Optimization of a Plant for Separation of Natural Gas

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OPTIMIZA TION OF A PLANT FOR SEPARATION OF NATURAL GAS F. Tolfo*,

J.

P. Vial** and

J.

P. Bulteau**

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Abstract. This paper reports on a stud y undertaken to demonstrate the usefulness of optimi z ation techniques to improve the performance of a plant for separation of natural g<'3. Ke ywords. Optimization; natural gas te chnolo gy; oil technolo gy modelling ; mathematical pro grammin g ; sensitivity analysis. INTRODUCTION

on-line computations which would tend to overload most process computers. In practice, the effort is concentrated on making the process inputs accurate and repeatable.

This paper deals with the on-line optimization of an existing plant for separation of natural gas. The study was undertaken in order to demonstrate the potential usefulness of optimization techniques in improving the performance of till' plant.

The second critical aspect is the process regulatory control. Fluctuations of process variables and outside conditions cause instabilities which may steer the process away from its setpoint. The scope of process regulatory control is precisely to keep the process at its setpoint or to bring it back to steady state as fast as possible and with minimum departure. It is clear that a good process regulatory control must be set before considering any practical on-line optimization. One cannot optimize a process to within 1 or 2 percent if the process conditions are fluctuatin g within 10 or 15 percent.

Although process optimization techniques were well known and have been shown to work very well for process design, on-line optimization has remained of very limited application in daily plant operations. It is worth looking into the causes. The perequisites for on-line optimization are two-fold. Firstly, one needs a mathematical model which provides a fair representation of the working conditions of the process. Of course such a model can only approximate the real process. However if the degree of accuracy of this approximation is not of a si gnificantly higher order of magnitude than the relative change in the operating point that the optimization eventually suggests, then the improvement can be illusory.

Modern technology has made possible substantial progress in the field of data validation and regulatory control. We consider that the prerequisites for a sensible use of optimization are nowadays met and will be so more and more in the future. In particular the mathematical model which underlies the regulatory control system may serve as a support for the optimization procedure.

Secondly an efficient regulatory control systen. is required in order to steer the process to the preassigned operating point and to maintain it at this value. Thus a first critical point is the reliability and the repeatability of the process inputs. In the process under study, all field inputs come from transmitters which have a certain range of accuracy (readings are distributed around the actual value according to a Gaussian law). Furthermore, electronic transmitters give a drift, i.e., a displacement with time of the average value "away" from the true value. This requires instrument recalibration and careful maintenance. Mathematical schemes for on-line process validation are available. They are very complex and require extensive

137

In our study the data come from an existing plant. The model is directly derived from the actual regulation system. As such it is of rather limited size. The starting point is a true working point chosen by the engineering designers. The proposed optimal point is a distinct operating point (from the standpoint of the regulatory control system) and it leads to a I percent improvement of the economic value of the output products of the plant less the energy costs. However this corresponds to a much higher percentage of the added value of the plant throughput, i.e., our objective function minus the economic value of the input. Considering the very high economic value of the daily flow in

F. [0110.

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a natural gas separation plant, the figures are quite impressive. In evaluating the performance of the optimization,one should take into account that the starting point being chosen by the engineering designers on their experience is very good. However should the external conditions change, due to price fluctuations for instance, a new satisfactory operatin g point would be found only after some lon g trial and error procedure. On the other hand, the optimization procedure we propose would select a new optimum in a fully automatic wa y which is a definite advantage. For the optimi zation procedure we have used two different codes, the generalized reduced gradient of Abadie and Carpenti e r (1969) and the Minos code of the Syst em Optimization Laboratory of Stanford Universit y (1982). Those codes have been chosen for their known robustness and efficiency, for their r e ady availability and for the extensive testing on real life problems which they have successfully been subjected to. Both methods gave the same results. However our objective is not to compare the codes. The statistics on the computational effort are reported in order to give an evidence that the optimization procedure with either one of the codes is compatible with the on-line context. The paper is organized as follows. In Section 2 we describe the p r0 c e s ~ and give a mathematcal model of it. In Section 3 we provide a brief account of the mathematical method that underlies both codes. In Section 4 we present the numerical results.

PROCESS DESCRIPTIO N AND MATHEMATICAL MODEL OF THE PLANT Distillation Process Natural gas is a mixture of hydrocarbons with a carbon chain length ranging from I (carbon dioxide C02, methane CH4) up to II ... 15. The main components are methane (Cl), ethane (C2), propane (C3), butane (C4), and pentane (C5). The natural gas is first stabilized by removal of the incondensibles (C02 and Cl). Then it 1S split between the various components : - ethane is used as feedst(lck for petrochemicals such as ethylene, PVC and various other plastic polymers - pro pane and butane are used as industrial and domestic fuels ; pentane and heavier h:;dr ocal'bons are used either as straight run gasoline or as blending compounds for commercial gasoline. The plant consists of a train of three distillation columns (see Fig. I) : - the de-ethanizer removes ethane as overhead product ; - the de-propanizer removes propane as overhead ; - the de-butanizer splits butane as overhead

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and gasoline as bottoms. Distillation columns ooerate on the orincipIe of selective separation between the light and heavy compounds of a mixture. At equilibrium, the vapour phase is richer in light compounds than the liquid phase. The column is a succession of plates (or trays), each containing liquid in equilibrium with its vapour. As the vapour ris e s in the column it will become gradually lighter while the liquid flowing down becomes gradually heavier. At the top, the overhead vapour is condensed and partly removed as distillate product. The rest is recycled on the first tray as reflux. At the bottom, part of the liquid is removed as bottom product. The rest is evaporated in the reboiler and returned in the column below the last tray. In this example, the heat of vapourisation is provided by a closed circuit of hot oil feeding the three reboilers. The removal of overhead vapours condensation heat is done in an atmospheric condenser for the de-propanizer and de-butanizer. In the de-ethanizer, overhead vapour is condensed by a closed loop propane refrigeration cycle. Liquid propane is evaporated by thermal exchange with the condensing ethane. The propane vapour is then compressed in a centrifugal compressor and condensed in an atmospheric condenser before returning to the ethane heat exchanger. Problem Definition The problem consists in finding the operating conditions (flow rates, product purity) which will maximize the net economic value of the process. This value is to be computed as the difference between the total value of the output products evaluated at market prices and the energy costs, mainly the cost of calories for the reboilers and the cost of frigories (negative calories) for the condensers. The input cost, i.e. the economic value of the feed, need not be taken into consideration in the optimization process since the flow rate and the composition of the feed cannot be freely selected at the plant level. Prices are subject to market variations. Energy costs are mainly electricity cost (e.g. propane compression at the condenser) and cost of burning propane (heating oil in the reboilers). They also vary. Therefore, in order to maintain optimality, the operating conditions should be adjusted according to market fluctuations. However those adjustments must be performed within certain ranges, dictated by the design of the equipment and the product defini tions . Indeed the products have quality specifications (maximum m01e percent of each impurity, minimum mole percent of product) which they must meet to be saleable on the market. On the other hand, the equipment design limitations are such as maximum condenser and re-

Optimization of a Plant for Separation of :-.Jatural Cas boiler heat exchanges, maximum reflux column feed rate and maximum reflux pump capacity. The latter is certainly the most stringent limitation. Beyond a certain feed rate, the internal flux of liquid and vapour inside the column becomes too large and liquid is entrained between the plates. This last occurrence is a major process upset requiring a long period to bring back the column back to steady operations with important costs of lost production and extra heat pump.

Material balances ----------------F. = D. + B. , i = ~ ~

n

xF .

~

V

n ~i=1 R.~

~i=1 Di' B

F. /F ~

~

~.

(I)

n

~i=1 Fi' D

1

1, •.• ,n;

~

F

1~9

xD.

= D/D

i

I, ... ,n

, (3)

~

B./B ~

(2)

R + D

(4)

The Model of One Tower Steady state operations for a single distillation column (Fig. 2) are described by mater~al and energy balances. The following notation will be used :

rn

i=1

(F. M . ~ F

number of components;

XF .' XD.' ~. = percent molar fraction of com~ ~ ~ ; ponent ~n F, D and B ;

-

D. MD. - B. LH . ) ~ ~ B

~

- QC

F,D,B = mass flow rate of feed, distillate and bottom respectively [K moles/secl; n =

~!!~EgL!?e!.e!!~~~

+

~

0

QH

~

(5)

,

with Qc = V AD

= (R

D)A D

+

(6)

Latent heat of vapourisation is much larger than enthalpies and, as a first approximation, one can write the energy balance as :

L

(7)

F. ,D. ,B. = mass flow rate of component in the ~ ~ ~feed, distillate and bottom, respectively [kmoles/secl; F.~ = FX -r. , D.~ = DX

D~.

~

,B.~ = B)L ; -~. ~

LH ., LH . = enthalpy of component i D~ B~ in the feed, distillate and bottom, respectively [kcal/kmolel ; C P.

specific heat of component [kcal/kg/oKl;

m.

molecular weight of component [kg/kmolel;

~

~

TF,TD,T

i i

= temperature of the feed, distilB late and bottom, respectively [OKl , LHF = C m. TF ;

i

Pi

~

heat removed by condensation of overhead vapour [kcal/secl ; heat removed by vapourisation of bottom liquid [kcal/secl

v R

mass flow rate of vapour up the column [kmole/secl;

The process quality is characterized by a separation factor S : (8)

where the indices £ and h refer to light and heavy key compounds, respectively. The separation that the column achieves is related to the internal flux of vapour (and by (4) to the internal reflux) by a correlation developed by Shinskey (1977). V = SF log S ,

(9)

where S is a constant which depends on the column design and the type of products to be separated.

A more compact and tractable mathematical model can be obtained by elimination of the variables X. , Y. , i = I, ... ,n and V. Indeed in vi~w of~(3) and (4), one gets: R + D = SF log (D£ /B h • Bh/BQ,)

In an optimization model, the process variables will be the B.'s,the Di' s, ... D, ~

mass flow rate of liquid down the column = internal reflux [kmole/secl

AD meters and the

latent heat of vapourisation/condensation of distillate [kcal/kmolel . It varies with the composition of the product. However within the range of specification it may be considered as constant. The process is described by the following set of relations :

(10)

F. 's ~

and

S

are fixed para-

must be considered as

input data. The model is fully described by the relations (I), (2), (6), and (10). Modellisation of a Three-Tower Train Figure 3 pictures a three-tower train. There are six components of interest (n = 6), namely C0 C , C , C , C , Cs and a last com2 2 I 3 4 ponent gathering all components from C to C . II 6

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F. Tolfo .

.J.

P. \'ial alld

.1. P. Bulteau

The mathematical model of the process is directly derived from the one-tower model. From the above analysis we retain the followin g variables

( 16) ( 17)

( 18)

F

and F. mass f low rate of the feed and of ~the i-th component in the feed, respectively ; and FB (F .) = mass flow rate of the B feed (and ~of the i-th component in this feed) of the de-propanizer and the de-butanizer co lumn respectively;

E (E ), P (Pi) , B (B ) are the mass flow i i rat es at the top of the de-ethanizer, de-propanizer and de-butanizer columns, r espectively;

g~~~~~~i~~~_~~_E~~~~£~_££~E£~i~i£~ (Specifi-

cation

constraints)

The end products must satisfy the following specifications. Zt~;n e cannot have more than 9.5% of Cl and 2.5% of C3. Pro;x:.ne must have at least 96% of Cl and 2.5% of C4. Butane must have at least 96% of C4 and at most 2.5% of C3 or CS. (~so~ine cannot have more than 5% of C4. A typical constraint is

are the mass flow rate s at th e bottom of the de-butanizer column.

G (G.) ~

Note that, due to the separation process, some of thes e va riabl es have value zero, namely E4 , E5 , E6 ; FpI ; PI' PS' P6 ; FBI' FB2 ; BI ,B 2 , B ; G , G and G . I 3 6 2 the model.

El

« (0.095) E.

( 19)

There are eigh t such constraints. Constraints on internal refluxes (Flooding

---~~~~tr~i~t~)-----------------

They are not needed in

and R are further ind exed by E ,P or B depending on whether they are related to th e de-ethanizer, the depropanizer or th e de-butanizer. Similarly the parameters AD and S are also indexed by E, P or D. The var~ables F and Fi are input data. Note however that th e feeds

The internal reflu x is limited by maximum values given as tower design limits beyond which flooding will occur. R

E

«R

RE,Max' riables

'R

E ,Max ' -1'

«R

P ,Max

~

«

RB,Max (20)

are data and the va' ~ ,Max RE ' Rp ,RB are computed from (10).

1» ,Max

For instance

Fp (Fp.) and FB (F .) a r e now true variables. B ~

(2 I )

~

The objective of the optimization procedure is to maximize the net throu ghpu t of the process (throughput value minus the energy costs). The full proble~ is modelled by a set of mathematical constraints (physi ca l and process constraints; co rr e lations) and an objective function. We first state the constraint.

are similar on the de-ethanizer (E), the depropanizer (P) and the debutanizer (B). For instance on (E) one gets : (22)

Mass balance constraint

(23)

p = 2: 4 E = ~3 E. P. i=l ~ ; i=2 ~

!l

B

,- 5 B. i=3 ~

Fp =

,,6

~i=2

G

Fp. ~

and

Finally we must include the

,,6 G. i=4 ~ FB

(11 ) 2: 6

i=3 FB.

All the variables must be nonnegative.

~

For each tower one ge ts constraints of the type It

~s

the difference of two components

(12) (24) Globally one gets

where (13) ( 14) ( IS)

Wo

is the value of the output, W the I value of the input and We is the energy cost. Since the input is fixed, we can work alternatively with Wo - We The value of the output depends on the market

Optimizatioll of a Plallt for Scp
l.

(25) The total value in [$/secl

W

o

of the output is then,

Wo = IT E a E E + IT P a p P + IT B a B B + IT G a G G.

(26)

The energy prices

W ' W , W (calories) HE HP HB and WCE ' WCP , WCB Cfrigories) are also known and are given in [S/secl :

I 1

We = QHEWHE + QCEWCE + QHpWHP

(27)

QcpWcp + QHBWHB + QCBWCB

For the optimization procedure, the size of the model can be significantly reduced by straightforward elimination of certain variables. Indeed in view of the mass balance equations (11) and (12), the correlation (21), the energy balance (22) and (23), and the molecular weights definition (25), we eliminate the variables E , P , B , G, Fp (Fp.)' FB (F B.) l.

l.

and also QCE ' QCP , QHP , QCB ' and QHB Furthermore by (13) and (18), El and G have 6 fixed values. We are left with a set of ten decision variables E , E , P , P , P , B , 2 3 2 4 3 3 B ,B ,and G ,G 4

5

5

6

To summarize, the problem is to minimize W Wo - We ' subject to : 4 mass balance equations (14) to (17); 8 product specification constraints such as (19); 3 reflux constraints such as (20), where the reflux values are given by nonlinear functions such as in (21); 10 nonnegativity constraints on the variables which are physical quantities. In the objective function Wo is given by (26) and We is obtained by replacing in (27) each term of the type QHEWHB by its value as given by (21) and (22). The nonlinearity comes from the three reflux constraints and from the term W in the obe jective function. THE OPTIMIZATION PROCEDURE Numerous algorithms have been proposed for solving nonlinear programming problems. For general problems it is only assumed that the functions in the objective and in the constraints are differentiable. The class of problems under consideration is

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very large and problems in that class can be different from one another. Consequently an algorithm can be very efficient with some problem and disastrous with another. Ri ght now one cannot claim that there exists a general purpose algorithm for solving these problems and care must be exercised in choosing among existing codes. This situation drastically constrasts with linear programming where Dantzi g 's simplex method is th e solution method. Our criteria for selecting a code were robustness, (as established by systematic testing and by extensive use in solving real life problems), efficienc y (in terms of computational effort measured by the number of required function evaluations) and availability to users. Since our problem is of small to medium size it should not prove difficult to solve. We choose the GREG of Abadie and Guigou (1969),(1978) and the MINDS/AUGMENTED code of the System Optimization Laboratory (S.O.L.) in Stanford (1982). Both are implementations of the reduced gradient method of \-lolfe (1963) . The former handles the nonlinear constraints via linearization. The latter uses dualization and a penalization scheme for the nonlinear constraints and is well suited to problems with few nonlinear constraints. GRG methods are ranked among the best in extensive test problem comparison (Sandgreen et al., 1982). In the literature in engineering optimization these methods seem to be l e ss popular than direct search methods. The most well-known is certainly the so-called simplex method (not to be confused with Dantzi g 's simplex al gorithm for linear programmin g) of Spendley, Hext and Himsworth (1982). The method derives its name from its us e of a regular simplex to explore the decision variable space and by replacing the worst vertex of the simplex, (with respect to the objective function), by its reflexion on the centroid of the others, thereby producing a new simplex so that the procedure can be repeated. For a detailed discussion we refer survey papers of Swan (1972), (1974). Direct search methods do not require gradient information and can be applied to problems where the functions are not smooth or not even continuous. However for smooth problems they are outperformed by gradient-like methods which are based on a proper use of the first derivatives for finding a search direction. Moreover it is not obvious that the ad hoc procedures which have been developed for handling simple bound constraint on the variables can perform efficiently with more general constraints, not to speak of nonlinear constraints. We believe that these methods are not suited to our problem despite the appeal of their apparent simplicity. Let us point out an essential difference between them. GREG is designed to maintain feasibility at each step, i.e. it generates a sequence of points which satisfies all the

F. Tolfo.

142

J.

P. Vial and

constraints, linear and nonlinear, and which monotonically improves the objective function. In MINOS/AUGMENTED, the nonlinear constraints may be violated. Actually in the optimization process, the nonlinear co nstraints are violated most of the time, but eventually the sequence converges towards a feasible and optimal point. Thus, should ~!INOS/ AUG~lENTED be stopped during the optimization process, either because of too slow a convergence or for any external reason, it would likel y produce an infeasible point which i s of no value to the user. This is not the case with GREG which always produces an improved feasibl e point, a definite advantage. For problems of the size and difficulty considered here, failure to convergence is highly improbable. However for extensive use on possibly lar ge r problems thi s feature should be kept in mind, especially for on-line optimization.

J.

P. Bulteau

is a gross underestimate of the actual relative profit one can expect from the optimization. The details of the results are summarized on Table 2 below. TABLE 2

Results of Optimization with Arbitrary Conditions

Components of the Objective Function

Monetary Values (S/day)

Total Value : Optimal Solution

1,045,364

Initial Solution -------------------------

____ lLQ~~L~Q2 ____

Contribution to Revenue Ethane Butane Propane Gasoline

353,137 118,073 446,712

Energy Costs

22,826

------------------------- ______ l~QL~~~ ____

THE RESULTS The two codes, GREG and MINOS/AUGMENTED, have been used to solve the same problem with the same set of data. In particular the initial point was the actual operating point of the plant. Each code is implemented on a computer facility in the Universite Catholique de Louvain. For external reasons those facilities are different. GREG was run on the IBM 370/158 and of the Computing Center whereas MINOS/AUGMENTED was run on the DG/MV 8000 of CORE. TABLE I

TABLE 3

Detailed Solutions

Output Volume and Composition ' I)

A

B

Production

49.696

50.722

Percentage of Cl Percentage of C2 Percentage of C3

6.5 92.7 0.8

6.37 91.19 1.84

Production

32.516

31.822

Percentage of C2 Percentage of C3 Percentage of C4

3.4 96.0 0.6

I. 95 96.6 I. 45

Ethane

2) Propane GREG IBM 370/158 NOF NCF NGOF NGCF CPU Time

174 705 61 23 6.4"

MINOS D.G. MV/OOOO 56 62 56 62 4.3"

NOF = #ob jective function evaluations NCF = #co nstraint function evaluations NGOF #e valuations of the gradient of the objective function NGC F #evaluations of the gradient of the constraint functions. To illustrate these methods we have arbitrarily set the input flow to 100 ton-moles /day and taken some arbitrary but r ea listic price for the products. In this example, ethane, propane, butane have equal price while gasoline is 15% more expensive. The operating point that was obtained from the plant - our starting point in the optimization process - led to an objective function value of 1,035,209 $/day. The optimized objective function value is 1,045,364 $/day, a 10,155 $/day improvement. Again we would like to stress that, since the objective function does not take into account the economic value of the input flow - a fixed value which is not relevant to the optimization itself - the 1% improvement

2

3) Butane Production

11.329

11.410

Percentage of C3 Percentage of C4 Percentage of C5

2.5 97.3 0.2

1.94 96.61 I. 45

2

4) Gasoline Production

6.46

Percentage of C4 Percentage of C5 Percentage of C6

Reflux constraint RE Reflux constraint Rp Reflux constraint

~

5.0 46 .0 49.0

6.046 0.95 46.71 52.34

2

76.818

71.311

64.245

2

55.624

22.291

2

19.393

A Optimized Solution B Initial Solution lVolumes are on ton-mole/day. The total feed is 100 ton-mole/day. Compositions are given in percentage. 2 Binding

constraints.

Optimization of a Plant for Sep;lration of :'\Jatllral (;as Finally an interesting by-product of the optimization procedure are the so-called dual variables. There is one such variable per constraint in the problem. At the optimum point they can be interpreted as the marginal economic value of the constraints. That is, should a constraint be relaxed by one unit, the objective function would be improved by an amount equal to the corresponding dual variable. These values are quite useful for sensitivity analysis. Though the interpretation may be difficult for some constraints such as the balance equations - for some other it is quite natural. In Table 4 we give the dual variables associated with the specification constraints and with reflux constraints. TABLE 4

Marginal Values

Constraints ~E~~~£~~~~~~~_~~~~~E~~~~~ C3 in propane C3 in butane C4 in gasoline All other constraints

Marginal Values

6,105 82 9,268 0

Reflux -----RE

0

Rp

57

~

33

As an example of interpretation, we consider the constraint on the admissible percentage of C4 in gasoline. The value of the dual variable associated to this constraints indicates the increase in the objective function one can expect by relaxing by one ton mole/ day the constraint G - 0.05 G ~ 0 . 4 In terms of percentage, if one allows for a 6% concentration, it corresponds to a relax2 ation of 10- 2 • (G + G /G ) = (6.46)105 6 4 (ton mole/day). Evaluated at the dual price of 9,268 $/ton mole/day it amounts to 598.7 $/day. Let us stress that stricto senSll the interpretation is valid at the margin, i.e. for minute variations in the constraint. The one percent variation may already be too large to produce a correct figure. REFERENCES Abadie, J. and J. Carpentier (1969). Generalization of the Wolfe reducedgradient method to the case of nonlinear constraint. In R. Fletcher (Ed.), Optimizat ion, Academic Press, New York. pp. 37-49. Abadie, J. (1978). The GRG method for nonlinear programming. In H. Greenberg (Ed.),

Design and Implemen t at ion of Optimizat ion

143

Soft war e , Sijthoff and Noordhoff, Alphen aan den Rijn. pp. 335-362. Haskins, D.E., F. Tolfo, and L. Chauvin (1983). The us e of group method ' calculations for distillation column advanced controls. To be published in Hydrocarl~n _Dy>,)cesBir;g , June 1985. Latour, P. tI979). On-line computer optimization. Hydrocar bon Processing, 58, 73-82 and 219-223. Murtagh, B.A. and ~1.A. Saunders (1982). A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints. In A.J. Buckl ey and J.L. Goffin (Ed s ) , /Jlgo! 'it:z>7!B .for Constrained Minimiza -

tion o_£' Smooth 'lonZinear Function . Ma thematical Program Stud!}, 16 . pp. 84-117. Nasi, M., M. Sourander, M. Tuomala, D.C. White, and M.L. Darby (1973). Experience with an ethylene plant computer control. Hydrocarbon Processing, 52, 74-82. Sandgreen, E. and K.M. Ragsdell (1982). On some experiments which delimit the utility of nonlinear programming methods for engineering design. Mat hematical Progr amming Stud!}, 16 . 118-1 36 . Shinskey, F.G. (1977). Distillation Contro l . McGraw Hill, New York. Spendley, W., G.R. Hext, and F.R. Himsworth (1962). Sequential Application of simplex desi gns in optimization and evolutionary design. Technometrics , 4, 441-461. Swann, W.H. (1972). Direct search methods. In : W. Murray (Ed.), Numer ical Met hods for Unconstra i ned Opt imization , Academic Press, New York. pp. 13-28. Swann, W.H. (1974). Constrained optimization by direct search. In P.E. Gill and Murray (Eds.), Numerical Methods fo r Constrain ed Optimization , Academic Press, New York. pp. 191-217. Wolfe, P. (1963). Methods of nonlinear programming. In R.L. Graves and P. Wolfe (Eds.), Recent Advances in iVathematical Programming, McGraw Hill, New York. pp. 67-86.

F. Tolfo . .1. P. \ ' ial and

l-!-!

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P. BlI\leall

_ - - -... c 3

REFRIGERATION CYCLE

ETHANE

AIR COOLING

AIR COOLING

BUTANE PROPANE NGL

DEETHANISER

DEPROPANISER

DEBUTANISER

FEED

GASOLlt

HOT

HOT OIL

Figure I.

HOT

OIL

NGL Separation Plant

o R

X01, ... ,XO n

F

v

B

XB1, ... ,XBn Figure 2.

Modellisation of a Sin g le Distillation Column

OIL

Optimil.atioll of a Plallt for Separatioll of \iatural Gas

p

E

B

r--------~------------------~---I

I I

I I

RB

I I

F I ------+1--.... ~1 F F F F F6 1,

2,

3,

4,

s,

De-C 2

I I I

!

y

~----~-----

F F F F Fps F F F FB6 L_______________________________________ --' p2,

PJ ,

p4,

ps,

B3 ,

B4 ,

BS ,

G Indices : Variables

CO 2 ,C l ; 2

E = Ethane

C2 ; 3

P

Figure 3.

=

C

3

Propane; B

4

=

C ; S 4

Butane

CS; 6

=

C ,··· ,C 6 ll

•

G = Gasoline; F = Feed.

Modellisation of the Distillation Train