Optimising entire lifetime economy of heat exchanger networks
Andreja Nemeta, Jiří Jaromír Klemešb, Zdravko Kravanjaa,*
a
Faculty of Chemistry and Chemical Engineering, University of Maribor, Maribor, Slovenia
Centre for Process Integration and Intensification-CPI2, Research Institute of Chemical and Process
Engineering – MÜKKI, Faculty of Information Technology, University of Pannonia, Veszprém,
Hungary
zdravko.kravanja@um.si
b
Published in Energy (2013), Volume 57, Pages 222-235
Summary
This contribution presents an optimisation methodology for Heat Exchanger Network (HEN) design
over its entire process lifespan. A consideration of fluctuating energy prices has been essential for
achieving optimal HEN design. The objective function presents a trade-off between investment and
operating cost. Considering higher energy prices give rise to larger investments compared to solutions
obtained with current prices. However, due to the uncertainty of utility prices forecast, the retrofit with
extension of HEN in future years of the lifespan is usually the common strategy. As there can be
various designs featuring similar initial investment, the objective is to identify one design that is the
most suitable for effective future extensions and preferably with lowest sensitivity to energy price
fluctuations. Those observations led to the development of a stochastic multi-period mixed-integer
nonlinear programming (MINLP) model for the synthesis of HEN designs with extensions accounting
for future energy prices. The objective of this work was maximising both Expected Net Present Value
with no risk assessment performed and Certainty Equivalent with risk assessment regarding future
utility prices and investment. The results obtained indicate that applying the proposed approach, a
design with improved economic performance could be obtained, especially with Total Annual Cost.
Background
The proper HEN synthesis targets improvement the process profitability. The Heat Integration (HI)
has been pioneered from the 70s of the last century by Linnhoff et al. (1982). Over the time it has been
still considerably developing by number of researchers worldwide. Nowadays, there are three main
directions of the research regarding HI: the thermodynamically based Pinch Technology, mathematical
programming (MP) and the combination of these two approaches. In the industry the degree of HI
depends on an appropriate trade-off between investments and operating cost. The extent of heat
recovery is naturally dictated by the economy: when the utility prices increase, the desire of the heat
recuperation also increases. A MP approach can efficiently optimise the energy/capital trade-off. One
of the first models for HEN synthesis was developed by Yee and Grossmann (1990). It offers a
solution of the problem however with some limitations and simplifications, e.g. the calculation of heat
exchanger area in this approach is based on stream-individual film and fouling coefficients. A
numerous extensions of this model have been made over time, however, none of the models can reflect
the future development and especially fluctuation of the utility prices. If the prices of energy are fixed
over the entire lifetime of the process, the results are unrealistic as prices considerably vary throughout
the process lifetime.
Suggested citation: Nemet, A., Klemeš, J. J., & Kravanja, Z. (2013). Optimising entire lifetime
economy of heat exchanger networks. Energy, 57, 222-235.
Aims
The aim of this work was to develop a multi-period MINLP model, where future utility prices are
considered. The model requires utility price projections. Therefore, a methodology to obtain future
forecasted utility prices is required as well. There are different possibilities when the optimisation is
based on the utility prices forecast. The aim is to consider different price projections separately –
deterministic approach and also simultaneously – stochastic approach, where all the scenarios are
considered simultaneously with assigned probabilities. Additionally, the aim is also to analyse the
decision about the scheduling: whether it should be performed at the beginning of the lifetime or an
extension should be performed some later time during lifetime. The second approach requires an
initial HEN, which could be easily extended (both economy and logistic should be considered), if the
utility prices increase. The proposed method thus considers future utility prices and aims at identifying
an initial HEN design with an investment similar to the one that would be obtained at current energy
prices, and yet being suited for efficient extensions later during the operation.
Methods
The superstructure developed by Yee and Grossmann (1990) is applied since it is a robust approach,
which could be extended for multi-period optimisation, with different price projection considered. It is
based on idea, that each hot stream can be potentially matched with each cold stream. The utilities are
placed at the extreme ends of the process streams. An isothermal mixing of streams at the outlets of
the matches is imposed within this superstructure.
In order to consider future utility prices, they have to be forecasted for the time horizon expected that
the optimised HEN design will be in use. In literature there are different approaches to predict
operation cost. In this work a price projections are based on the historical data for gasoline prices
(IndexMundi, 2012) has been applied. A monthly basis was applied in order to obtain more precise
data for projections. The data time period was 10 y, from April 2002 to April 2012. The forecasting
for hot and cold utilities has been needed since both utility prices can vary. Different projections at
different probability levels using Gaussian distribution for cost coefficients are derived in order to
consider uncertainty in future prices: a very optimistic one for underestimated price coefficients at
probability level pl = 0.068 (Projection 1 – P1), optimistic at 0.2417 (Projection 2 – P2), average at
0.383 (Projection 3 – P3), pessimistic at 0.2417 (Projection 4 – P4), and very pessimistic projection for
overestimated price coefficients at probability level 0.0668 (Projection 5 – P5), Fig. 1.
-1
0.23
cHU/€ (kWh)
y = 0.086e0.0083x
0.21
0.19
y = 0.0904e0.0063x
y = 0.0835e0.006x
0.17
y = 0.0779e0.0058x
y = 0.0759e0.0056x
0.15
0.13
0.11
0.09
0.07
0
20
40
60
80
100
t/ month
120
Fig. 1: Different basis for further projections for hot oil
Suggested citation: Nemet, A., Klemeš, J. J., & Kravanja, Z. (2013). Optimising entire lifetime
economy of heat exchanger networks. Energy, 57, 222-235.
Determining probabilities of a HEN design being at a certain price projection and time period
Starting from the current price, the utility price can follow many different price scenarios over HEN
lifetime, jumping from one to other price projections, Fig. 2. There are approximately 3∙10 10 different
scenarios (determined as 515,), if 5 different utility price projections are proposed and 15 y of lifetime
is assumed. As the Expected Net Present Value (ENPV) is defined as a sum of their individual ENPVs
multiplied by their probabilities, the corresponding optimisation model would be too large to be solved
even for shorter lifetimes. Rather than considering these scenarios separately with their individual
probabilities, combined probabilities, pn,v , were proposed. It is a probability for a HEN design being
at a certain price projection v and time period n, which are determined in order to perform stochastic
multi-period synthesis of HEN. The probabilities are now determined as a sum of individual
probabilities of all the scenarios being at a certain price projection and time period. By utilising this
approach the individual scenarios are composed into combined ones, one for each projection. The
number of scenarios for 15 y is now significantly reduced - down to 5.
The combined probabilities are defined in the following way. Each of price transition, from any
current price projection u to any other projection v in the next period, has its own transition
probability, tru,v. The probability of a specific price projection in a certain period, pn,v, is defined as the
sum of the probabilities, that a price scenario will follow the projection on a current position from all
projections at the previous period. The probability of the jump from a previous projection u to the
current one v is defined as a multiplication of previous probability pn-1,u by the corresponding transition
probability, tru,v (see e.g. for Projection 3 - highlighted transitions, Fig. 2). The calculation of
probabilities pn,v starts from the root node (Fig. 2). If the current, starting price lies on one of the
projections, the probability p0,v for this projection is 1, and it is 0 for the rest of projections. If the price
lies somewhere in-between of two projections, it can be expressed as a linear combination of the
adjacent projections’ prices. The coefficients from the linear combination then represent probabilities
p0,v for the two projections.
Period Projection 1
n-1
Projection 2
Projection 3
Projection 4
Projection 5
n
n+1
pn,v
pn,u
tru,v
Fig. 2: Time-projection grid for the determination of probabilities
Results
The ENPV of the stochastic HEN design obtained with this model is compared to the ENPV which
would be realised, if the reference HEN design, synthesised by the MINLP deterministic programming
model at current utility prices, without later extensions is exposed to the same future prices and
probabilities as the stochastic HEN design. Note that the reference ENPV was -12,774.3 k€.
Considering all possible future price scenarios simultaneously in this stochastic approach, the
Suggested citation: Nemet, A., Klemeš, J. J., & Kravanja, Z. (2013). Optimising entire lifetime
economy of heat exchanger networks. Energy, 57, 222-235.
extension becomes economically unreasonable after eleventh year of lifetime (Fig. 3), as this would
lead to higher incremental investment compared to the money savings achieved from the reduction of
utility consumption.
ENPV/ k€
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 n15
ext / y
Figure Error! No text of specified style in document.: Impact of the year of extension on the ENPV
when applying the stochastic approach to Case Study 1
Acknowledgments
The authors acknowledge the financial support from EC FP7 project ENER/FP7/296003/EFENIS
‘Efficient Energy Integrated Solutions for Manufacturing Industries – EFENIS’, from the Hungarian
State and the European Union project TAMOP-4.2.2.A-11/1/KONV-2012-0072 – Design and
optimization of modernization and efficient operation of energy supply and utilization systems using
renewable energy sources and ICTs, and from the Slovenian Research Agency (Program No. P20032).
References
IndexMundi. www.indexmundi.com; 2012 [accessed 21.07.12]
Linnhoff, B., Townsend, D., Boland, D., Hewitt, G., Thomas, B., Guy, A., Marsland, R. (1982) A user
guide on process integration for the efficient use of energy, IChemE, Rugby.
Yee, T., Grossmann, I. (1990) Simultaneous optimization models for heat integration II. Heat
exchanger network synthesis. Computers and Chemical Engineering, 14(10), 1165-1184.
Suggested citation: Nemet, A., Klemeš, J. J., & Kravanja, Z. (2013). Optimising entire lifetime
economy of heat exchanger networks. Energy, 57, 222-235.