-
.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: [email protected] 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
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( )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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( )V. Kumar et al.rFuel Processing Technology 73 2001 121 3
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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( )V. Kumar et al.rFuel Processing Technology 73 2001 1214
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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( )V. Kumar et al.rFuel Processing Technology 73 2001 121 5
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
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( )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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( )V. Kumar et al.rFuel Processing Technology 73 2001 121 7
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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( )V. Kumar et al.rFuel Processing Technology 73 2001 1218
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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( )V. Kumar et al.rFuel Processing Technology 73 2001 121 9
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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( )V. Kumar et al.rFuel Processing Technology 73 2001 12110
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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( )V. Kumar et al.rFuel Processing Technology 73 2001 121 11
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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( )V. Kumar et al.rFuel Processing Technology 73 2001 12112
. .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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( )V. Kumar et al.rFuel Processing Technology 73 2001 121 13
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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( )V. Kumar et al.rFuel Processing Technology 73 2001 12114
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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( )V. Kumar et al.rFuel Processing Technology 73 2001 121 15
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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( )V. Kumar et al.rFuel Processing Technology 73 2001 12116
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
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( )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 .
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( )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
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( )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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