CHEMICAL ENGINEERING TRANSACTIONS
VOL. 76, 2019
A publication of
The Italian Association
of Chemical Engineering
Online at www.aidic.it/cet
Guest Editors: Petar S. Varbanov, Timothy G. Walmsley, Jiří J. Klemeš, Panos Seferlis
Copyright © 2019, AIDIC Servizi S.r.l.
ISBN 978-88-95608-73-0; ISSN 2283-9216
Batch Process Integration: Management of Capacity-Limited
Thermal Energy Storage by Optimization of Heat Recovery
Jan A. Stampflia, Edward J. Lucasa,*, Donald G. Olsena, Pierre Krummenacherb,
Beat Welliga
a
Lucerne University of Applied Sciences and Arts, Competence Center Thermal Energy Systems and Process Engineering,
Technikumstrasse 21, 6048 Horw, Switzerland
b
Haute Ecole d'Ingénierie et de Gestion du Canton de Vaud, Institut de Génie Thermique, Avenue des Sports 20,1401,
Yverdon-les-Bains, Switzerland
edward.lucas@hslu.ch
Integration of batch processes is preferably accomplished by indirect heat recovery using thermal energy
storage. Such processes may have brief peaks in energy demand, necessitating high storage capacity within
short time periods. However, practical space constraints often limit maximal storage volumes, restricting the
potential capacity to recover process heat. Consequently, the required utility costs of storage-limited
integration solutions are increased, influencing their economic viability. Given increasing importance in the
industry to utilize thermal energy efficiently, process operators may want to explore what is maximally possible
energetically, within current space constraints, before contemplating expansion and further capital
expenditure. Therefore, linear programming is utilized to determine storage integration solutions which
maximize heat recovery per batch for volume-limited sensible stratified storage, specified by an insight-based
approach from Pinch Analysis. The results produce a process-specific capacity limitation chart of batch-wise
maximal heat recovery as a function of limited capacity, allowing generation of optimal storage loading and
unloading profiles. Total batch costs (investment and operating cost per batch) are used to estimate the
influence of limited capacity. The methodology is demonstrated in a case study. The resulting capacity
limitation chart shows that for a stratified storage with four VSUs, which would require a volume of 97.4 m
3 to
achieve 100 % of the indirect heat recovery potential, approximately 60 % can be covered by an 8 m3 storage.
1. Introduction
In batch and non-continuous processes, heat can be recovered indirectly through the integration of thermal
energy storage (TES). If direct heat recovery (HR) potential is achieved, further heat integration can only take
place via indirect HR using intermediate loops (ILs), and TESs also termed as heat recovery loops. Usually,
needed storage capacity is determined using a time dependent energy balance of the TES and often
optimized in terms of annualized costs (i.e. Atkins et al. 2012). A common form of TES is sensible thermal
energy storage (STES), whereby heat is stored by temperature differences between layers of storage media
(volume storage units, VSUs). Currently, no work regarding optimization of possible HR under storage volume
constraints has been published, representing a gap in the available literature, which is addressed in this
paper. A general aim of the work is to enable the finding of smaller storage tanks which can cover the major
portion of the possible HR. This causes lower investment costs and saves space. Further interests lie in the
management of the operation of such capacity-limited storages.
2. Methodology
A thermodynamic optimization model for maximizing HR for a given storage volume is presented. The
optimization assumes pre-specification of the TES, graphically, using the Indirect Source Sink Profile (ISSP)
method (Krummenacher, 1991). Information on using ISSP to determine TES VSU temperatures is given by
1027
DOI: 10.3303/CET1976172
Paper Received: 16/03/2019; Revised: 04/04/2019; Accepted: 04/04/2019
Please cite this article as: Stampfli J.A., Lucas E.J., Olsen D.G., Krummenacher P., Wellig B., 2019, Batch Process Integration: Management of
Capacity-Limited Thermal Energy Storage by Optimization of Heat Recovery, Chemical Engineering Transactions, 76, 1027-1032
DOI:10.3303/CET1976172
Olsen et al. (2016). Although the optimization model presented here uses the ISSP to determine VSU
temperature levels, it is also compatible with more sophisticated mathematical methods.
2.1 Thermodynamic optimization model
In Figure 1 the superstructure for STES is given. Subscript h (1...H) denotes hot process streams and c (1…C)
cold process streams. Generally, process streams are indexed with subscript s. Subscript k (1...K) refers to
the IL and also the VSU, whereby the top VSU is k = K + 1. Subscript l (1...L) represents the current TS.
Figure 1: Superstructure of stratified storage with utility re-balancing HEX on the ILs
Hh and Cc represent hot and cold process streams. Tk, and Ts,k represent VSU temperature and stream cut-off
temperature; both provided by the ISSP. These time independent temperatures appear before and after each
process heat exchanger (HEX). Qs,k,l represents heating and cooling of circulated storage mass (ms,k,l) by
process streams, per stream, IL and TS. QHU,c,ISSP and QCU,h,ISSP represent the time-independent utility
requirements, assuming only vertical heat transfer, given by the ISSP. Process streams excluded due to the
ISSP must also be covered by these external utilities. QHU,k,l and QCU,k,l refer to utility re-balancing, with
associated mass transfers mHU,k,l and mCU,k,l; introduced within each IL to reduce the storage volume.
Mk,l represents the mass inventory of each VSU per TS (l = 0...L), where l = 0 symbolizes initial mass
inventory. Generally, mass transfers are time-dependent and change as the storage is loaded or unloaded.
For modelling, storage medium density, heat capacity flowrates and film heat transfer coefficients of both
streams and storage flows, are all assumed constant throughout operation. Additionally, the stratification of
VSUs is considered ideal (no mixing). All heat losses and reversibilities are assumed to be zero. Stream utility
demands QHU,c,ISSP and QCU,h,ISSP , are given by:
, , = ∆ , − , (1)
, , = ∆ , − , (2)
where, ∆tc and ∆th is the duration, CPc and CPh the capacity flow rate, and Tc,T and Th,T the target temperature,
of the cold and hot process stream. Heat supplies and demands Qs,k,l, and corresponding transferred mass
ms,k,l, within each TS are given by:
, , = ∆ , − , (3)
, , = , ,, ( − ) (4)
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Thereby, Ts,k and Ts,k+1 are the corresponding cut-off temperatures, cp,sm the storage media specific heat
capacity, and Δtl is the TS duration. The VSU mass inventory at the end of each TS, Mk,l+1, is layer dependent.
Eq(5) describes the general mass balance for each intermediate VSU. Eq(6) and Eq(7) describe the mass
balance for the bottom and the top VSU.
, = , + , , − , , − , , + , , + , , − , , − , ,+ , , (5)
, = , − , , + , , − , , + , , (6)
, = + , , − , , + , , − , , (7)
Thereby mass inventories and mass transfers have always to be equal or larger than zero. The needed utility
for the re-balancing, QHU /CU ,k,l , is given by:
/ , , = / , , , ( − ). (8)
Required HEX areas are defined by Eq(9). UHEX is the HEX overall heat transfer coefficient, according to the
individual film heat transfer coefficients of media flowing through the HEX. Logarithmic mean temperature
difference for countercurrent flow is used to calculate ΔTm. ≥ ,∆ ∆ (9)
The optimization maximizes possible HR for a given volume, and the objective function is defined by:
= , , − , , = , , − , , (10)
Eq(10) includes all heat inputs and outputs, excluding utility rebalancing. Both sides give the same result, as
mass inventory at the start and end of a batch cycle have to equate:
, = , (11)
Additionally, the possible range of mass inventories is constrained, whereby Mk,max is the maximal mass
inventory of each VSU within a batch cycle and is given by. 0 ≤ , ≤ , ≤ . (12)
In stratified storages, the volume of each VSU is not static and is constrained only by total volume as follows: = , (13)
To solve the optimization problem the open source solver Clp (COIN OR linear programming) which is a
simplex algorithm from the optimization suite COIN-OR is used (Loungee-Heimer, 2003).
2.2 Cost model
To determine how limiting storage affects total costs, total batch costs (TBC) are used (Krummenacher, 1991).
TBC give costs per batch, accounting for investment costs via a batch-wise annuity factor ab (N batches;
interest i and period n) and operating costs Cop of all streams. QHU/CU,k,l and cHU/CU represent utility costs.
Investment costs for HEXs and TESs of size X, are estimated by a generalized six-tenths method, for a base
cost Cinv,b, reference size X0 and cost Cinv,0, with associated degression factor fd,X:
= , + ; , = , + , , ; = , , + , , (14)
= (1 + )(1 + ) − 1 1 (15)
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3. Illustrative case study: Modified single product batch plant
A three-stage batch process first introduced by Gremouti (1991), and later modified (Eiholzer, 2014), has been
selected as the case study. The process comprises two batch reactors and a distillation column. Relevant
stream data is shown in Table 1. Table 2 gives the utilized investment cost parameters.
Table 1: Stream data – modified SPBP
Stream Tin °C Tout °C CP kW/K Δh kW h W/m
2K tα h tω h
Distillcondenser
Distillsubcool
Refluxcondenser
Productcooling 1
Productcooling 2
Feed preheat
Distillreboiler
Feed B preheat
Feed C preheat
Reactantheating
Productreheating
111
110
135
140
85
10
115
16
65
74
72
110
50
134
75
35
60
116
78
100
95
88
403.9
0.8
917.7
19.4
17.4
24.4
905.1
22.5
6.4
35.8
43.1
403.9
46.2
917.7
1,259.4
871.8
1,222.2
905.1
1,419.4
223.1
751.6
688.8
4,000
1,000
2,000
1,000
200
500
2,000
800
500
500
500
3.08
3.08
6.33
7.83
9.00
0.00
3.08
5.58
5.68
6.08
8.60
5.25
5.25
7.83
8.50
9.67
0.50
5.25
6.08
5.98
6.33
8.90
Table 2: Cost function parameters for Eq.(14)
Investment Cinv,b (£) Cinv,0 (£) Ref. dimension X0 fd,X
HEX
TES
0
0
40,000
150,000
Area (m2)
Volume (m3)
100
100
0.78
0.71
Utility costs are given as 80 £/MWh (hot) and 5 £/MWh (cold). Storage media costs (water) are assumed
negligible. Batch-wise annuity factor is calculated for a 5 y period at 10 % interest for 2,000 batches/y.
4. Results and discussion
The STES is first defined using the ISSP (Figure 2a) which allows exploration of trade-offs between VSU
numbers (black dots), their operating temperatures, and HR (black lines; enthalpy span indicates HR within
IL).
Figure 2: (a) ISSP of the SPBP with HR = 2.9 MWh per SROP for SROP. (b) Loading/unloading profile of a 3-
IL STES.
As only VSU temperatures and HR are defined explicitly using the ISSP, storage sizing is completed by mass
and energy balancing within each TS. The shaded grey area represents an area of design freedom, termed an
”assignment zone”, within which VSU operating temperature can be chosen by graphical placement.
Placement also defines the enthalpy ranges of neighboring ILs. Zone generation is done algorithmically, to
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minimize the number of VSUs for a given HR. HR of 2.9 MWh allowed an adequate trade-off between HR, and
IL number liked to system complexity; the maximum amount of HR for a STES comprising four VSUs. The
VSU operating temperatures have been chosen according to minimizing the number of process streams which
are connected to more than one IL, which minimizes the number of HEXs required and the complexity of the
system. High temperature differences between VSUs facilitate smaller storage volumes. For the top IL, which
transfers energy between condensation and vaporization, a smaller temperature difference is allowed. Figure
2b shows the loading and unloading profile of the unlimited storage, as defined by the ISSP. This profile
shows how TES inventory is partitioned between individual VSUs during operation. As the TES is loaded, fluid
from cooler layers is heated within an IL and passed to hotter layers. In doing so, VSU volumes of hotter
layers will grow at the expense of cooler layers. The reverse is true during unloading. Over a stream-wise
repeated operating period (SROP), VSU volumes must eventually return to their initial partitioning, to begin the
loading cycle again.
During optimization, total storage volume was increasingly limited from the unlimited case (97.4 m
3 for 2.9
MWh) to zero volume. The results of the optimization for maximizing HR under these conditions are shown
(Figure 3a). The plot shows how total HR (indirect HR of all ILs plus direct HR) reduces as the capacity of the
storage decreased, and is termed the Capacity Limitation Chart. The plotted black line shows to what extent
indirect HR could be maximized for each limited volume, by the optimization model. In general, as maximum
volume is reduced, total HR is decreased from the maximum, to that provided only through direct HR.
Figure 3: (a) Capacity Limitation Chart of the modified profile of one SPBP for STES. Black dot: maximum
volume. (b) Loading and unloading SROP for the 3-IL STES limited to 40 m3.
It can be observed that maximum HR per SROP, as determined by optimization, transitions through three
phases of behavior. As volume is increasingly limited, the loading and unloading profiles of the storage will
also change. At any interstitial volume limitation, the loading and unloading profiles can be generated. Figure
3b shows the storage profile when limited to a total volume of 40 m3, marked by the green dot (Figure 3a). In
comparison to the unlimited profiles, relative partitioning of the VSU volumes depends on the degree of
storage limitation. The profiles are generated using a strategy, whereby VSU are only allowed to empty at the
end of a TS, achieved by modulating the flow of storage media within each IL. As a result, the loading and
unloading rates of the VSUs (slopes in Figure 3b) and maximal volume per VSU are changed. The smaller
mass and heat flows within each TS results in smaller required IL HEXs.
Slope differences in the black line (Figure 3a), indicate two critical changes in how effective the STES system
is recovering heat under limitation. Since optimization always reduces the VSUs first, which reduces capacity
least (smaller temperature differences between VSUs result in less capacity), two slope changes of the HR
curve occur whenever a new VSU becomes empty and cannot be refilled. The two located points are at 18 m
3
and 8 m3. The initial limitation from maximal volume to 18 m3 reduces HR approximately 887 kWh. From 18
m3 to 8 m3 HR loss is 239 kWh. Limitation to 0 m3 causes a further 915 kWh HR loss, which is more than
reducing from maximum to 18 m3. Throughout limitation, direct HR is constant at 944 kWh. A storage with a
volume of just 8 m3 nearly doubles the possible HR to 1,859 kWh. A further increasing of the volume to the
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maximal needed volume of 97.4 m3 causes an additional HR of 1,125 kWh. Consequently, 60 % of the total
maximum HR can already be achieved within the initial 8 m2, with total HR severely reducing below this limit,
representing a minimum recommended volume target of the storage.
Table 3: Costs of SPBP TES under fully limited, partially limited and unlimited conditions
Volume (m3) HR (kWh) HR relative (%) ab.Cinv (£/SROP) Cop (£/SROP) TBC (£/SROP)
0.0
8.0
97.4
944
1,748
2,900
32.55
60.28
100.00
58.12
58.35
69.97
243.59
170.00
74.95
301.71
228.35
144.92
As expected TBC were found to be minimum when the storage volume is unlimited (Table 3). Nevertheless, it
can be seen that TBC are increased nearly by the same amount by removing an 8 m3 storage or limiting the
storage volume to 8 m3. For TBC, operating cost per batch are the dominant contributor. Investment costs
affect TBC relatively less, as these are distributed across batches. However, when the volume is limited, two
possibilities emerge: Either, storage volume can be kept limited, or space extensions can be considered.
Costs for building extensions are not considered in the TBC. By considering these costs, it may be more
economical to reduce storage volume.
The optimized arrangement and desired loading/unloading profiles present a potentially challenging control
problem, as during operation constant inlet temperatures to the storage are required to prevent severe
degradation of the stratified thermocline. Therefore, HEX control strategies should also be considered in future
research. Additionally, although HR was maximized, TBC are not minimized under the condition of maximized
HR (Krummenacher, 1991). Optimized TBC would allow a better exploration of the trade-offs between HR and
relaxing space constraints, provided localized space costs are known.
5. Conclusions
The model maximizes total HR within a process utilizing a HEN and TES, under limited volume conditions.
The Capacity Limitation Chart directly shows the relationship between HR and storage volume constraints,
demonstrating how detrimental storage volume constraints are to potential future energy savings. It identifies
critical storage volumes, where the HR-storage volume relationship critically changes and indicates the
minimum recommended storage volume sizes. For the given case study, using the optimization model to
locate an arrangement of VSUs and loading profiles, a minimum recommended storage volume of 8 m2 was
identified, which could still provide 60 % of the available HR potential.
By adding an economic optimization it could be indicated when relaxing space constraints by further capital
expenditure would be appropriate. Where only energy savings are prioritized or no space extension of the
plant is possible, the linear programming approach as presented is adequate to perform the optimization.
Acknowledgements
This research project is financially supported by the Swiss Innovation Agency Innosuisse and is part of the
Swiss Competence Center for Energy Research SCCER EIP.
References
Atkins M.J., Walmsley M.R.W., Neale J.R., 2012, Process integration between individual plants at a large
dairy factory by the application of heat recovery loops and transient stream analysis. Journal of Cleaner
Production, 34, 21-28.
Eiholzer T., 2014, Indirect Heat Integration in Batch Processes with Variable Schedules. Master dissertation,
Lucerne University of Applied Science & Arts, Lucerne, Switzerland.
Gremouti I.D., 1991, Integration of batch processes for energy savings and debottlenecking. Master
dissertation, University of Manchester Institute of Science and Technology, Manchester, UK.
Lougee-Heimer R., 2003, The Common Optimization INterface for Operations Research: Promoting open-
source software in the operations research community. IBM Journal of Research and Development, 47(1),
57-66.
Krummenacher P., 2001, Contribution to the heat integration of batch processes (with or without heat
storage). PhD thesis, École polytechnique féderale de Lausanne, Lausanne, Switzerland.
Olsen D., Abdelouadoud Y.L., Wellig B., Krummenacher P., 2016, Systematic thermal energy storage
integration in industry using pinch analysis. In The 29th International Conference on Efficiency, Cost,
Optimization, Simulation and Environmental Impact of Energy Systems, pages 1–14, Portoroz, Slovenia.
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