.Fuel Processing Technology 73 2001 121www.elsevier.comrlocaterfuproc

A crude distillation unit model suitable foronline applications

Vineet Kumar 1, Anuj Sharma, Indranil Roy Chowdhury,Saibal Ganguly 2, Deoki N. Saraf )

Department of Chemical Engineering, Indian Institute of Technology, Kanpur-208016, IndiaReceived 1 June 2000; received in revised form 1 February 2001; accepted 1 April 2001

Abstract

A steady state, multicomponent distillation model particularly suited for fractionation of crudeoil has been developed based on equilibrium stage relations. For a mixture of C components, thepresent formulation uses Cq3 iteration variables namely the mole fractions of the components,temperature, total liquid and total vapor flow rates on each stage. This choice of variables makesthe present model numerically stable and robust rendering a separate initial guess computationunnecessary. An improved scheme of numbering the equilibrium stages when side strippers arepresent, was found to be advantageous with respect to computation time. Selected exampleproblems have been included from literature as well as industry to demonstrate the efficacy andusefulness of the method. The accuracy of predictions and speed of solution of the modelequations are particularly suited for online applications such as online optimization. q 2001Elsevier Science B.V. All rights reserved.

Keywords: Multicomponent distillation model; Crude oil; Online applications

1. Introduction

The petroleum refining industry is one of the largest users of distillation technology.The crude distillation unit is one of the most important refinery operations fractionating

.preheated crude oil into respective product fractions like Heavy Naphtha HN , Kerosene

) Corresponding author. Tel.: q91-512-597-827; fax: q91-512-590-104. .E-mail address: dnsaraf@iitk.ac.in D.N. Saraf .

1 Dr. Vineet Kumar is Assistant Professor in the Department of Chemical Engineering, Thapar Institute ofTechnology, Patiala, India.

2 Dr. S. Ganguly is Associate Professor in the Department of Chemical Engineering, Indian Institute ofTechnology, Kharagpur, India.

0378-3820r01r$ - see front matter q2001 Elsevier Science B.V. All rights reserved. .PII: S0378-3820 01 00195-3

( )V. Kumar et al.rFuel Processing Technology 73 2001 1212

. . . .SK , Aviation Turbine Fuel ATF , Light Gas Oil LGO , Heavy Gas Oil HGO , .Reduced Crude Oil RCO , etc. Therefore, it becomes extremely important to model the

crude distillation unit to predict the composition of products from various crudes, whichare processed under different operating conditions. The model thereby acts as anessential tool for production planning and scheduling, economic optimization andreal-time online control and performance optimization. Additionally, such a model isalso an essential prerequisite for a project engineer attempting either design of new unitsor rating of existing units.

2. The model

The model equations for an ordinary equilibrium stage of a simple distillationcolumn, commonly known as Mass balance, Equilibrium, Summation and Enthalpy

. w xbalance MESH equations, have been given by several workers 17 . These fundamen-tal material and energy balance equations are available in literature in terms of differentnomenclatures and variable definitions to facilitate numerical stability and ease of

.convergence. For a general equilibrium stage see Fig. 1 , we present one set of theseequations in Table 1.

Before proceeding any further, it must be stated that from a practical view-point, it isnot possible to represent the feed crude oil or its distillation products in terms of actualcomponent flow rates or mole fractions since crude oil is a mixture of several hundredconstituents which are not easy to analyze. A generally accepted practice is to expresscomposition of crude in terms of a finite number of pseudocomponents. Each pseudo-component, which is treated as a single component, is in fact a complex mixture ofhydrocarbons with a range of boiling points within a narrow region say 25 8C wide.Each pseudocomponent is characterized by an average boiling point and an averagespecific gravity.

Fig. 1. Schematic diagram of an equilibrium stage.

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Table 1Model equations for multicomponent, multistage distillation .1 Component material balance equation on ith stage

V L w x s l qD qD PartialCondenser2, j 1, j j j

L w x w x s l qD TotalCondenser is1; js1, . . . ,C2, j 1, j j

L V . . . .l q l q q y l qw y qw q f s0.iy1, j p, j iq1, j q, j i, j i, j i, j i, j i, jw x w x .is2, . . . , Ny1; js1, . . . ,C l s qB isN; js1, . . . ,C 1Ny1, j N , j j

L V . .f may be liquid f or vapor f feed or a mixture of both. The liquid feed enters above the feed stagei, j i, j i, jand vapor feed enters below it. .2 Liquid summation equation

Cw xL s l is1, . . . , Ni i j

.js1 2

.3 Vapor summation equation

. w x w xV s L rRR TotalCondenser is11 1

Cw xV s is2, . . . , N if TotalCondenser else is1, . . . , Ni i, j

.js1 3

.4 Enthalpy balance equation

C C C C CL .l h q l h q H q H y l qw h iy1, j iy1, j p, j p, j iq1, j iq1, j q, j q, j i, j i, j i, j

js1 js1 js1 js1 js1

C CV F . w xy qw H q f H "Q s0 is2, . . . , Ny1 i, j i, j i, j i, j i, j i

js1 js1

C C Cw xl h s H q l h isN Ny1, j Ny1, j N , j N , j N , j N , j

.js1 js1 js1 4

.5 Equilibrium relation

w x .y sK x is1, . . . , N; js1, . . . ,C 5i, j i, j i, j .In case of total condenser is2, . . . ,N with

1 i, jx si, j Liand

i, jy si, j Vi

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There are several ways of grouping the variables for numerical solution of the set ofw xnonlinear algebraic equations. For a simple column, Naphtali and Sandholm 1 arranged

the equations so as to yield a block-tridiagonal matrix structure. This type of groupingreduced the required data storage capacity by taking advantage of the tri-diagonal

structure of the resultant Jacobian matrix. The authors replaced mole fractions 2 NC. .variables and total flow rate 2 N variables by component flow rates to reduce the

. .number of variables. Thus, N 2Cq3 stage variables were reduced to N 2Cq1 . Forcomplex columns with pumparounds and side strippers, off diagonal elements appear

w xapart from the tri-diagonal structure. Hofeling and Seader 3 used a modified Thomasalgorithm to solve the model equations for complex columns using the Naphtali andSandholm formulation.

w xTo reduce the matrix size, there are other types of formulations 2,6,8 with different . .variable groupings of Cq2 and Cq3 variables per stage. In these methods, the

remaining variables are calculated explicitly. A list of independent variables, explicitlycalculated variables and model equations to be used in different formulations arepresented in Table 2.

In the NaphtaliSandholm method, variables are grouped component-wise and theentire equation set is solved simultaneously. Tomich used stage-wise grouping ofvariables and solved the problem in two stages. In the outer computation loop the V andiT are upgraded in each iteration, whereas an inner loop solves for l . While Tomichi i jmethod has been found to be more suited for columns with fewer stages, NaphtaliSandholm works better for columns having fewer components. The inside-out algorithm

w x w xof Boston 5 which was latter modified by Russel 6 is considered to be suitable forproblems where both number of stages as well as components are large such as in crudefractionation. It, however, uses three levels of convergence to solve the problem. Thepresent method is simultaneous implying all model equations are solved simultaneouslyallowing all variables to be upgraded at the same time, which makes this method morerobust and efficient.

2.1. Numbering of stagesThe crude distillation units have pumparound streams and side strippers, which result

in off-diagonal elements in the Jacobian matrix. The location of the off-diagonal

Table 2Number of variables and equations involved in different distillation modelsNo. of variables Independent Explicitly defined Model equations

variables variables . w x . . .N 2Cq1 1 l , , T L sSl , V sS , Eqs. 1 , 4 and 5i j i j i i i j i i j

x s l rL , y s rVi j i j I i j i j I . w x . . .N Cq2 2 l , V , T L sSl , x s l rL , Eqs. 1 , 3 and 4i j i i i i j i j i j I

y sK xi j i j i j . w x . . .N Cq3 6 l , L , V , T x s l rL , Eqs. 1 , 2 , 3i j i i i i j i j I

.y sK x and 4i j i j i j . . . .N Cq3 Present x , L , V , T y sK x Eqs. 1 , 2 , 3i j i i i i j i j i j

.work and 4

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elements with respect to the main tridiagonal band has been found to influence theconvergence path and CPU time considerably during the present study. Conventionally,the stages in the main distillation column are numbered from top to bottom and then theside stripper trays are numbered in a sequence. This nomenclature generates off-diagonalelements far removed from the main tridiagonal band resulting in a very large computa-tional effort. Actually, farther an element is positioned with respect to the band, largerwill be computational load. The stages were, therefore, renumbered from top down insuch a way that when connection with a side-stripper was reached, the stages of thatside-stripper were numbered in succession, returning to the main column and continuingfurther. This scheme of numbering ensured that the off-diagonal terms were as close tothe diagonal as possible thus reducing computation time as compared to the conven-tional scheme of numbering.

2.2. Solution procedure

The method of solution involves solving simultaneously the system of nonlinearequations representing component mass conservation, energy conservation and thesummation equations for each stage of the distillation column. Traditionally, a set ofnonlinear algebraic equations is solved using the NewtonRaphson method. In thismethod, the nonlinear equations are linearized at every iteration and because of whichthe procedure is known to diverge for highly nonlinear equations when the initial guessis far removed from the final solution. If the number of nonlinear equations is large thenthe resultant Jacobian matrix may become ill-conditioned leading to slow convergenceor even at times to non-convergence. Several modifications have been suggested to

w x w xovercome the convergence problems 9,10 . Rogoza and Gorodetskaya 11 suggested amultilevel solution method in which the equation set is decomposed into subproblems

w xleading to substential reduction in computation times. Hu 12 discussed an algorithm inwhich a sparse large nonlinear system of equations is solved using parallel processing

w xcomputations. Martin and Rivera 13 presented a parallel algorithm based on anasynchronous scheme, which permitted high performance when the Jacobian matrix was

w xsparse. Shahadat Hossian and Steihaug 14 discussed an efficient method for estimationof large sparse Jacobian matrix employing forward and reverse mode of automaticdifferentiation. Homotopy methods have been applied to difficult-to-solve distillation

w xcolumn problems 15,16 in which a homotopy curve is tracked to force the convergencew xto the desired solution. Recently, He 17 described an algorithm in which the conven-

tional perturbation method was coupled with a homotopy technique for improvedefficiency. In the present study, the correct choice of independent variables set reducedthe nonlinearity of the model equations allowing conventional NewtonReplson methodto converge even from far away initial guess. A sparse matrix method further enhancedthe efficiency of solution. We demonstrate the stability and efficiency of the techniquehere.

2.2.1. Soling a system of nonlinear equations . n nLet f x :VR be a system of nonlinear equations, where V:R , xgV ,

T . .T . . .. . nx s x , x , . . . , x , f x s f x , f x , . . . , f x and f x :RR is continu-1 2 n 1 2 n i

( )V. Kumar et al.rFuel Processing Technology 73 2001 1216

ously differentiable with respect to each component of x for is1,2, . . . ,n. Let us) ) . )assume that there exists x gV such that f x s0. Let x be an estimate for x . To

.calculate the correction D x, such that f xqD x s0 Taylor series expansion isemployed.

f xqD x s f x q f X x D xqg x ,D x , 6 . . . . . . .where g x,D x is the error in the linear approximation.From Eq. 6

y1 y1X XD xsyf x f x y f x g x ,D x . 7 . . . . .

.Since g x,D x is not known and depends upon D x, hence D x is estimated asy1X

D xsyf x f x . 8 . . .The correction D x is applied repeatedly to the new estimate of x) to obtain the final

) . .estimate of x . From Eq. 7 , we can conclude that a formulation f x of a problemwhich results in a relatively lower error of linear approximation for a given D x andequivalent estimates of x) will converge in less number of iterations and its depen-dence on the choice of initial estimate will also decrease. This is the reason for theconvergence of a system of linear equations in one iteration starting from any initial

w xestimate 18,19 as there is no error of linearization for linear equations.

2.2.2. Model equationsFor the ith stage of a multicomponent distillation problem for a simple column, the

Cq3 formulation uses x , L , V and T as independent variables to write thei, j i i ifollowing equations.

Mass balanceDC sV K x qL x yL x yV K xi , j iq1 iq1, j iq1, j iy1 iy1, j i i , j i i , j i , j

Energy balanceDH sV K x H qL x h yL x hi iq1 iq1, j iq1, j iq1, j iy1 iy1, j iy1, j i i , j i , j

yV K x Hi i , j i , j i , jSummation equation

DV sV yV K xi i i i , j i , jDL sL yL xi i i i , j

Here DC , DH , DV and DL are the discrepancies in the model equations whichi, j i i ivanish at the solution.

The above formulation is refered to as Cq3 formulation, since there are Cq3equations in the model and as many variables to be calculated.

2.2.3. Comparision of Cq2 and Cq3 formulationsw xCq3 formulation is a modification of Cq2 formulation 2 . The modification has

been suggested by the need to minimize the inflationary tendency of the error of linearapproximation.

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The variables of Cq2 formulations are l , V and T .i j i iMass balance

V K l V K liq1 iq1, j iq1, j i i , j i , jDC s q l y l yc ci , j iy1, j i , jl l iq1,k i ,k

ks1 ks1

Energy balancec cViq1DH s K l H q l h ci iq1, j iq1, j iq1, j iy1, j iy1, j

js1 js1l iq1,kks1

c cViy l h y K l H ci , j i , j i , j i , j i , jjs1 js1l i ,k

js1

Summation equationcViDV sV y K lci i i , j i , j

js1l i ,kks1

The reason for multiplying the summation equations in Cq3 and Cq2 formulationsby the respective total molar flow rates is that their order of magnitude becomecomparable to the mass and energy balance discrepancies.

We now show that the error of linearization in Cq2 formulation has a greatertendency to inflate as compared to the Cq3 formulation. For this comparison, let usconsider a single stage distillation problem. A two component feed with F moles of1component 1 and F moles of component 2 is fed to this stage which is being kept at2temperature T. Since the temperature is known, energy balance discrepancy is notrequired.

The Cq2 formulation of this problem is

DC sF y l yV K l r l q l .11 1 11 1 11 11 11 12DC sF y l yV K l r l q l .12 2 12 1 12 12 11 12DV sV yV K l qK l r l q l . .1 1 1 11 11 12 12 11 12

The discrepancies of the above problem in Cq3 formulation are as follows.DC sF yL x yV K x11 1 1 11 1 11 11DC sF yL x yV K x12 2 1 12 1 12 12DV sV yV K x qK x .1 1 1 11 11 12 12DL sL yL x qx .1 1 1 11 12

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It is clear that in Cq3 formulation the discrepancies are linear with respect to theindependent variables x , x , V , L and, therefore, the error of linear approximation11 12 1 1will be zero and hence the problem will converge starting from any initial estimate. Thisdecrease in the nonlinearity of the system by choosing the correct set of independentvariables is the major gain of Cq3 formulation over Cq2 formulation which makes itconverge faster and the dependence on initial estimate also decreases. This stability ofCq3 formulation has been tested with a number of practical problems. The componentliquid flow rate appears in the denominators of the equations of the Cq2 formulation.This makes the error of linearization inflate if all the liquid component flows on a traytake on small values during any iteration. These remarks apply to all those methodswhich use l as iteration variables as distinguished from x which has been used ini, j i, j

w xthe present case. Russels method 6 which, although uses Cq3 variables, suffers fromw xthe same error of inflation as Cq2 formulation of Tomich 2 as it too uses l asi, j

iteration variables.

2.2.4. Solution of model equationsThe independent variables which are iterated upon in Cq3 formulation for the ith

stage are x , V , L , T . Let x k be the present estimate of the solution then the nexti, j i i iestimate is calculated as

y1Xkq1 k k kx sx yb f x f x , 9 . . .where b is the step length and is calculated by minimizing

Tkq1 kq1minf x f x . . .b

For nonlinear problems, it is well known that the choice of an initial guess plays a veryimportant role in finding the solution. If the initial guess is far from the final solution, analgorithm may either not converge or take large computation time. This is because of theerror of linearization, which is likely to be substantial if the initial guess is far away.Any effort in reducing the error of linearization is, therefore, expected to make thealgorithm more robust and stable. Most existing algorithms for distillation columnmodeling solve model equations approximately or solve a simplified model to obtain aninitial guess for component flow rates or mole fractions before embarking on actualsolution procedure. This is unnecessary in the present case and feed composition servesas a satisfactory initial guess for the iterated variables, x .i j

. X k .y1 k .The major computational effort in solving Eq. 9 is in calculating f x f xwhich is obtained by solving the system of linear equation

f X x k D xs f x k . 10 . . .Suppose a distillation problem has 80 stages with 25 components, then the system of

.linear equations is of dimension 80 25q3 s2240 equations. This implies that theJacobian of such a large system is of dimension 2240=2240. To store such a largematrix in single precision, it requires at least 40MB of memory, which is available even

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in personal computers these days. Hence storage of such large a matrix in computermemory is no longer a problem. The only problem is the computation time in solvingsuch a large system. To reduce the computation time advantage is taken of the sparsity

X k .of the Jacobian matrix f x . Usually not more than 5% of the elements of theJacobian are nonzero. The fundamental algorithm for solving the system of linear Eq. .10 is Gaussian elimination with partial pivoting which has been modified to takeadvantage of the sparsity of the Jacobian.

3. Thermodynamics

Crude characterization is commonly based on the method proposed by Miquel andw x .Castells 20,21 for petroleum fractions, which requires the true boiling point TBP

curve along with the average specific gravity for the fraction. For breaking the crudeinto pseudocomponents, the given TBP data are regressed in a piece-wise manner usingsplines. Using an iterative procedure as given by Miquel and Castells, the values of .T and S are obtained for each pseudocomponent. Thermodynamic quantities likeavg j j

. . .critical temperature T , critical pressure P and acentric factor w can then bec j c j jw xcalculated by using suitable correlations like those proposed by Riazi and Daubert 22

w xand Edmister and Lee 23 . .For a distillation column simulator, computation of equilibrium constants K ofi j

various components present and enthalpies of different streams as functions of tempera-ture and composition are essential. Since petroleum fractions are complex mixtures ofhydrocarbons, single pure component thermodynamics is not applicable. In estimation ofthese thermodynamic properties, the use of empirical or semi-empirical correlations isquite popular. Some of the commonly used techniques are based on the cubic equation

w x w x w xof state proposed by PengRobinson 24 , RedlichKwong 25 and Soave 26 .Thermodynamic properties of vaporliquid mixtures are generally predicted by

calculating deviations from ideality of both the vapor and liquid phases by using any ofthe above mentioned equations of state. In a second method, the equation of state isapplied only to the vapor phase while liquid phase deviations from ideal solution

w xbehavior are calculated using thermodynamic excess functions 2729 . For a rigorouscrude distillation simulator, it is important to use prediction models for the thermody-namic properties, which are continuous functions, and are applicable in the entire range

.of temperature say 0500 8C for the lighter as well as the heavier components.Additionally, to ensure smooth convergence, there should not be any discontinuity ofreal roots for the equations of state in the entire domain of operation of the crudedistillation unit. While, it is still possible to use an equation of state or a combination ofsome of the above methods to cover the entire boiling point range, the computationaleffort required in this approach is prohibitive as the thermodynamic properties arerequired to be calculated repeatedly for each iteration. For online usage, the computationtime is of utmost concern and hence, equation of state approach is not convenient to use.

In view of above, a correlation was developed in the present work using dataobtained from PengRobinson equation for the lighter hydrocarbons and those from

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Fig. 2. Comparison of equilibrium constants calculated by various methods for a low boiling pseudo-compo- .nent T s292.18 K .b

Fig. 3. Comparison of equilibrium constants calculated by various methods for a middle range boiling .pseudo-component T s442.93 K .b

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Fig. 4. Comparison of equilibrium constants calculated by various methods for a high boiling pseudo-compo- .nent T s795.40 K .b

.Braun-K BK10 for both medium and heavier fractions in the temperature range10w x0500 8C and pressure near one atmosphere. The equation has the form 30

ln P srP s 1qw f T , 11 . . . .c r

Fig. 5. Parity plot for calculated values of equilibrium constants with data obtained from various sources.

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. .where f T is a function of reduced temperature.Using Eq. 11 , K-value for jthrcomponent can be calculated from

sP Pj c jK s s exp 1qw f T . 12 . . .j j r jP PFigs. 24 show the comparison of K-values predicted by various methods for lighter,intermediate and heavier fractions of a crude oil. Fig. 5 presents a parity plot of all thedata available with predictions from the proposed thermodynamic model.

Enthalpies for the liquid and the vapor phases can be obtained from Kesler and Leew x w x31 modification of JohnsonGrayson 32 charts.

4. Prediction of petroleum product properties

The petroleum products coming out of the crude distillation column are blended withproducts from various processing units and are rated based on certain product propertieslike RVP, flash point, pour point, specific gravity, recovery at 366 8C, etc. To quantifythese properties before the blending operations and validate the simulator, productproperties of run down streams were experimentally measured. The distillation columnsimulator, which predicts product TBPs, was coupled with a property estimation

w xpackage developed in-house 33,34 . These predicted properties have been comparedwith the experimentally measured ones in Table 6.

5. Case studies

The crude fractionation unit model developed during the present work was tested on avariety of problems collected both from literature as well as the industry. Somerepresentative samples are being presented here.

.Fig. 6. Column temperature profile Case 1 .

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w xCase 1. A pipestill problem from literature 4 , which consists of four side strippers andone pumparound configuration. The input specifications for this problem are available in

w xRef. 4 . The crude distillation model presented in this paper was run using the inputspecifications of this problem. The converged results are presented in Figs. 6 and 7. Fig.6 shows a comparison of the temperature profile obtained from the model with theresults of Hess and Holland. Also included in this figure are the results obtained using a

.commercial simulator Aspen Plus, Aspen Tech., USA for the same input data. Fig. 7

.Fig. 7. Product TBP curves Case 1 .

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Table 3Feed TBP for Case 2The average specific gravity of the feed oil is 0.8445.

. .Cumulative volume % Temperature 8C

0 125 52

10 8530 20550 33570 44090 61095 703

100 796

shows a comparison of the product compositions reported in literature with thosepredicted using the present model and the commercial simulator. It is evident from thecurves that the proposed model is found to have good match with the data published inliterature as well as given by the commercial simulator. The calculated vapor and liquid

.Fig. 8. Product TBP curves Case 2 .

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Table 4Feed TBP data for Case 3

.vol.% distilled TBP Temperature K

0.00 280.005.00 318.00

10.00 348.5015.00 370.6020.00 392.7530.00 437.4540.00 482.4050.00 527.5060.00 572.5070.00 618.2580.00 670.4590.00 746.2595.00 793.00

100.00 844.75

profiles in the column showed similar agreements but have not been included here. Anexcellent overall match with the published results confirmed that the present formulationis satisfactory.

Table 5Input specification of operating conditions for Case 3

3 .Feed flowrate m rh 1228.200 .Coil outlet temperature 8C 328.350

3 .Reflux flow rate m rh 250.000 .Condenser temperature 8C 89.195

.Reflux temperature 8C 39.100 .Water reflux rate tonrh 0.2 .Bottom steam rate tonrh 8.380 .Steam temperature 8C 330.000

3 .HN flow rate m rh 72.4003 .KERO flow rate m rh 224.250

3 .LGO flow rate m rh 181.8103 .HGO flow rate m rh 38.070

.Steam rate for HN Stripper tonrh 1.5900 .Steam rate for KERO Stripper tonrh 2.6969

.Steam rate for LGO Stripper tonrh 0.6666 .Steam rate for HGO Stripper tonrh 0.7800

3 .HN pump-around flow rate m rh 685.6203 .KERO pump-around flow rate m rh 408.800

3 .LGO pump-around flow rate m rh 416.340 .HN pump-around return temperature 8C 125.510

.KERO pump-around return temperature 8C 115.840 .LGO pump-around return temperature 8C 163.100

2 .Column pressure kgrcm gage 3.073

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Case 2. This example consists of a 25-stage petroleum distillation column with two sidestrippers and three pumparound flows. The side strippers with two stages each drawfrom stages 8 and 17 and return to stage 7 and 15, respectively, of the main column. Thepumparound flows are from stages 3, 9 and 17 to stages 2, 8, 15 of the main column,respectively. A feed of 70,000 bblrday at 339 8C and 32 atm enters above stage no. 21of the main column. The column overhead is subcooled to 40 8C in a condenser givingboth vapor and liquid products. The column operates at a pressure of about 40 psi. Therundowns from the two side strippers are 7200 and 9000 bblrday, respectively. Thepumparound circulation rates are 47.7, 133.9 and 226.25 m3rh, respectively, with returntemperatures of 90 8C, 130 8C and 220 8C. The feed oil assay is given in Table 3.

Table 6Comparison of calculated parameters and properties with the measured values)For straight run naphtha; NR: not reported.Column parameters and product Model generated values Measured

.properties plant valuesSimulated With With efficienciesresults efficiencies and reconciliation

.Top plate temperature 8C 115.000 124.700 125.000 124.810 .HN pump-around temperature 8C 159.719 160.846 159.474 161.870 .HN column draw temperature 8C 150.860 154.033 153.824 155.000

.HN product temperature 8C 133.000 142.767 141.073 142.500 .KERO pump-around temperature 8C 223.730 220.788 222.408 220.260 .KERO column draw temperature 8C 194.230 204.170 202.881 199.850

.KERO product temperature 8C 181.160 191.522 191.517 190.500 .LGO pump-around temperature 8C 277.770 267.560 272.942 278.000 .LGO column draw temperature 8C 277.770 267.560 272.942 278.000

.LGO product temperature 8C 270.400 264.217 269.902 268.450 .HGO column draw temperature 8C 302.850 312.790 318.432 318.940

.HGO product temperature 8C 287.610 294.695 303.745 305.050 .Bottom plate temperature 8C 315.750 311.931 314.238 312.6803 .Top distillate flow rate m rh 187.853 247.335 274.903 278.000

.Top distillate mass flow rate tonrh 135.742 180.814 200.628 196.0003 .RCO flow rate m rh 506.719 447.243 420.026 428.650

) .Top distillate density grcm 0.6977 0.7060 0.70616 0.7197) .Top distillate RVP atm 0.6394 0.5378 0.5682 0.4000

.HN density grcm 0.7402 0.7540 0.7600 0.7650 .HN RVP atm 0.0930 0.0379 0.0405 NR

.HN Flash Point 8C y1.500 9.540 12.030 11.00 .Kero density grcm 0.7736 0.7862 0.7948 0.8098

.Kero Flash Point 8C 28.86 40.15 44.97 44.00 .LGO density grcm 0.8188 0.8301 0.8424 0.8370.847

.LGO Flash Point 8C 69.71 87.65 82.06 78.088.0 .LGO Pour Point 8C y17.83 y10.28 y8.15 y9.00

.HGO density grcm 0.8433 0.8530 0.8714 0.8780 .HGO Flash Point 8C 87.63 100.03 105.64 101.00

.HGO Recovery @ 366 8C % 100.00 90.42 66.78 64.00 .RCO density grcm 0.9117 0.9182 0.9250 0.9258

.RCO Recovery @ 366 8C % 30.84 27.72 19.37 1427

( )V. Kumar et al.rFuel Processing Technology 73 2001 121 17

.This problem was taken from the commercial simulator itself Aspen Plus where it waspresented as an illustration. The crude TBP was split into 40, 30 and 25 pseudocompo-nents and the problem was solved using the present model. The liquid, vapor andtemperature profiles were identical in all the cases. Using 25 components, the calculated

.product TBPs are compared with those from the commercial simulator see Fig. 8 andagain the match is quite good.

Case 3. Data were collected from an operating crude distillation unit in a refinery havingfour side strippers and three pumparound flows. A theoretical analog of the unit consists

.Fig. 9. Product TBP curves Cases 3 and 4 .

( )V. Kumar et al.rFuel Processing Technology 73 2001 12118

of 34 stages with crude entering above the fourth stage from the bottom at a flow rate of1200 m3rh at 330 8C and 271 kPa. The column has a partial condenser with both liquidand vapor distillate products. The side strippers consisted of two theoretical stages each.

.The crude from an Indian source TBP data are given in Table 4 and the other inputspecifications are included in Table 5. The calculated column profiles for temperature,vapor and liquid flows are not included since no measured profiles were available forcomparison. However, measured values of some of the parameters were available atspecific locations in the plant and those have been compared with the model predictionsin Table 6. Fig. 9 shows a comparison of calculated product TBPs with the measuredvalues. The model results appear to generally match well with the plant data except at afew points. There can be two possible reasons for the mismatch observed in somecolumn parameters and the product TBPs. The theoretical analog is not perfect and stageefficiencies are required to be introduced to better match the column parameters. Thesecond reason is that the TBP used in the simulator is not representative of the crudebeing processed at that time. The actual crude TBP has been found to deviate somewhatfrom that measured in the laboratory during crude assay on account of spatial variationsin the oil reservoir and also because of stratification in the storage tank. In the next casestudy, these two discrepancy sources have been accounted for.

Case 4. The crude distillation unit as well as the feed crude were same as in Case 3.Stage efficiencies were incorporated in the equilibrium relations as y sh K xi j i j i j i jwhere h are the efficiencies for jth component on ith stage. The feed TBP curve wasi jalso reconciled. For the details of efficiencies, calculation and TBP reconciliation, the

w xreader is referred to Basak 35 .Using these, the model predictions matched very well with measured values for both

. .column parameters see Table 6 and product TBPs Fig. 9 . Fig. 10 shows that the

.Fig. 10. Reconciled feed TBP curve Case 4 .

( )V. Kumar et al.rFuel Processing Technology 73 2001 121 19

crude being processed has a slightly different composition in comparison to its standardTBP. In Table 6, columns 3 and 4 show a comparison of column parameters and productproperties before and after TBP reconciliation. An improved match with the measureddata after reconciliation brings out the importance of feed TBP curve reconciliation.Similarly, the importance of stage efficiencies can be viewed by comparing columns 2and 3 in Table 6.

6. Conclusions

A transport phenomena model based simulator has been developed successfully foran industrial crude oil distillation column. The choice of independent variables made themodel more stable and robust and facilitated quicker convergence even from a far offinitial guess. Numbering of equilibrium stages in a specific order further led to thereduction in computation time. It has been observed that equilibrium constants andenthalpy prediction using an equation of state approach increases the computational timeto a large extent. Use of empirical correlations significantly reduced computation timeand also led to a closer match between the results of the simulator and the actual plantdata. Additionally, results of such a simulator gives complete TBP curves for all theproducts that can be used to predict other product properties such as RVP, flash point,pour point, etc. Comparison of the results of the present simulator with those fromliterature as well as from actual plant indicates that the predictions based on presentsimulator are reasonably good. An efficient equation-solving algorithm has been usedwhich utilizes sparcity of the Jacobian matrix and further reduces computation time. TheCPU time required was reduced to about 58 s on a Pentium 266 MHz machine makingthe model suitable for online process monitoring andror supervisory online optimiza-tion.

NomenclatureBj bottom flow rate for jth componentC total number of pseudocomponents in the feedD total distillate flow rateDL liquid distillate flow rateDLj liquid distillate flow rate for jth componentDV vapor distillate flow rateDVj vapor distillate flow rate for jth componentf Li j liquid feed flow rate for jth component to ith stageF Vi j vapor feed flow rate for jth component to ith stageHi j vapor enthalpy for jth component on ith stageH Dj enthalpy of jth component in vapor distillateH Fi j vapor enthalpy of jth component in the feed to ith stagehi j liquid enthalpy for jth component on ith stagehFi j liquid enthalpy of jth component in the feed to ith stageKi j phase equilibrium constant of jth component on ith stage

( )V. Kumar et al.rFuel Processing Technology 73 2001 12120

L1 reflux flow rateLi total liquid flow rate from ith stageli j liquid flow rate of jth component from ith stageN total number of stages in the columnPc j critical pressure of jth componentP sj vapor pressure of jth componentQB heat duty of the bottom stage reboilerQC condenser heat dutyQi heat duty of the ith stageRR .reflux ratio LrDS specific gravity of crude oilSj specific gravity of jth pseudo-component .Tavg j mean average boiling point of jth pseudocomponentTc j critical temperature of jth componentTi temperature of ith stageTr reduced temperatureVi total vapor flow rate from the ith stagei j vapor flow rate of jth component from ith stagewj acentric factor of jth componentwLi j liquid side stream of jth component from ith stagewVi j vapor side stream of jth component from ith stagexi j mole fraction of jth component in liquid phase on ith stageyi j mole fraction of jth component in vapor phase on ith stagehi j efficiency factor of jth component on ith stage

SubscriptsM bottom plate of main column and side stripperp pump around liquid stream from stage pq side stripper vapor stream from stage q

SuperscriptL refers to liquid phaseV refers to vapor phase

Acknowledgements

The financial grant received from the Center for High Technology, New Delhi isgratefully acknowledged.

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