Energy input to ideal and non-ideal distillation sequences

Letters

to the

Editor

‘Evolutionary Concerning: thermodynamic synthesis of zeotropic distillation sequences’, J. Koehler, P. Aguirre and E. Mass Gas Separation & Purification (1992) 6 (3) Dear Editor We have much appreciated the referenced paper for its in-depth analysis and some original ideas. We would like to comment on the statement made on page 156, column 2, saying: ‘. . . as has been stated erroneously by Kaiser and Picciotti’. A development of our ideas follows under the heading ‘Energy input to ideal and non-ideal distillation sequences’. In essence we claim that the ideal column sequences are the only ones having a zero exergy loss overall, including feed conditioning. Further we show that other sequences will need more exergy input, although there seems to be no generally valid mathematical proof for this statement. Also it is shown how this hypothesis can be checked in a real world application. As a conclusion we think it is excessively severe to say our statement is ‘erroneous’. We think more appropriate to say ‘ins~ciently qualified’.

would perform the same separation at zero exergy value loss overall, i.e. W, = 0. Indeed, to this system applies the optimality principle of R. Bellmann, which states: ‘if in an acyclic system all elements are optimized relative to the feed they receive, then the whole system is optimized relative to the defined optimality criterion.’ The criterion here is ~nirn~ exergy value loss, Wp But WL can be only positive or zero, so this latter is the minimum optimal value. Let us now take a particular situation when all outgoing exergy streams are sent to cooling water, hence represent an exergy value loss, then the exergy balance is written for each column: E,,=

-E,+E,+E,+

= -(ER+E;)=

W,,>O

(2)

Note that ER and E, are negative exergy streams (outgoing), therefore W,, is always positive. The net exergy input to each column i,j is Ei,i, always positive. Adding up all Ei,j values, we get the total net exergy rhroughput of this separation scheme, per definition. All other separation schemes can be derived from Figure I by deleting or combining columns. For instance, the direct separation scheme, one component at a time, can be obtained by deleting all columns except 1.I, 2.2, 3.3 and 4.4 and taking the lightest component as pure distillate in each of them. Let us now create a new sequence by deleting only column 3.1 (see Figure 2). Assume that in column 2.1 we produce the same distillate quantity as previously from column 3.1. Then all columns perform the same duty and treat the same amount as in Figure I, except: column 2.1, requiring a sharp separation A/C and sending more of B into bottoms product (this is a non-ideal separation creating an exergy value loss W,,);

Energy input to ideal and non-ideal distillation sequences Figure I shows an ideal column sequence for the separation of a five-component mixture into pure compounds. Assume that all temperatures are above the exergy reference temperature r,. For each column we can write the exergy balance: -E,+E,+E,fE;=

W,=O

(1)

where EU is the net exergy difference on distillate plus bottom minus feed, ER is the exergy removed from the rectifying section, Es is the exergy supplied to the stripping section, and Ef is the exergy supplied for feed conditioning (if any). Considering that this sequence is acyclic, that all columns show zero exergy value loss and that feed conditioning can be made reversibly as a limit, it is certain that no other sequence can be devised which 0950-4214/93/03018503 @ 1993 Butterworth-tieinemann

Ltd

L..

c!_e

Figure 1

ideal separation columns in sequence

Gas Separation

& Purification 1993 Vol 7 No 3 185

letters to the Editor

It also shows that other sequences will have exergy value loss added to the ideal exergy input. Comparing the total exergy throughput of ideal and non-ideal sequences, it is made clear that generally the latter will have a higher net exergy throughput. It is also shown how to check such a hypothesis in a real-world situation.

A-B,

M. Picciotti and V. Kaiser TPL, Societi di ingegneria e costruzioni, Roma, Italy 24 November 1992

C C

Figure 2

Alternative sequence

column 3.2, which must treat more of components B and C. The exergy throughput can be written for columns 2.1, 3.1 and 3.2 for both sequences: ideal (3)

& + E,., + G.2 = w&d) non-ideal (1 +_W2.1+

WL.D+(~

+.&%2=

Wdn

-id)

(4)

Knowing that both W&d) and W, (n - id) are positive, let us check which is larger: W& - id) - W&d) =.f&

+ WL, +_fX2 - &,

(5)

Is the value loss difference in Equation (5) positive? Then the non-ideal system has larger exergy throughput. Per definition all of Ez,,, W,, and E,,z are positive. This means that the difference in Equation (5) can be negative only when E,,, is particularly large relative to E2., and E,,. But this would imply a difficult separation between A and C (purpose of column 3.1). We have to realise that the non-ideal scheme performs this same separation A/C in the non-ideal column 2.1, hence under more unfavourable conditions. The additional exergy input to the non-ideal column 2.1 over the ideal one is (6) (1 +_O%., + WLD-E,., =_fS2., + WLD This additional exergy input replaces the separation in the ideal column 3.1, so it is likely that

(7) _f&., + WLD - Ex, ' 0 Comparing with Equation (5), we see if Relation (7) is true then the non-ideal sequence has certainly a larger exergy value loss and hence a larger exergy throughput than the ideal one. Although there is no mathematical proof for Relation (7) being true, the present method permits direct checking of such hypothesis on actual systems to be studied. This is in essence its advantage and strength.

Conclusion The analysis presented here shows that the ideal column sequence is the only one having a zero exergy value loss.

188

Gas Separation

& Purification 1993 Vol 7 No 3

Concerning: Your letter to the Editor commenting on our paper ‘Evolutionary thermodynamic synthesis of zeotropic distillation sequences’ Dear Editor Thank you very much for sending us the comments made by V. Kaiser and M. Picciotti with respect to the above given publication. We would like to state the following: The brief communication given by Dr Kaiser and Dr Picciotti explains that the reversible distillation arrangement requires the lowest exergy throughput of all distillation sequences, which can be designed to achieve a given separation. We agree on these arguments, since by definition the exergy loss of the reversible scheme is zero. But we feel that the headline should be changed into ‘Exergy input to . . .’ in order to describe the content better. However, in the publication of V. Kaiser and M. Picciotti (Hydrocarbon Processing November 1988, 57-61), which we quoted in our paper, it is stated that the energy throughput of the reversible sequence is a unique minimum for the desired separation, because each column of the sequence requires a minimum energy throughput. But, of course, it must be distinguished carefully between exergy and energy ‘consumption’. If a multicomponent mixture is to be separated, the reversible distillation scheme always requires the lowest exergy input of all possible sequences. More precisely, if energy supply and removal is made continuous along columns and if pressure losses are neglected, only the thermodynamic minimum amount of work is necessary. Any other distillation sequence, which, for instance, may include sharp separations between neighbouring key components and which does not contain infinitely many heat-exchangers produces exergy losses and, hence, requires more exergy throughput. The relation between exergy (E) and thermal energy (Q) is defined by the Carnot-temperature: E = Q(1 - T&f), where T is the temperature level at which the energy Q is supplied or removed. In a conventional column arrangement, e.g. the direct sequence, in all but the binary columns the extent of separation is larger than in the columns of the reversible arrangement. In the direct sequence the first column