressure, using exposed thermometer with no stem correction

ASTM Method D216 Distillation of natural gasoline at atmospheric pressure

ASTM Method D1160

For heavy petroleum products which can be vaporized partially or completely at a maximumtemperature of 750°F (399°C) at absolute pressures down to 1 mmHg and condensed as liquids at pressure of test. Pressures range from 1 to 760 mmHg. Temperature is measured with thermocouple

ASTM Method D2887Simulated distillation using gas chromatography. Applicable to all petroleum fractions with final boiling point of 1,000°F (538°C) or less. Boiling range must be greater than 100°F (38°C)

True Boiling Point (TBP)Distillation in column with 15 to 100 theoretical stages at high reflux ratios (5:1 or greater)and at pressures between 10 and 760 mmHg. No standardization of method

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sample mixture is nearly thermodynamically ideal,which is approximately the case for crude oils anddistillate products. A plot of temperature againstvolume distilled would show a series of stair-steps,with width of each step corresponding to thevolume of an individual component and the heightof the step being its boiling point. In crude oilthere are literally thousands of components, withvery close boiling isomers. This causes the stair-step curve to become almost smooth andcontinuous.

Because the degree of fractionation is muchgreater in the TBP distillation than the D86, the TBP Initial Boiling Point (IBP) is lower thanthe corresponding D86 IBP and the TBPEnd Boiling Point (EBP) is higher than the D86EBP. The curves intersect nearthe 50% point.

There is a further type of laboratorydistillation, called Equilibrium FlashVaporization (EFV). The EFV curve is also a plotof temperature vs. volume percent distilled. Asample is heated in a closed vessel in such amanner that the total vapour produced is kept incontact with the unvaporized liquid until thedesired temperature is reached for the pressure atwhich the experiment is being done. The volumepercent vaporized is recorded. Each point on theEFV curve represents a separate vapour-liquidequilibrium experiment and the number ofexperiments that must be done depends largelyon the shape of the curve. At least fiveexperiments are usually required. The componentseparation achieved in an EFV experiment is lessthan in the ASTM and TBP distillations. Theinitial and final boiling points, (the final boilingpoint being the temperature at which the entiresample is just vaporized), correspond to thebubble and dew points of the mixture beinganalysed. EFV distillations can be run at several

different pressures. There is no standard testprocedure for EFV distillations and, because theprocess is tedious and time consuming to run,EFV distillations are seldom done.Fig. 1 shows the TBP, D86 and EFV curves for atypical kerosene stream.

The API technical data book provides a set ofprocedures that can be used to interconvert onetype of distillation curve to any other. The goal, forthe purpose of doing any analysis or design workon a crude distillation column is to produce theTBP curve for the crude oil. If the D86 curve ismeasured, API procedure 3A1.1 provides themeans to convert to TBP. If, as is becoming morepopular, the D2887 simulated distillation curve isavailable, API procedure 3A3.1 providesconversion to D86 and procedure 3A1.1 is thenused to convert to TBP.

EFV curves are seldom produced in thelaboratory, but a knowledge of the EFVcharacteristics of a stream is useful (see Section2.1.3) for determining the temperature to which acrude oil stream must be heated in order to producethe required distillate products. In fact, thevaporization process in the flash zone of thedistillation column is correctly represented by theEFV curves. In the ASTM and TBP distillation thevapours are separated by the liquid immediatelyafter their formation, and this is not the case of thecontinuous industrial distillation. API Procedure3B1.1 provides an empirical mechanism for theinterconversion of ASTM and EFV curves atatmospheric pressure. Procedure 3B3.1 can be usedto interconvert any above atmospheric pressureEFV curve with its corresponding atmosphericpressure curve.

An assay of a crude oil always includes, inaddition to an ASTM or TBP distillation, anaverage or whole crude gravity. This is usually

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Table 3. Typical ASTM D86 laboratory distillation

Mid-liquid volume percent

Temperature (°C at 760 mmHg)

8 57.2

25 98.9

43 187.8

67 296.1

75 351.7

82 426.7

92 532.2

400

350

300

250

200

150

1000 10 20 30 40 50 60

percent distilled (liquid volume basis) 70 80 90 100

EFVD86TBP

tem

pera

ture

(°C

)

Fig. 1. TBP, D86 and EFV curves for a kerosene stream.

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measured by the ASTM D287 test procedure andreported in degrees API (or API gravity), where:

141.5[8] API gravity �11111111121�131.5

specific gravity (60°F/60°F)

Water has an API gravity of 10. Many crude oilshave API gravities in the range from 10 to 40. Thelighter (less dense) the sample, the higher is the APIgravity.

With the knowledge of the TBP curve of thecrude oil and its K factor, derived from theaverage gravity and boiling point, the wholecrude can be divided into a number of narrowboiling fractions, or pseudocomponents. Eachpseudocomponent has an average boiling pointand, assuming a constant K, a specific gravitycan be derived.

For the purposes of illustration, assume acrude oil has the analysis shown in Table 4 for its

light-end components and Table 5 for its TBPdistillation. Assume, also that the average APIgravity is 29.2.

The crude oil can be represented by a seriesof defined components: the light-ends, plus anumber of pseudocomponents over the remainingportion of the curve (the curve volumepercentages are assumed to include the light-endcompositions). Applying a cutting profile for thepseudocomponents, whereby a number of equallyspaced intervals of temperature are defined asfollows: from 37.8°C to 426.7°C, 28 cuts (13.9°C, or 25°F intervals); from 426.7°C to648.9°C, 8 cuts (27.8°C, or 50°F intervals); from648.9°C to 871.1°C, 4 cuts (55.6°C, or 100°Fintervals), produces a series of pseudocomponents depicted by the histogram-like barsin Fig. 2.

The profile above is quite arbitrary and ischosen to create a manageable number ofpseudocomponents that will capture the shape ofthe original curve. Too few components, and itwill be impossible to reproduce the boilingranges of the actual material in any of thedistillate products. If too many components arechosen, this will add to the computational effortto do any distillation calculations, withoutyielding any appreciable increasein accuracy.

For each pseudocomponent, there is an averageboiling point temperature, which is the integratedaverage of the volume of material boiling betweenthe upper and lower cut-point temperatures. Ingeneral this will be close to the arithmetic averageof the two temperatures, but curvature within thisrange can cause minor deviations from this value.Knowing the average boiling point for eachpseudocomponents and the K for the whole crude,

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FUNDAMENTALS

Table 4. Measured light-ends analysis

Component Volume percent of crude oil

Ethane 0.1

Propane 0.2

Isobutane 0.3

n-butane 0.7

Isopentane 0.5

n-pentane 1.2

Total 3.0

Table 5. Laboratory true boiling point (TBP) distillation, corrected to 760 mmHg

Liquid volume percent TBP temperature (°C)

3 36.1

5 65.0

10 97.8

20 165.6

30 237.2

40 310.0

50 365.6

60 410.0

70 462.8

80 526.7

100 871.1

10 20 30 40 50 60 70 80 90 100

800

900

700

600

500

400

300

200

100

0

�100percent distilled (liquid volume basis)

input TBP datafitted TBP curvecomponent cuts

tem

pera

ture

(°C

)

1,000

Fig. 2. Pseudocomponent representation of crude oil.

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which can be assumed to apply to each individualpseudocomponent and in the absence of any otherinformation about the distribution of paraffins,olefins, naphthenes and aromatics, the specificgravity for each pseudocomponent can becalculated. The techniques in the API technicaldata book can then be applied to generate all thenecessary thermo-physical property informationrequired for the simulation of any distillationprocess. Required properties include molecularweight, critical temperature, critical pressure,acentric factor (w), solubility parameter, ideal gasenthalpy equation coefficients and correlationcoefficients for other temperature-dependentthermo-physical properties, such as liquid density,viscosity and thermal conductivity. For example,the methods of Kesler and Lee (Kesler and Lee,1976) can be used to calculate critical temperatureand critical pressure:

[9] Tc�341.7 �811.0SG �(0.4244 �0.1174SG)Tb�(0.4669 �3.2623SG)�105�Tb

lnPc�8.3634 �0.0566�SG �(0.24244 �2.2898�SG �0.11857�SG2)�10�3Tb�(1.4685�3.648�SG�0.47227�SG2)�10�7Tb

2�(0.42019 �1.6977�SG2)�10�10Tb

3

where Tc and Tb are the critical and normalboiling temperatures (degrees Rankine), Pc is thecritical pressure in psia and SG is the specificgravity (60°F/60°F). The acentric factor w isestimated from an earlier work by Lee and Kesler(1975):

[10] w �(lnPR, b�5.92714 �6.09648�TR, b�1.28862�lnTR, b�0.169347TR, b

6)�(15.2518�15.6875�TR,b�13.4721lnTR, b�0.43577TR, b

6)

where R and b indicate reduced properties evaluated atthe normal boiling point.

The ideal gas enthalphy (in Btu/lb-mole) iscomputed bu integrating the following equation forideal gas:

[11] Cp0��0.33886�0.02827K�(0.9291�1.1543K�

0.0368K 2)�10�4T�1.6658 �10�7T2�(CF)[0.26105 �0.59332w �(4.56 �9.48w)�10�4T�(0.536 �0.6828w)�10�7T2 ]

The factor CF is given by:

[12] CF �[(12.8 �K)(10 �K)�(10w)]2

where K is KUOP factor, T is the temperature indegrees Ranking and w is the acentric factor.

API Procedure 2B2.1 can be applied to estimatethe molecular weight of a pseudocomponent, using thefollowing equation:

[13] MW �20.486[exp(1.165 �10�4Tb�7.78712SG�1.1582 �10�3TbSG)]Tb

1.26007SG4.98308

where SG is the specific gravity and Tb is the normalboiling point in degrees Rankine.

Once all pseudocomponents are characterizedand, assuming all property data are available forthe defined light-end components, a suitablethermodynamic method can be chosen for use inany computer simulation of the distillationprocess. In the 1970s, the method of Grayson andStreed (1963), who modified the Chao-Seader(Chao and Seader, 1961) correlation forequilibrium K-values, was often used with goodresults. In more recent times, equations of state,such as Soave-Redlich-Kwong (Soave, 1972) andPeng-Robinson (Peng and Robinson, 1976) havebeen increasingly used. The results of anysimulation are more sensitive to the choices made when characterizing the pseudocomponentproperties than from the choice ofthermodynamic method.

2.1.3 Simulation of crude oildistillation column

Assume we desire to make an initial split of thecrude oil described in Tables 4 and 5 into naphtha,kerosene, diesel and Atmospheric Gas Oil (AGO)fractions. A column to achieve this separation mightlook like the one depicted in Fig. 3. Called anatmospheric tower or topping still, this column takespartially vaporized crude oil, from which most of thewater, sediment and salts have been removed, from afurnace and rectifies it at a column pressure usuallyslightly above atmospheric pressure and less than2.7 bar absolute.

To control the initial boiling points (IBP) ofthe distillate products, side-streams from themain column are sent to side-stream stripperswhere steam is injected to remove some of thelighter components, which affect the IBP.Alternatively, these side strippers can be reboiled,but use of steam is more common. Steam isinjected into the base of the main column tolower the hydrocarbon partial pressure and toallow vaporization of the hydrocarbons at lowertemperatures, thus minimizing thermaldecomposition.

Reflux to the column is provided, in thisexample, from four sources. A conventionaloverhead condenser provides reflux to the topsection and three pumparound circuits providereflux to the lower sections. The presence of

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DISTILLATION PROCESSES

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these pumparound circuits serves to reduce thereflux requirements on the condenser, whileallowing heat to be removed from the column at ahigher temperature than at the condenser. Heat istransferred from these pumparound circuits intoheat exchangers that preheat the incoming crudeoil feed. The pumparound is attractive from thepoint of view of energy recovery. Pumparoundrates and heat exchange are used to control thedegree of overflash in the feed zone of thecolumn. The furnace must vaporize sufficient of

the feed to meet the distillate productrequirements and provide a small amount ofreflux (the overflash) from the trays immediatelyabove the feed entry point tothe flash zone.

Additional distillates in the 400°C to 600°Cboiling range (light and heavy vacuum gas oils) canbe recovered from the topped crude by furtherrectification in a vacuum distillation column. Such columns are designed to operate at very lowoverhead pressures, usually in the 100 mmHgrange.

For the purposes of the example, assume thedesired product qualities are described in Table 6.

Examining the TBP curve for the crude oil andmaking some assumptions about the number oftheoretical stages in sections of the column, thebehaviour of the column can be simulated with the aidof commercial software programs such as PRO/II,from Invensys/SimSci-Esscor and Aspen Plus fromAspen Technology. The pseudocomponents obtainedby applying the cutting profile to the TBP curve inFig. 2 are shown in Table 7. The molecular weights andcritical properties are calculated using the equationslisted above.

From Tables 1 and 6, the TBP mid-points of thedesired products can be approximated as 100°C,225°C, 305°C and 380°C for the naphtha,kerosene, diesel and atmospheric gas oil,respectively. These points can be reasonablyassumed to lie on the TBP curve of the crude oil.If the chemical components in the crude oil couldbe separated into fractions where there were nooverlapping components (i.e. a clean separationbetween components with adjacent boiling points)the individual distillate products would have TBPcurves that corresponded to the relevant portion ofthe crude oil TBP curve. For example, the TBPcurve of the topped crude, would be the same asthe final part of the TBP curve of the crude oil.

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FUNDAMENTALS

crudecolumn

crude oil

steam-1

topped crude

steam-2

steam-3

steam-4

kerosenestripper

kerosene

naphtha

diesel

gas oil

dieselstripper

gas oilstripper

Fig. 3. Typical refinery atmospheric crudedistillation column.

Table 6. Example product qualities from atmospheric crude unit

*TBP Temperature

Volume del liquido %

ASTM D86 temperatures (°C)

Liquidvolume % Naphtha Kerosene Diesel Gas oil Topped

crude

0 150 230 256

5 190 270 326 375*

95 170 270 350 475*

100 188 290 370 510*

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80 ENCYCLOPAEDIA OF HYDROCARBONS

DISTILLATION PROCESSES

Table 7. Selected properties of pseudocomponents derived from assay

Componentname NBP (°C) Specific

gravity KUOPMolecular

weightTC (°C) PC (kPa) Acentric

factor ( w)

Ethane �88.63 0.3564 19.43 30.070 32.30 4,883.05 0.0986

Propane �42.07 0.5077 14.70 44.097 96.67 4,248.87 0.1529

Isobutane �11.73 0.5631 13.81 58.124 134.98 3,647.10 0.1772

n-butane �0.50 0.5844 13.50 58.124 152.00 3,799.06 0.2013

Isopentane 27.85 0.6227 13.09 72.151 187.24 3,380.65 0.2290

n-pentane 36.07 0.6310 13.04 72.151 196.50 3,368.50 0.2506

NBP 44 44.34 0.7073 11.73 75.203 217.54 3,890.08 0.2344

NBP 59 59.04 0.7181 11.73 81.525 234.93 3,691.13 0.2543

NBP 73 72.94 0.7280 11.73 87.757 250.98 3,515.39 0.2744

NBP 86 86.74 0.7375 11.73 94.202 266.58 3,351.68 0.2954

NBP 100 100.07 0.7465 11.73 100.674 281.34 3,203.07 0.3166

NBP 114 114.04 0.7557 11.73 107.738 296.54 3,056.28 0.3397

NBP 128 127.99 0.7647 11.73 115.081 311.45 2,918.39 0.3636

NBP 142 141.92 0.7734 11.73 122.720 326.09 2,788.53 0.3882

NBP 155 155.84 0.7820 11.73 130.673 340.50 2,665.97 0.4135

NBP 169 169.75 0.7903 11.73 138.948 354.69 2,550.24 0.4395

NBP 183 183.62 0.7985 11.73 147.550 368.66 2,440.95 0.4661

NBP 197 197.50 0.8065 11.73 156.509 382.44 2,337.45 0.4932

NBP 211 211.38 0.8144 11.73 165.843 396.06 2,239.24 0.5209

NBP 225 225.26 0.8221 11.73 175.569 409.53 2,145.99 0.5491

NBP 239 239.14 0.8296 11.73 185.709 422.85 2,057.33 0.5779

NBP 253 253.05 0.8371 11.73 196.294 436.06 1,972.89 0.6072

NBP 267 266.96 0.8444 11.73 207.329 449.15 1,892.51 0.6370

NBP 280 280.86 0.8516 11.73 218.834 462.11 1,815.95 0.6673

NBP 294 294.78 0.8586 11.73 230.833 474.96 1,742.91 0.6980

NBP 308 308.70 0.8656 11.73 243.355 487.71 1,673.14 0.7292

NBP 322 322.60 0.8724 11.73 256.397 500.35 1,606.66 0.7607

NBP 336 336.49 0.8791 11.73 269.996 512.88 1,543.14 0.7926

NBP 350 350.39 0.8858 11.73 284.184 525.32 1,482.40 0.8250

NBP 364 364.28 0.8923 11.73 298.982 537.67 1,424.31 0.8576

NBP 378 378.10 0.8987 11.73 314.341 549.89 1,369.00 0.8905

NBP 391 391.89 0.9050 11.73 330.332 561.99 1,316.08 0.9237

NBP 405 405.71 0.9112 11.73 347.052 574.05 1,265.22 0.9572

NBP 419 419.64 0.9174 11.73 364.647 586.14 1,216.06 0.9914

NBP 440 440.58 0.9266 11.73 392.558 604.17 1,145.91 1.0434

NBP 468 468.34 0.9384 11.73 432.495 627.88 1,059.25 1.1134

NBP 495 495.20 0.9496 11.73 474.580 650.60 981.72 1.1822

NBP 523 523.14 0.9610 11.73 522.309 674.03 907.02 1.2549

NBP 551 551.24 0.9722 11.73 574.751 697.40 837.51 1.3289

NBP 579 579.16 0.9830 11.73 631.738 720.46 773.45 1.4034

NBP 607 607.02 0.9936 11.73 693.896 743.29 714.20 1.4785

NBP 634 634.85 1.0040 11.73 761.744 765.95 659.19 1.5542

NBP 675 675.10 1.0186 11.73 871.359 798.50 586.44 1.6644

NBP 729 729.02 1.0376 11.73 1,042.540 841.70 500.19 1.8130

NBP 784 784.67 1.0564 11.73 1,253.926 885.86 422.95 1.9653

NBP 842 842.10 1.0752 11.73 1,516.885 931.06 354.12 2.1186

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However, fractionation is imperfect betweendistillates and there is a considerable overlap ofcomponents between adjacent products. Thiscauses the TBP curves for the distillate products tohave lower initial and higher end points than thecorresponding part of the original crude oil fromwhich they were obtained. The concept of a cutpoint, relative to the original crude oil TBP curve,is still used and is useful in determining therespective quantities of each distillate product thatcan be obtained from a given crude oil.

It is at this point that knowledge of theEquilibrium Flash Vaporization (EFV)characteristics of the crude is valuable. For thecrude oil in this example, assume the maximumtemperature to which the crude oil feed can beheated in the furnace is limited to approximately375°C to avoid decomposition of the heaviermaterials and subsequent coking of the furnacetubes. Fig. 4 shows the EFV curve at the furnaceoutlet pressure of 1,406 mmHg (188 kPa)overlaid on the TBP curve at 760 mmHg for thecrude oil. The EFV temperature of 375°Ccorresponds to a fraction distilled ofapproximately 60% and an equivalent TBPtemperature of 420°C. This means that thecolumn and furnace should be able to separate60%, by volume, of the crude oil into distillateproducts, leaving 40% as topped crude. The cutpoint between the heaviest distillate product (theatmospheric gas oil and the topped crude) wouldbe approximately 420°C.

With this expected cut point between the AGOand the topped crude, the mid-point temperatures ofthe distillate products can be applied in decreasingorder to obtain the cut point temperatures for theother distillates. For example, with the AGO to

topped crude cut point as 420°C and the AGO mid-point as 380°C, the temperature range is(420�380)�40°C. Applying this range from themid-point of the AGO, gives a cut point for thediesel to AGO at (380�40)�340°C. For the dieselto kerosene cut point, the temperature range to themid-point of the diesel is now (340�305)�35°C.Applying this from the mid-point of the diesel givesa diesel to kerosene cut point of (305�35)�270°C.

Repeating the process gives the cut points and thecorresponding volume percentages of the originalCrude Oil, which can be read from the TBP curve(Tables 8 and 9).

The results of simulating this distillation withPRO/II are shown in Fig. 5. The original TBP curvefor the crude oil is overlaid with the ASTM D86curves for the resulting naphtha, kerosene, dieseland atmospheric gas oil. The TBP curve for thetopped crude is also shown. The curves for theproducts show significant ‘tails’, indicating thatthere is a considerable overlap of componentsbetween adjacent products. For example, thepresence of heavier boiling point components fromthe diesel cut in the kerosene cause the end pointof the kerosene to be higher than the original TBPcurve and, similarly, more volatile componentsfrom the kerosene cut are present in the diesel,giving it a lower initial boiling point. Clearly,separation could be improved with additionalreflux or more stages in the column, but thistranslates to higher furnace duty (and operating

81VOLUME II / REFINING AND PETROCHEMICALS

FUNDAMENTALS

percent distilled (liquid volume basis)

tem

pera

ture

(°C

)

EFV curve at 1,406 mmHgTBP curve at 760 mmHg

0

1,000

800

600

400

200

�200

10 20 30 40 50 60 70 80 90 100

Fig. 4. EFV curve for crude oil at furnace outletpressure and corresponding atmospheric TBP curve.

Table 8. Cut point temperatures between products

Cut Cut pointtemperature (°C)

AGO to topped crude 420

Diesel to AGO 340

Kerosene to diesel 270

Naphtha to diesel 180

Table 9. Approximate percentages of products based on whole crude

Product Volume % of crude oil

Topped crude 39.9

AGO 14.9

Diesel 10.9

Kerosene 12.4

Naphtha 21.9

Total 100.0

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cost) and increased capital cost for the column.The additional separation is unnecessary, as longas the distillate products meet their volatilityspecifications.

2.1.4 Mathematical modellingof distillation columns

BackgroundFor many years computer modelling of crude

oil distillation columns was considered verydifficult. However, with modern desktopcomputers and advances in algorithms, numerical analysis of crude towers is a standard

design tool. This section outlines the designequations for modelling crude oil distillationand presents algorithms for solving the equations.

The equilibrium model, depicted in Fig. 6, is represented by a set of equations commonlyknown as the MESH equations. MESH standsfor: Material balances, Equilibrium balances,Summation equations, entHalpy balances. Material balances are used to ensure that there is a material balance around each stage; the equilibrium balances ensure vapour-liquid equilibrium between the liquid and thevapour; the summation equations ensure that themole fractions sum to 1; the enthalpy balancesensure that there is an enthalpy balance around thestage.

There have been many different solutionalgorithms proposed for solving the MESH equations.The most popular algorithms are Newton based algorithms and Inside/Out (I/O)algorithms.

Newton based algorithms are attractive due to thewide range of systems which can be easily modelled.Design specifications are solved simultaneously withthe MESH equations. Newton methods requirereasonable starting estimates for the algorithm toconverge. The thermodynamic properties of K-valuesand enthalpies are not usually included in the matrix of

82 ENCYCLOPAEDIA OF HYDROCARBONS

DISTILLATION PROCESSES

10 20 30 40 50 60 70 80 90 100

fitted TBP curve naphtha D86

kerosene D86

diesel D86

gas oil D86

topped crude TBP

naphtha-kerosene cut point

kerosene-diesel cut point

diesel-gas oil cut point

gas oil-topped crude cut point

percent distilled (liquid volume basis)

tem

pera

ture

(°C

)

1,000

800

900

700

600

500

400

300

200

100

�100

0

Fig. 5. Original crude oilTBP curve with productassay curves overlaid.

VjV

VjV �1

LjL �1

LjL

Fig. 6. Equilibrium stage.

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equations being solved simultaneously, but are solvedin external functions.

The Inside/Out class of algorithms (Boston andSullivan, 1974; Russell, 1983) defines a strippingfactor (KV/L). For a set of stripping factors and sidestream withdrawal factors and a simple K-valuemodel, the component molar flows and traytemperatures can be computed directly. The Inside/Outalgorithm is particularly well suited for crude columnsimulation.

In the I/O algorithm each material balance issolved with constant K-values in an inner loop. Inthe outer loop, the enthalpy balances and designspecifications are solved by manipulating thenatural log of the stripping factor and thesidestream withdrawal ratios to drive the enthalpybalance errors and design specification errors tozero. The log transformation is used to keep thestripping factors and sidestream withdrawal ratiospositive.

In the following a distillation column will beconsidered with all auxiliary equipment (i.e.condenser and reboiler); however, it should be pointedout that the topping column is not equipped with anyreboiler, as shown in Fig. 3.

MESH equations and variablesThe MESH equations can be written using

component molar flows or mole fractions asindependent variables. The formulation presentedhere will use mole fractions. When far from thesolution, Newton solvers have a tendency tooverpredict the corrections to the independentvariables. Mole fractions are limited to the range of0 to 1 because most thermodynamic sub-routinesexpect this. In particular, cubic equation of statescan encounter negative square roots if the molefractions do not sum to 1.The independent variables are shown in Table 10. In this formulation, there are (2NOC+3)variables for each equilibrium stage, assuming noside draws (NOC is the Number Of Components).

For the purposes of this model it is assumed that eachtray operates at a specified fixed pressure.

Following are the MESH equations:• Material balance equation:

[14] mbi, j��xi, j�1Lj�1(1�SRLj�1)�xi, jLj�yi, jVi, j�

yi, j �1Vj �1(1�SRVj �1)�

nf

�k�1

Fjkzi, k

where Fjk is total flowarate of the (k-th) feed to stagej, zi, k is the mole fraction of the (i-ith) component inthe (k-th) feed to stage j and nf is the number of feedsto stage j.• Vapour/liquid equilibrium equation:

[15] eqi, j�yi, j�K(x,y,T)i, j xi, j

• Summation equations:

[16] sxj�noc

�i�1

xi, j�1

[17] syj�noc

�i�1

yi, j�1

• Energy balance equations:

[18] ej ��Lj�1(1�SRLj�1)H

Lj�1(T,x)�LjH

Lj (T,x)�

Vj HVj (T,y)�Vj�1H

Vj�1(T,y)�

nf

�k�1

FkHkF

There are a total of (2NOC + 3) equations for eachequilibrium stage (excluding side draws).

2.1.5 Solving the MESH equations

The first step solving the equations refers to adistillation column without any auxiliary equipment(conventionally called absorber).

Solving the MESH equations is generally done with Newton’s method (also knownas the Newton-Raphson algorithm) or somemodification of Newton’s method. Newton’s methodconsiders only the first derivative and uses this tocompute corrections so that all of the equations aresolved using one linear correction term to each

83VOLUME II / REFINING AND PETROCHEMICALS

FUNDAMENTALS

Table 10. Independent variables in mathematical model

xi,j Liquid phase mole fraction of component i on stage j

yi,j Vapor phase mole fraction of component i on stage j

Lj Total liquid phase molar flowrate leaving stage j

Vj Total vapor phase molar flowrate leaving stage j

Tj Temperature of liquid and vapor phases on stage j

SRLj Liquid side stream withdrawal ratio on stage j, 0�no draw, 1�total draw

SRVj Vapor side stream withdrawal ratio on stage j, 0�no draw, 1�total draw

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independent variable. In matrix form Newton’smethod is expressed as:

[19] Dx��J �1f (x)

where J is the (n�n) Jacobian matrix of firstderivatives and f (x) is the vector of equationresiduals from the MESH equations. For an absorberthe Jacobian matrix J has the block tri-diagonalstructure illustrated in Fig. 7. This was first reportedby Naphtali and Sandholm (1971).

In Fig. 7, the A sub-matrix represents theJacobian coefficient contributions from the liquidentering from the stage above, the B sub-matrix isthe contributions from the liquid and vapour leavingthe stage and the C sub-matrix is the contributionsfrom the vapour below. Each of these sub-matrixblocks will contain their own sparsity pattern.Outside of these blocks the remaining entries in theJacobian are all zeros.

The structure shown in Fig. 7 can be solvedusing a block tri-diagonal form of the Thomasalgorithm for solving tri-diagonal systems. However,in practice this approach is not used because it is not

flexible enough to handle the addition ofpumparounds and design specifications.

One of the problems with using Newton’smethod is that the corrections returned from theNewton update formula may result in one or more ofthe independent variables going outside ofphysically meaningful bounds. For example, it ispossible that one or more mole fractions couldbecome greater than one or less than zero if the fullNewton step is applied. To avoid this, a dampingfactor is typically applied

[20] xik�1�xi

k�aDxik

where x is any variable and a is a scalar between 0 and1. The scalar a is determined so that variables do notexceed upper and lower bounds and so that the variabledoes not change beyond some reasonable value.

When solving wide boiling systems and inparticular crude oil distillation problems, it isparticularly important that if a given mole fraction isbelow some tolerance, it is not included in the decisionto determine the limiting value of a. Often duringsolution a trace component on a stage may get acorrection large enough to influence a. Typically somecomponent with a mole fraction less than 1.0 �10�6

may have a negative correction larger than the value ofthe mole fraction. Suppose some mole fraction of1.0 �10�10 has a correction of �1.0 �10�8: this wouldresult in an a value of 0.01 and if used would impedethe convergence. For this reason some tolerance mustbe set to determine if a variable and its correction areto be used in determining a.

When a trace component mole fraction has anegative correction from the Newton step, some actionmust be taken to prevent the mole fraction frombecoming negative. One heuristic that works well is tomove the variable from the current value half way tothe lower bound. Alternatively the value of a can beused in the update expression to facilitate linesearching for the minimum in the search direction.For these special trace components the followingupdate formula can be used for negative corrections:

[21] xik�1�xi

k�a(xik�xLO)0.5

where the constant 0.5 indicates that for a full step thevalue of x moves half way to the lower bound. Thissort of heuristic is very important for successfulsolution of crude oil distillation problems usingNewton’s method.

2.1.6 Condensers and reboilers

Adding condensers and reboilers isstraightforward using Newton’s method. Fig. 8

84 ENCYCLOPAEDIA OF HYDROCARBONS

DISTILLATION PROCESSES

B C

A B C

A B C

A B C

A B C

A B

Fig. 7. Block tri-diagonal matrix structure.

overheadvapour

distillate product

overheadliquid

distillate product

reflux returnto top of

tray section

vapourfeed

from top oftray section

energy stream

Fig. 8. Equilibrium condenser.

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shows the schematic diagram of a condenser withboth a liquid and vapour distillate product as wellas the reflux stream returning to the top of thetray section. Because the formulation chosen hereuses total liquid and vapour rates as independentvariables, the mass balance at the condenser isquite straightforward:

[22] mbi, j�xi,1L1�yi,1Vi,1�

yi, j �1Vj �1(1�SRVj�1)�

nf

�k�1

Fkzi, k

The enthalpy balance becomes:

[23] e1�L1HL1 �V1HV

1 �V2HV2 �

nf

�k�1

FkH Fk �Q1

where L and V represent the total liquid and vapourleaving the stage.

The mole balance for stage 2 is given as follows:

[24] mbi,2��xi,1L1(1�SRL1 )�xi,2L2�

yi, jVi,2�yi,2�1V2�1(1�SRV2�1)�

nf

�k�1

Fkzi, k

There is no change to the material balance at thereboiler but the enthalpy balance becomes:

[25] er��Lr�1HLr�1�LrHL

r �Vr �

V2HV2�

nf

�k�1

FkHFk �Qr

Adding the condenser and reboiler hasintroduced three new independent variables, shownin Table 11. These three new variables introducethree degrees of freedom into the problem. Thisrequires three design specifications to be made tofully specify the system.

2.1.7 Design specifications

One of the strengths of Newton’s method is the widerange of design specifications that are possible. Forthis example, the following design specifications willbe added: vapour distillate rate, liquid distillate rate,reflux ratio.

The vapour distillate rate specification is easy toimplement because the total vapour leaving eachequilibrium stage is an independent variable. If V1

SP

represents the specified vapour flowrate, the designspecification equation is:

[26] sp1�V1�V1SP

The liquid distillate rate specification must be castin a form that uses the liquid side stream withdrawalratio. As above, let represent the specifiedliquid distillate flowrate. The design specification is:

[27] sp2�L1SRL1 �L1

SP

where L1 is the total liquid leaving the condenser andSRL

1 is the fraction of the total liquid removed as a sidedraw product.

For this definition of the reflux ratio the vapourdistillate will be ignored. Taking the reflux ratio as theratio of the reflux flowrate to the liquid distillateproduct and RRSP as the specified reflux ratio givenresults in the design specification of:

L1(1�SRL1 )

[28] sp3�112121�RRSPL1SRL

1

This reduces to:

1[29] sp3�SRL

1 �1121RRSP�1

2.1.8 Solving the MESH equationsfor the fully equippeddistillation column

Adding in design specifications changes thestructure of the Jacobian matrix. Often design

85VOLUME II / REFINING AND PETROCHEMICALS

FUNDAMENTALS

Table 11. Additional variables associated with condenser

Qc Condenser duty

Qr Reboiler duty

SRL1

Side stream withdrawal ratio for liquid distillate product at condenser

B C

A B C

A B C

A B C

A B C

A B

design specifications (equations)

Fig. 9. Block tri-diagonal block bordered matrix structure.

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specifications are placed on the bottom rows ofthe matrix and the additional variables are addedto the right hand side of the matrix. This is doneto keep each B sub-matrix square. Strictlyspeaking this is not necessary because the rank ofthe Jacobian is not a function of the location ofthe design specification equations, but ittypically makes programming easier. Fig. 9 shows the structure of the resulting blocktri-diagonal block bordered matrix that emergesfrom summing the design specificationsand addition variables to the Jacobianmatrix.

2.1.9 Pumparounds

Pumparounds are used as a heat transfer mechanismin crude oil distillation columns. Due to the wideboiling nature of the crude mixture and the largetemperature change across the crude distillationtower, pumparounds are used to remove heat andhence create a more even distribution of liquidreflux. Fig. 10 shows the schematic diagram of apumparound.

Pumparounds introduce additional terms into theheat and material balances as follows:• Material balance:

[30] mbi, j��xi, j �1Lj �1(1�SRLj �1)�

xi, jLj�yi, jVi, j�yi, j �1Vj�1(1�SRVj �1)�

nf

�k�1

Fkzk, i�nf

�k�1

LkSRLk xi, k

where the term nf

�k�1

LkSRLk xi, k represent the contribution

from pumparounds on other stages entering stage j.• Energy balance:

[31] ej��Lj �1(1�SRLj �1)HL

j �1(T,x)�

LjHLj (T,x)�Vj HV

j (T,y)�Vj �1HVj �1(T,y)�

nf

�k�1

FkHFk �

nf

�k�1

LkSRLk HL

k

where the term nf

�k�1

Lk SR Lk H L

k represents the enthalpy

contribution for each pumparound entering stage j.

Design specifications for pumparoundsPumparounds add variables for the side stream

withdrawal ratio used to determine the flowrate ofthe pumparound and the energy added or removed inthe pumparound. Therefore each pumparoundintroduces two additional degrees of freedom tothe equation set.

Pumparound rate specifications are oftenincluded in the design equations. Usually the rate is

specified in standard liquid volume units, reflectingstandard design practice. The other degree offreedom can be a constant duty specification or atemperature drop across the pumparound heatexchanger. These rating specifications are used todetermine the separation for a fixed amount of heattransfer.

Design specifications are sometimes made foronly one pumparound quantity, allowing the otherdegree of freedom to be used for a performancespecification: for example, the D86 cut point may bespecified. This allows the engineer to ask thequestion how much cooling needs to be provided in

86 ENCYCLOPAEDIA OF HYDROCARBONS

DISTILLATION PROCESSES

Fig. 10. Pumparound schematic diagram.

B C

A B C D

A B C

A B C

A B C

A B

design specifications (equations)

Fig. 11. Jacobian structure with pumparound.

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order to achieve this distillation cut pointspecification.

Crude distillation towers may typically containthree pumparounds. In this situation, while thereare interactions between the pumparounds and theside products from the crude tower, a givenpumparound will have the strongest effect on thedraw tray closest to the pumparound moving downthe tower. This is because the pumparoundcauses an increased flow of reflux which movesdown the tower and provides additionalrectification for product draws below thepumparound.

Jacobian matrix with pumparoundsAdding pumparounds to a distillation column

results in off-diagonal blocks containing non-zerocomponents. This occurs because the pumparoundlinks stages that are not adjacent. Fig. 11 shows theresulting Jacobian matrix structure. Sub-matrixblock D is the result of the pumparoundcontribution.

2.1.10 Side-strippers

The final component needed for modelling a crudedistillation tower is a side-stripper. Side-strippersare used to perform stripping on distillationproducts. Usually stripping steam is fed to thebottom of the side-stripper, although some side-strippers are reboiled. Side-strippers provide anadditional degree of operational control todetermine product initial and end points ofdistillation curves. Fig. 12 shows the schematicdiagram of a stem fed side-stripper.

References

API (American Petroleum Institute) (1983) Technical data book.Petroleum refining, Washington (D.C.), API, 2v.; v. I.

Boston J.F., Sullivan S.L. Jr. (1974) A new class of solutionmethods for multicomponent, multistage separationprocesses, «Canadian Journal of Chemical Engineering»,52, 52-63.

Chao K.C., Seader J.D. (1961) A general correlation ofvapor-liquid equilibria in hydrocarbon mixtures,«American Institute of Chemical Engineering Journal»,7, 598-605.

Grayson H.G., Streed C.W. (1963) Vapor-liquid equilibriafor high temperature, high pressure hydrocarbon-hydrocarbon systems, in: Proceedings of the 6th Worldpetroleum congress, Frankfurt am Main, 19-26 June.

Kesler M.G., Lee B.I. (1976) Improved prediction ofenthalpy of fractions, «Hydrocarbon Processing», 55,153-158.

Lee B.I., Kesler, M.G. (1975) A generalized thermodynamiccorrelation based on three-parameter corresponding states,«American Institute of Chemical Engineers Journal», 21,510-527.

Maples R.E. (2000) Petroleum refinery process economics,Tulsa (OK), PenWell.

Naphtali L.M., Sandholm D.P. (1971) Multicomponentseparation calculations by linearization, «American Instituteof Chemical Engineers Journal», 17, 148-153.

Peng D.Y., Robinson D.B. (1976) A new two-constant equationof state, «Industrial and Engineering ChemistryFundamentals», 15, 59-64.

Russell R.A. (1983) A flexible and reliable method solvessingle-tower and crude-distillation-column problems,«Chemical Engineering», 90, 53-59.

Soave G. (1972) Equilibrium constants from a modifiedRedlich-Kwong equation of state, «Chemical EngineeringScience», 27, 1197-1203.

Twu C.H. (1984) An internally consistent correlation forpredicting the critical properties and molecular weights ofpetroleum and coal-tar liquids, «Fluid Phase Equilibria»,16, 137-150.

David BluckInvensys SimSci Esscor

Lake Forest, California, USA

87VOLUME II / REFINING AND PETROCHEMICALS

FUNDAMENTALS

sideproductsteam feed

Fig. 12. Side-stripper schematic diagram.

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