Linear approximation: a new method for the computation of complex distillation columns

ChpmrcaiEnglneenngSnence

1974, Vol

29, p 287

Linear approximation:

Pergamon Press

Prmted m Great Bntam

a new method for the computation

(Fwst recewed

1 January

1973, zn reusedform

A new method, as an unprovement of the tndmgonal matnx algonthm has been developed for the computation of complex dlstdlatlon columns which, accordmg to Its basic idea, may be called hnear approxlmatlon There are generally four sets of equations which must be satisfied m a ngorous calculation the matenal balance (M) and eqmhbnum (E) equations, summation of the mole fractions (S), as well as the heat balance (H) equations [l] The M equations w&h the E equations mcorporated form a hnear equation set urlth a tndlagonal matnx, for each component Solving these equation sets, the qj hqmd mole fractions (where I = 1 n is the plate,

6 March

columns

1973)

form where the second order terms are neglected This equation set can be easily solved and we obtam the Ax*_, correctlons as hnear functions of the Ari temperature corrections Thereafter these corrections can be summed up for each component and tinally we obtam a hnear equation set for the At, corrections needed to satisfy the S equations The vapour-hqmd profile for the next iteration can be calculated from the H equations as IS common m other methods The results of two numerical examples compared with the ongmal Wang-Henke (W H ) method are as follows

1 Example WH La method method Computation tune of one iteration Number of iterations needed Total computation time

of complex distillation

1 15 15

and J= 1 m 1s the component mdex) can be determmed for each component on every plate, but equations S are generally not satisfied The new idea m our method 1s that mstead of the bubble point (dewpomt) calculation generally used (see e g [l]) we modify the

2 Example WH La method method

18 5 9

1 27 27

24 8 19 2

In the first example there are 5 light hydrocarbon components, a 15 plate column with two feeds 1 clrculatlon reflux, 1 hqmd and 1 vapour side streams In the second example there are 11 hght hydrocarbon components a 38 plate column with 2 clrculatmg refluxes and 3 hqmd side streams The convergence cntenon was (l/n): 1--~q,l

< IO-4 (1)

aixi-1~ + hxi J+ W++Ij= 4 > equations with simultaneous linear approxlmatlon new xij mole fractions and ti temperature profile a,(x,-,j+A&-lj)

It can be seen that the number of iterations depends only shghtly on the size of the problem of plates and components, complexity of the which 1s a very advantageous feature of the new Detmls wdl be published later

of the

needed (number column) method

+ (b,+P,)(xij+A4 +(c,+Y,)(x,+lj+~+lj)=d,,

(2)

where

At, and

Y, =

(dc,>L=t,+lAfi+~ r

Equation set (2) m this form applies only to ideal solutions Otherwise further conslderatlons are needed Equation set (2) can be treated m various ways One 1s to transform to the

P JEDLOVSZKY Research Instltutefor Automation of the Hunganan Academy of Sciences Kende utca 13-17 Budapest XI Hungary

REFESWNCE [l]

a,Ax,-,,+b,Ax,,+c,hx,+,,=-P,x,j-rixt+11

WANG J C and HENKE G E , Hydrocarbon 1966 45 155

(3) 281

Proc