Heat Exchanger Network Retrofit Using the Reduced Superstructure Synthesis Approach

Abstract

This paper presents a new synthesis method for retrofitting heat exchanger networks using a two-step procedure. In the first step, the problem data for the network to be retrofitted is extracted and solved for a grass-root scenario using the stage-wise superstructure synthesis method. The matches selected in the solution of this first step, together with the existing units in the original network, constitute the candidate matches used to initialise a reduced superstructure in the second step. These initialising matches are the binary variables of the model, which is solved as a mixed integer non-linear model. The reduced superstructure is systematically initialised considering the sizes of the existing units as a guide. This is done so as to ensure that the heat transfer areas of the existing units are utilised as much as possible before making additional investment. One of the key benefits of this new synthesis approach for retrofitting heat exchanger networks is that the resulting reduced superstructure is relatively computationally less intensive to solve. The proposed method of this paper has been applied to two examples from the literature and the solutions obtained compare well with existing solutions.

Appendix

The traditional SWS model equations (see Yee and Grossmann, 1990, for details) adopted in modelling the superstructure, are shown below.

Overall enthalpy balance for hot and cold process streams

$$ \left({T}_{\mathrm{i}}^{\mathrm{s}}-{T}_{\mathrm{i}}^{\mathrm{t}}\right){F}_{\mathrm{i}}=\sum \limits_{\mathrm{k}\in \mathrm{K}}\sum \limits_{\mathrm{j}\in \mathrm{CP}}{q}_{\mathrm{i},\mathrm{j},\mathrm{k}}\kern0.5em i\in HP $$

$$ \left({T}_{\mathrm{j}}^{\mathrm{t}}-{T}_{\mathrm{j}}^{\mathrm{s}}\right){F}_{\mathrm{j}}=\sum \limits_{\mathrm{k}\in \mathrm{K}}\sum \limits_{\mathrm{i}\in \mathrm{HP}}{q}_{\mathrm{i},\mathrm{j},\mathrm{k}}\kern1.25em j\in CP $$

where HP represents set of hot process streams and hot utilities; CP represents set of cold process streams and cold utilities. ${T}_{\mathrm{i}}^{\mathrm{s}}$ and ${T}_{\mathrm{i}}^{\mathrm{t}}$ are the supply and target temperatures of hot streams, while ${T}_{\mathrm{j}}^{\mathrm{s}}$ and ${T}_{\mathrm{j}}^{\mathrm{t}}$ are supply and target temperatures of cold streams. F_i and F_j are heat capacity flowrates of hot and cold streams. q_{i, j, k} is quantity of heat exchanged between hot stream i and cold stream j in interval k of thee superstructure.

Stage enthalpy balance for hot and cold streams, respectively:

$$ \left({t}_{\mathrm{i},\mathrm{k}}-{t}_{\mathrm{i},\mathrm{k}+1}\right){F}_{\mathrm{i}}=\sum \limits_{\mathrm{j}\in \mathrm{CP}}{q}_{\mathrm{i},\mathrm{j},\mathrm{k}}\kern0.75em k\in K,\kern0.75em i\in HP $$

$$ \left({t}_{\mathrm{j},\mathrm{k}}-{t}_{\mathrm{j},\mathrm{k}+1}\right){F}_{\mathrm{j}}=\sum \limits_{\mathrm{i}\in \mathrm{HP}}{q}_{\mathrm{i},\mathrm{j},\mathrm{k}}\kern1.25em k\in K,\kern0.75em i\in HP $$

where t_{i, k} represents hot stream intermediate temperature along the superstructure, while t_{j, k} represents cold stream intermediate temperature along the superstructure.

Temperature feasibility along superstructure interval

$$ {t}_{\mathrm{i},\mathrm{k}}\ge {t}_{\mathrm{i},\mathrm{k}+1}\kern2.75em i\in HP $$

$$ {t}_{\mathrm{j},\mathrm{k}}\ge {t}_{\mathrm{j},\mathrm{k}+1}\kern2.75em j\in CP $$

Logical constraint:

$$ {q}_{\mathrm{i},\mathrm{j},\mathrm{k}}-{\Omega}_{\mathrm{p}}{y}_{\mathrm{i},\mathrm{j},\mathrm{k}}\le 0 $$

where Ω_p represents maximum heat load that can be formulated as the minimum of the available heat in each of the two streams participating in a match. y_{i, j, k} represents the binary variable in the SWS model of the grass-root solution.

Hot end (dt_{i, j, k}) and cold end (dt_{i, j, k + 1}) exchanger approach temperatures for calculation of heat exchanger area:

$$ {dt}_{\mathrm{i},\mathrm{j},\mathrm{k}}\le {t}_{\mathrm{i},\mathrm{k}}-{t}_{\mathrm{j},\mathrm{k}}+\phi \left(1-{y}_{\mathrm{i},\mathrm{j},\mathrm{k}}\right)\kern2.75em k\in K $$

$$ i\in HP,\kern0.5em j\in CP $$

$$ {dt}_{\mathrm{i},\mathrm{j},\mathrm{k}+1}\le {t}_{\mathrm{i},\mathrm{k}+1}-{t}_{\mathrm{j},\mathrm{k}+1}+\phi \left(1-{y}_{\mathrm{i},\mathrm{j},\mathrm{k}}\right)\kern2.25em k\in K $$

$$ i\in HP,\kern0.5em j\in CP $$

where ϕ is a specified value that the approach temperature would be if no match exists between hot stream i and cold stream j, which implies that the binary variable y_{i, j, k} will be 0.

EMAT calculation:

$$ {dt}_{\mathrm{i},\mathrm{j},\mathrm{k}}\ge \mathrm{EMAT}\kern2.5em k\in K,\kern0.5em i\in HP,\kern0.5em j\in CP $$

Paterson (1984) approximation of the logarithmic mean temperature difference:

$$ {LMTD}_{\mathrm{i},\mathrm{j},\mathrm{k}}=\frac{2}{3}{\left(\left({dt}_{\mathrm{i},\mathrm{j},\mathrm{k}}\right)\left({dt}_{\mathrm{i},\mathrm{j},\mathrm{k}+1}\right)\right)}^{1/2}+\frac{1}{3}\left(\frac{\left({dt}_{\mathrm{i},\mathrm{j},\mathrm{k}}\right)+\left({dt}_{\mathrm{i},\mathrm{j},\mathrm{k}+1}\right)}{2}\right) $$