Area-based optimization approach for refinery heat exchanger networks

Applied Thermal Engineering 129 (2018) 606–617

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Area-based optimization approach for refinery heat exchanger networks Lluvia M. Ochoa-Estopier a, Megan Jobson a,⇑, Lu Chen b a b

Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, Sackville Street, Manchester M13 9PL, UK Process Integration Limited, Station House, Stamford New Road, Altrincham, Cheshire WA14 1EP, UK

a r t i c l e

i n f o

Article history: Received 18 February 2017 Revised 19 September 2017 Accepted 8 October 2017 Available online 10 October 2017 Keywords: Preheat train Crude oil distillation unit Retrofit Operational optimization

a b s t r a c t This paper presents a new approach to optimize large-scale heat exchanger networks (HENs). The approach is particularly suitable for operational optimization and retrofit of industrial crude oil preheat trains, but it can be applied to HENs from other processes. Two main features distinguish this approach: first, an area-based simulation model that significantly simplifies the optimization, while capturing the details of the existing HEN. Second, a decomposition procedure to divide the large-scale HEN into two simpler HENs, which are optimized sequentially. This approach includes additional features that provide a more realistic representation of preheat trains, such as temperature-dependent heat capacities, the dependence of heat transfer coefficients on flow rate variations, and new types of stream splitters and mixers for the distillation products in the HEN. An industrial case study illustrates the application of the methodology, showing that the approach identifies opportunities to reduce energy consumption with minimal changes to the HEN structure. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction The optimization of heat exchanger networks (HENs) has been a topic of industrial and academic interest for more than three decades. From simple procedures based on thermodynamic principles to sophisticated computer algorithms, the optimization of heat exchanger networks continues to be a challenging area of process engineering. Early design approaches based on thermodynamic principles, such as pinch analysis introduced by Linnhoff [1], continue to provide useful insights to evaluate and target the energy consumption of existing HENs. However, the use of mathematical programming, as this paper shows, allows the consideration of more details and the evaluation of more design options. Various approaches have been developed to perform retrofit of HENs; a comprehensive review of retrofit approaches can be found in [2]. These approaches can employ simple thermodynamic principles, optimization algorithms, or a combination of both. Graphical methods based on thermodynamic principles have been developed to retrofit HENs, such as methods based on pinch analysis [3], bridge analysis [4] or Retrofit Thermodynamic Diagrams [5]. Because of their ability to analyze complex heat exchanger networks in a simplistic manner, these methods tend to provide optimistic solutions that often prove impractical and less cost-effective once a more detailed assessment is carried out [6]. For this reason, ⇑ Corresponding author. E-mail address: [email protected] (M. Jobson). https://doi.org/10.1016/j.applthermaleng.2017.10.049 1359-4311/Ó 2017 Elsevier Ltd. All rights reserved.

thermodynamic principles are often employed along with optimization algorithms that can carry out more detailed economic calculations and can handle more practical constraints. Examples of these combined approaches are the works of Pan et al. [7] and Rohani et al. [8], who used the concepts of ‘network pinch’ [9] and ‘bridges’, respectively, to build HEN superstructures that are optimized using MINLP. Even though optimization-based approaches for HEN retrofit facilitate the consideration of more practical constraints, these approaches still make simplifying assumptions that may produce impractical and inaccurate solutions. Regarding the retrofit of crude oil preheat trains, three aspects are typically simplified: a) the type of structural modifications considered in the optimization, b) the prediction of properties and, c) the representation of the heat exchanger network. 1.1. Approaches used to simplify the HEN optimization problem Optimization approaches reported suitable for large-scale HENs can introduce structural inflexibilities that bias the search process for retrofit solutions. For example, the predefinition of the location and number of matches and splitters in a superstructure stage [10] and the failure to consider relevant retrofit modifications, such as stream splitting [7] and relocation of existing heat exchangers [11]. Other works, such as the approach of Bagajewicz et al. [6], consider retrofit modifications relevant to crude oil HENs, such as adding new matches, additional shells and heat transfer area,

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Nomenclature Latin letters A vector of heat transfer areas A heat transfer area b vector of the indices of outlet streams related to the split fraction C vector of utility prices CP vector of heat capacity flow rates CP vector of average heat capacity flow rates CP heat capacity flow rate Cp vector of heat capacities Cp heat capacity Cps heat capacity at the supply temperature Cpt heat capacity at the target temperature EMAT vector of calculated exchanger minimum approach temperatures EMAT exchanger minimum approach temperature F volumetric flow rate Ft exchanger temperature correction factor H film heat transfer coefficient LMTD logarithmic average of the temperature difference M incidence matrix m vector of flow rates N number of HEN elements NTU number of transfer units q heat exchanger duty QU vector of utility energy requirements sp split fraction matrix for open-ended splitters S number of edges T vector of temperatures T temperature TS vector of specified supply temperatures TS supply temperature specification TT vector of specified target temperatures TT target temperature specification U overall heat transfer coefficient Greek letters a vector of split fractions for conventional splitters b vector of split fractions for open-ended splitters DT vector of temperature change specifications

stream splitting and relocation of existing exchangers. However, the approach of Bagajewicz et al. [6], based on the model of Nguyen et al. [12], assumes constant temperature-dependent properties (e.g. heat capacity). Considering the effect of temperature on heat capacity is important when streams undergo significant temperature changes; such is the case of crude oil and its products. It is reported [13] that assuming constant heat capacities in crude oil preheat trains can lead to prediction errors in the furnace inlet temperature of more than 25 °C. Stochastic optimization approaches allow more details (e.g. non-linear cost functions, temperature-dependent heat capacities, non-isothermal mixing, maximum number of modifications) to be incorporated in the HEN retrofit problem, compared to deterministic optimization approaches. The reason for this is that stochastic optimization does not rely on the calculation of derivatives to find a solution. Details such as temperature-dependent heat capacities [14] and variable heat transfer coefficients [15] have been considered in HEN retrofit approaches that employ simulated annealing [14] and genetic algorithms [15]. However, the main drawback of these stochastic approaches is that they are computationally expensive [16].

DT DH

w

temperature difference vector of enthalpy change specifications heat capacity ratio

Subscripts + matrix of positive elements ADD additional area c cold stream CALC calculated value h hot stream HEN indicates overall HEN I tube side INST installed area min minimum value O shell side PH exchangers in the primary HEN PS unbroken streams in the primary HEN S shell side SH exchangers in the secondary HEN SS streams in the secondary HEN T tube side x indicates stream break points Superscripts ⁄ new specification HE heat exchangers mx open-ended mixers PD demand units PDS demand units in the secondary HEN PRH unit operations specified in terms of enthalpy PRT unit operations specified in terms of temperature SP conventional splitters sp open-ended splitters T transpose of an array util utility Mathematical operators diag diagonal matrix operator ° Hadamard product

Other simplifications typically made for the optimization of crude oil preheat trains relate to the modeling of the network. Most of the works in the literature specify the heat exchangers in terms of duty, instead of area. The advantage of using duty-based models is that exchangers are easier to simulate, compared to area-based models. However, with duty-based models, it is more difficult to capture the real-life area constraints of installed equipment during retrofit optimization. When heat exchangers are specified in terms of area, relevant variables (e.g. area installed in the network, per exchanger, additional area requirements) can be readily monitored and optimized. This paper presents a methodology that overcomes some of the simplifications typically made when optimizing crude oil preheat trains. In particular, this paper considers retrofit modifications relevant to crude oil heat exchanger networks, temperaturedependent heat capacities, the variation of overall heat transfer coefficients with flow rate changes and exchangers specified in terms of area, and applies a more accurate model to represent the mixing and splitting of two or more crude oil products. The advantage of considering these details in the optimization problem is that more accurate and industrially-relevant solutions can be

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achieved with little additional computational effort. A decomposition procedure that divides the HEN into two simpler networks is introduced in this work to facilitate the solution of the optimization problem. 1.2. Consideration of operational optimization and changes in the distillation process Operational optimization can be addressed using a simpler formulation than that for the retrofit problem. With the limitation of fixed HEN structure and heat transfer area, the available degrees of freedom include stream split ratios, heat exchanger bypass ratios and process stream conditions (e.g. supply and target temperatures and flow rates). While changes to splitters and bypass ratios can be made relatively easily at the HEN level, changes to stream conditions involve operational changes to the background process (e.g. the distillation process). Procedures based on pinch analysis [17] or exergy analysis [18] can help to identify process changes that could potentially increase heat recovery, but neglect constraints related to the crude oil distillation unit (CDU) [17] or HEN [18]. To obtain energy savings from operational optimization, changes to the distillation process need to be exploited. Similarly, additional economic benefits can be achieved when HEN retrofit is carried out together with changes to the distillation process. Approaches to optimize CDUs and HENs simultaneously that consider their practical constraints (e.g. product quality, installed heat transfer area per exchanger) have been developed [19,20]. These approaches develop surrogate models for the CDU and implement them in an optimization framework for operational optimization [19] and retrofit [20]. The methodology presented in this paper proposes a new HEN model and retrofit algorithm suitable for simultaneous optimization of CDUs and the associated HEN. The development of CDU models and their implementation into the optimization framework is discussed in detail elsewhere [21]. The limitations of existing models, e.g. related to structural options in the HEN and to heat transfer area being a dependent variable, motivate the development of a new model for simulation, operational optimization and retrofit of HENs. A case study illustrates the new modeling and optimization approach; its results indicate that the approach successfully identifies opportunities to reduce energy consumption with minimal or no retrofit modifications. 2. Methodology This work proposes a new simulation model and retrofit algorithm for industrial HENs. The proposed methodology extends the work of Ochoa-Estopier et al. [22] to provide a more accurate representation of complex HENs, for example, crude oil preheat trains, and to improve the computational performance of the algorithm responsible for ‘repairing’ the violation of HEN constraints. To deliver a more appropriate representation of the HEN, new features include the specification of heat exchangers in terms of area, rather than heat load, consideration of the variation of heat transfer coefficients with flow rate changes and new types of mixers and splitters that represent arrangements typically found in crude oil preheat trains. The approach is formulated in two levels, as shown in Fig. 1. The first level (Section 2.2) performs HEN retrofit modifications, while the second level of the approach (Section 2.3) addresses heat recovery and the violation of HEN constraints. The first level of the approach is an MINLP problem that is solved using a simulated annealing (SA) algorithm. SA randomly selects which retrofit modification to perform from a list of feasible candidates, based on predefined probabilities. The second level of the approach is an NLP

Fig. 1. Proposed two-level optimization framework.

problem which is solved using an interior-point algorithm. The second level of the algorithm is referred to in this work as a ‘repair algorithm’ since its objective is to ‘repair’ the violation of HEN constraints (e.g. exchanger minimum approach temperature, EMAT; existing heat transfer areas and enthalpy balances). A new feature of this repair algorithm is the decomposition of the complex HEN into two simpler HENs, which are optimized sequentially. This decomposition is useful to reduce the size of the optimization problem and thus it is easier for the algorithm to handle constraints. The proposed two-level approach employs a HEN simulation model (see Fig. 1), which is central to the methodology (Section 2.1). The simulation model is a linear model that calculates flow rates and temperatures. This model is used to assess any violation of constraints and to calculate operating costs. This simulation model, extended from the model by de Oliveira Filho et al. [23], is specified in terms of heat transfer area rather than heat loads. This consideration significantly simplifies monitoring the extent to which installed heat transfer area is ‘used’ and facilitates identification of additional heat transfer area requirements. 2.1. Simulation model The HEN simulation model calculates the inlet and outlet temperatures and flow rates of each heat exchanger, mixer and splitter in the HEN. In this model, the HEN structure is represented using the formulation of de Oliveira Filho et al. [23]. An incidence matrix M (dimension N
S) concisely stores and allows manipulation of this structural information, where N vertices represent the number of elements of the HEN (e.g. supply and demand units, heat exchangers, mixers, splitters) and S edges represent the inlets and outlets of each of these HEN elements. The mass and energy balances are linear equations formulated in terms of this incidence matrix. For more details on the original model formulation, the reader is referred to [23]. The next sections of this paper describe extensions to this simulation model. 2.1.1. ‘Open-ended’ stream splitters and mixers New open-ended mixing and splitting elements are illustrated in Fig. 2(a), namely mixer M2 and splitter S2. Mixer M2 in Fig. 2 (a) mixes streams H1 and H2 into one stream, H4. Splitter S2 in Fig. 2(a) divides stream H3 into two streams, H5 and H6, which can have different target temperatures. This open-ended mixer configuration is typically found when distillation products exchange heat in the HEN, are mixed into a single product, and continue to cool down in the network (e.g. diesel

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Fig. 2. (a) Example of HEN with open-ended mixer (M2) and splitter (S2); (b) Graphical representation of old and new modeling approaches. S1, conventional splitter; M1, conventional mixer; P1, simple unit operation; EMAT, exchanger minimum approach temperature; EMATmin, minimum allowed EMAT for the heat exchanger network.

with gas oil). Fig. 2(b) compares the representation of heat exchanger 1 (HE1) using the new and old simulation models. In the old model, HE1 is decomposed into two exchangers (HE1a and HE1b) with a total heat transfer area equal to that of HE1. However, this poor representation of HE1 results in the EMAT of HE1b being less than the acceptable value of EMATmin. When this situation occurs during optimization, the optimizer unnecessarily tries to avoid the violation of the minimum EMAT constraint and to reach an acceptable value of EMAT for HE1b. Furthermore, outlet temperatures, heat transfer areas and retrofit modifications cannot be accurately represented using a model that treats a single exchanger (HE1) as two independent heat exchangers (HE1a and HE1b). Another option to represent streams H1, H2 and H4 without using M2 would be to specify these streams – and their corresponding supply and target temperatures – separately (similar to streams H3, H5 and H6 in the old model). While this option does not need to divide HE1 into HE1a and HE1b, it fixes the final temperatures of H1 and H2 and initial temperature of H4 during HEN optimization, which undermines the flexibility of the HEN. Eqs. (1)–(3) describe the new type of mixer added to the structural model of de Oliveira Filho et al. [23]:

Mmx m ¼ 0

ð1Þ

Mmx ½diagðCPÞT ¼ 0

ð2Þ

CP ¼ m  Cp

ð3Þ

where Mmx (dimension Nmx
S) is the section of the incidence matrix corresponding to the Nmx open-ended mixers, m (dimension S
1) is the vector of flow rates of the HEN, 0 is a vector of zeros, T (dimension S
1) is the vector of temperatures of the HEN, CP (dimension S
1) is the vector of heat capacity flow rates of the HEN streams, Cp (dimension S
1) is the vector of heat capacities, operator diag indicates a diagonal matrix, and ° indicates the Hadamard product, otherwise referred to as element-wise multiplication. Contrary to the mixer-splitter model described in [23], the number of mixers in the new model can be different to the number of splitters. The open-ended splitter configuration (e.g. S2 in Fig. 2a) is typically found in side draws of vacuum distillation units, where a

stream is withdrawn from the column, cooled down and then split into two streams: a vacuum distillation product and a pumparound. Fig. 2(b) compares the new and old modeling approaches. The main difference between these models is that the new model considers the final temperature of stream H3 equal to the initial temperatures of H5 and H6 (T1 = T2 = T3) keeping T1 unconstrained, while the old model does not consider the dependence of T2 and T3 on T1. This dependence is important during optimization, as changes in the HEN structure, heat transfer area and/or stream conditions unbalance the HEN and can lead to T1, T2 and T3 having different values. The new approach constrains T1 = T2 = T3 regardless of the value of T1. Eqs. (4) and (5) represent the new type of splitters included in the model of de Oliveira Filho et al. [23]:

"

"

# Msp m¼0 diagðbÞMsp þ  sp Msp ½diagðCPÞ Msp þ  sp

ð4Þ

# T¼0

ð5Þ

where Msp (dimension Nsp
S) is the section of the incidence matrix sp corresponding to the Nsp open-ended splitters, Msp þ (dimension N
S) is the matrix with the positive elements of Msp. Vectors b and b (dimensions Nsp
1) and matrix sp (dimension Nsp
S) are introduced to express the mass balance, Eq. (4), in terms of the incidence matrix. b is the vector of split fractions of the new type of splitters, b indicates the edges for which the split fractions are specified and sp is a matrix such that spij = 1 if bi = j; otherwise spij = 0. Eqs. (1)–(5) are formulated in the same way as the conventional mixers and splitters of the model by Oliveira Filho et al. [23]. However, the open-ended mixers and splitters described in Eqs. (1)–(5) have fewer degrees of freedom available during HEN optimization. More specifically, split and mix ratios for the new types of splitters and mixers remain fixed unless operational changes to the associated process take place. For example, only changes to the CDU product flow rates can change the mixing ratio of distillation products H1 and H2 in Fig. 2(a). Another difference between the new type and conventional mixers is that the new approach permits more realistic calculation of a stream’s heat capacity, Cp. For the new type of mixers, the

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mixed stream is a combination of two process streams, which can have different dependencies of Cp with temperature. For conventional mixers, Cp must be calculated based on a single process stream. 2.1.2. Simple unit operations Another extension to the model by Oliveira Filho et al. [23] is the inclusion of simple unit operations, such as desalters and heat recovery steam generation units. These simple unit operations may result in an enthalpy change in the corresponding stream without exchanging heat in the HEN. This element is identified as P1 in Fig. 2(a) and can be specified in terms of enthalpy change or temperature change. Eqs. (6) and (7) describe this HEN element:

"

"

# MPRT m¼0 MPRH h

#   PRT DT  M i PRH T ¼ PRH diag CP M DH

ð6Þ

ð7Þ

where MPRT (dimension NPRT
S) and MPRH (dimension NPRH
S) are the sections of the incidence matrix related to the unit operations specified in terms of temperature change (NPRT) or enthalpy change

Fig. 3. Procedure to simulate HENs considering the correction of heat transfer coefficients and temperature-dependent heat capacities.

(NPRH), CPPRH (dimension NPRH
1) is the average heat capacity flow rate in each unit operation NPRH, DT (dimension NPRT
1) is the temperature change specification and DH (dimension NPRH
1) is the enthalpy change specification.

tions for process stream i. Note that for process streams using open-ended mixers, the heat capacity of the mixed stream is calculated based on the heat capacities of the unmixed streams and the corresponding mixing ratio.

2.1.3. Correction of heat transfer coefficients The HEN simulation model is extended in this work to represent the dependence of heat transfer coefficients on flow rate. Flow rates change if the splitter split fractions vary during HEN optimization or if changes to the background process are performed (e.g. changes in CDU yields or pump-around flow rates). The dependence of heat transfer coefficients on flow rate can be approximated using Eqs. (8) and (9) [24]:

2.2. Level 1: Retrofit modifications

 0:8 hT2 F I2 ¼ hT1 F I1

ð8Þ

 0:64 hS2 F O2 ¼ hS1 F O1

ð9Þ

where h represents film transfer coefficients, F represents volumetric flow rates, subscripts T and I indicate the tube side of the heat exchanger, subscripts S and O indicate the shell side of the heat exchanger and subscripts 1 and 2 indicate initial and new (updated) flow rates. Fig. 3 shows the implementation of Eqs. (8) and (9) into the HEN simulation procedure. 2.1.4. Temperature-dependent heat capacities HEN optimization approaches typically consider constant heat capacities to simplify the formulation of the optimization problem. However, this assumption is not valid when streams undergo phase change or significant temperature variations, as is the case in crude oil distillation [13]. This work uses linear equations to account for the dependence of heat capacities on temperature. The heat capacity of process stream i at a given temperature T can be calculated using linear interpolation [21]:



Cp ¼

   Cpsi ðwi  1Þ Cpsi ðTT i  wi TSi Þ Tþ TT i  TSi TT i  TSi

ð10Þ

where Cpsi is the heat capacity at the supply temperature, wi is the ratio between the supply and target heat capacities (i.e. wi = Cpti/ Cpsi), TSi and TTi are the supply and target temperature specifica-

The retrofit algorithm used in this work modifies the HEN structure at random potentially-feasible locations. Here, feasible refers to HEN structures that meet constraints specified by the user, such as the maximum number of new heat exchangers and splitters in the HEN and per stream, forbidden matches, the maximum addition of heat transfer area to the HEN or to an exchanger, and minimum exchanger approach temperatures. The modifications considered are: add, remove or relocate a heat exchanger, add or remove a stream splitter, add new area to an existing exchanger, and change the split fraction of a stream splitter. The retrofit algorithm of Ochoa-Estopier et al. [22] is modified to use the area-based simulation model. The new procedure developed for the ‘additional area’ modification identifies the requirements for additional heat transfer area in each exchanger based on the estimated number of transfer units (NTU = UA/CPmin). First, the simulation model calculates the NTU of each exchanger. Shell-and-tube heat exchangers with NTU values greater than approximately 4 are discarded as candidates for the ‘additional area’ modification, as increasing the area of these exchangers would not significantly increase heat transfer [25]. Heat exchangers identified by the user as unable to accept additional area (e.g. due to space or budget restrictions) are also discarded. The remaining exchangers are ranked according to their installed area and NTU value. The retrofit algorithm randomly selects a candidate for modification by applying probabilities. These probabilities are assigned to exchangers according to their weighted contributions to total installed area and NTU value. A constraint is set to limit the amount of area that can be added to a selected exchanger without exceeding an NTU value of 4. 2.3. Level 2: Repair algorithm After the HEN has been modified using the Level 1 algorithm, stream split fractions and heat duties will have changed throughout the network. As a result, some of the operational constraints

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will not be met. These operational constraints are: used heat transfer areas are less or equal than installed areas; total additional heat transfer area in the network is below a user-specified value; EMAT for each exchanger is greater or equal than EMATmin; stream enthalpy balances are met (i.e. calculated and specified target temperatures are equal). The repair algorithm firstly readjusts heat and material flows in the network to meet constraints. Many solutions can be found that ‘repair’ the HEN (i.e. meet constraints), but these solutions do not all perform equally well with respect to heat recovery. The second role of the repair algorithm is to optimize heat and material flows in the HEN. Thus, the role of the repair algorithm is to ensure that operational constraints of the HEN are met and to minimize energy costs. The repair algorithm pursues practicable solutions; in particular, it meets constraints relating to minimum additional area per exchanger, as it may be impractical or expensive to install small increments. Together, these features of the repair algorithm introduce considerable computational complexity. Therefore, this work modifies the repair algorithm of Ochoa-Estopier et al. [22] to simplify the optimization problem. The main modification is the decomposition of the HEN into two simpler HENs, which are solved sequentially. This approach is particularly useful for large-scale networks. As the network becomes larger in size and more modeling details are considered (e.g. temperature-dependent heat capacities, variation of heat transfer coefficients), it becomes harder for the optimizer to handle the many variables and constraints involved in the optimization. To decompose the HEN, utility heat exchangers located at the end of the process streams are removed and placed into a ‘secondary’ HEN, while the remaining exchangers form the ‘primary’ HEN. Fig. 4 illustrates this decomposition: utility heat exchangers 5 and 6 are moved to the secondary HEN (Fig. 4b) while process exchangers 1–4 remain to form the primary HEN (Fig. 4c). To decompose the HEN, it is also necessary to estimate the new temperature specifications at the points where the streams are broken (e.g. points Tx,1 and Tx,2). These new temperature specifications, TT⁄, ensure that exchangers moved to the secondary HEN do not violate any constraints when the full HEN (e.g. Fig. 4a) is simulated again. TT⁄ is a column vector with a number of rows equal to the number of streams in the secondary HEN (i.e. dimension NPDS
1). TT⁄ is equal to the temperatures of the streams entering the secondary HEN such that:

max f ðASH Þ ¼ ATSH ASH

ð11Þ

s.t.

ASH  AINST;SH

ð12Þ

EMATSH  EMATmin

ð13Þ

TTCALC;SS ¼ TTSS

ð14Þ HE

HE

where A (dimension N
1) is the used heat transfer area, N is the total number of heat exchangers in the original HEN, AINST (dimension NHE
1) is the installed heat transfer area, EMAT (dimension NHE
1) is the calculated exchanger minimum approach temperature. TTCALC and TT (dimensions NPD
1) are vectors for calculated and specified target temperatures of the original HEN. NPD is the number of ‘demand units’ of the simulation model described in Section 2.1. Subscripts SH and SS indicate vector elements corresponding to heat exchangers and streams in the secondary HEN. Once Eqs. (11)–(14) are solved, the calculated TT⁄ is used to constrain the final temperature of the broken streams in the primary network, Tx (dimension NPDS
1). Eqs. (15)–(22) are applied to the primary HEN to reduce operating costs of the original HEN and to address the violation of the remaining constraints:

min f ðAPH ; aÞ ¼ CT QU

ð15Þ

APH  AINST;PH

ð16Þ

AADD;PH  AADD;min

ð17Þ

X

AADD;i  AADD;HEN

ð18Þ

i2PH

EMATPH  EMATmin

ð19Þ

TTCALC;PS ¼ TTPS

ð20Þ

Tx;c P TT c

ð21Þ

Tx;h  TT h

ð22Þ

where a (dimension N
1) is the split fraction of the N conventional splitters, C and QU (dimensions Nutil
1) refer to the prices and energy requirements for the Nutil utility streams in the original HEN. AADD,min represents the lower threshold for additional area, AADD,HEN is the maximum total additional area that can be installed in the network. Subscript PH refers to exchangers in the principal HEN, subscript PS refers to unbroken streams in the principal HEN, subscripts c and h indicate cold and hot streams. QU needs to include the utility requirements of the primary and secondary HENs. For Eq. (15), the heating and cooling requirements related to the secondary HEN are calculated using Tx, rather than TT⁄, together with the equation q = CP DT. SP

SP

Fig. 4. HEN decomposition. TT, stream target temperatures; TT*, new temperature specifications for primary and secondary networks; Tx, temperatures at the stream break points.

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Eqs. (11)–(22) decompose the overall optimization problem into two simpler problems, to be solved sequentially. After the values of APH and a are optimized, the values of ASH are adjusted to account for the new optimized value of Tx. The original HEN is then simulated with the optimized APH, a, and adjusted ASH, to confirm than the network meets all operational constraints. This decomposition procedure is mostly useful for large-scale networks, where a reduction in the problem size facilitates manipulation of variables and handling of constraints. For smaller-sized networks, this decomposition procedure may be unnecessarily burdensome, without substantially improving the performance of the optimizer. 2.4. Consideration of operational changes to the crude oil distillation unit (CDU) Fig. 5 illustrates how operational changes to the CDU can be considered in the proposed optimization framework. This framework uses a CDU model to account for changes in operating conditions that affect stream data and that can help to reduce energy consumption. The CDU model used in this work is an artificial neural network (ANN) model obtained using the approach of OchoaEstopier et al. [21]. In this approach, a surrogate ANN model is built with data from rigorous simulations. Eqs. (23) and (24) describe the CDU model used in this work:

a¼f

1

y¼f

2

  1 W1 x þ b



2

W2 a þ b



ð23Þ ð24Þ

where x is the vector of inputs (e.g. CDU operational variables), y is the vector of outputs (e.g. CDU stream data used to simulate the HEN) and a is the output vector of the hidden layer of the ANN model. W is the matrix of weights and b is the vector of biases which are calculated during model regression. Superscripts 1 and 2 indicate the hidden and output layers. Transfer function f1 is a hyperbolic tangent function while f2 is an identity function (i.e. g (x) = x). In the first level of the optimization framework described in Fig. 5, the optimizer can either propose operational changes to the CDU or changes to the HEN structure. When the optimizer selects changing the CDU operation, the algorithm selects at random new sets of CDU operating conditions until a set that meets all CDU constraints is found. The distillation model (Eqs. (23) and (24)) is used to check whether a set of operating conditions meets all distillation constraints (e.g. related to product quality and column flooding), and to predict the new stream data used to simulate the HEN (supply and target temperatures, flow rates, heat capacities). If the optimizer selects changing the network structure, the retrofit algorithm chooses at random one potentially-feasible retrofit modification from a set of options (Section 2.2). Given new CDU process stream data or a new network structure, the repair algorithm attempts to meet HEN operational constraints (Section 2.3). If the repair algorithm is successful, the objective function is calculated and the optimizer accepts or rejects the design option. The optimization in the first level continues until a termination criterion is reached.

3. Case study – results and discussion

Fig. 5. Two-level optimization framework considering operational changes to the distillation process and heat exchanger network retrofit.

This section describes the application of the proposed methodology to a medium-size petroleum refinery located in Europe. The case study considers changes to the preheat train as well as operational changes to the atmospheric distillation unit (ADU). The ADU comprises 50 stages, two pump-arounds, one condenser, three side strippers and five distillation products. A flash separation unit is located upstream of the ADU. Four distillation products and streams from the pump-arounds and condenser provide heat to the crude oil feed in the preheat train. Two of these distillation products are mixed together before leaving the preheat train to continue further processing downstream. Flue gas from the furnace is considered as the hot utility, while three different utilities are used for cooling: air, cooling water and steam generation. A desalter unit treats crude oil heated to an intermediate temperature. The HEN has 13 process-to-process heat exchangers, 4 coolers, one heat recovery steam generation unit, 2 conventional stream splitters and one open-ended mixer to mix the distillation products. The total installed area of the network is 30,000 m2. Due to confidentiality, sensitive client information (e.g. full HEN structure, installed heat transfer areas, exchanger inlet and outlet temperatures and flow rates) cannot be shared. This study considers operational optimization and retrofit of the overall distillation system. In Case 1, only operational optimization changes are allowed; that is, the operational variables of the distillation column and heat transfer system are manipulated to minimize demand for fired heating. In Case 2, limited HEN retrofit changes are permitted, so operational variables of both the column and HEN and structural variables for the HEN are manipulated to minimize fired heat demand. Table 1 lists the main constraints for the ADU and HEN that need to be considered by the optimizer to ensure that solutions generated are practicable. The distillation system is optimized using the procedure described in Section 2.4 and illustrated in Fig. 5. The objective

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Reference/reason

Inlet temperatures of desalter, preflash unit and ADU Flow rates of pump-arounds T95% ASTM D86 cut points of two distillation products No more than: – 2 new heat exchangers – 2 exchangers with additional area – 1 relocated exchanger – 1 new stream splitter Forbidden matches Exchangers and stream splitters that should not be removed or relocated Total new area from new and existing exchangers should be less than 1300 m2 Maximum additional area for exchanger i: min (1300 m2, AINST,i, area when NTUi = 4) Minimum additional area for exchanger i: max (50 m2, 0.1*AINST,i)

Equipment datasheets

function for Level 1 of the optimization framework is to minimize the furnace duty. A distillation model developed using the methodology proposed by Ochoa-Estopier et al. [21] is employed in this case study to optimize and simulate the ADU, while the models described in this paper are used to optimize and simulate the HEN. The distillation model applies product quality and flooding constraints, so that column operational changes do not compromise operability and the quality of the separation taking place. For Case 1 – operational optimization – the HEN retrofit algorithm is not applied. Heat transfer coefficients were updated with flow rate variations using Eqs. (8) and (9) for all shell-and-tube heat exchangers. Linear heat capacity models (as in Eq. (10)) were developed for all process and utility streams without phase change. These streams include pump-arounds and distillation products. The crude oil is divided into three ‘segments’, each with its own temperaturedependent heat capacity model: before the preflash, after the preflash and before the furnace, and within the furnace. Fig. 6 plots the heat capacity model used for the three crude oil segments. For streams with phase change (condenser and generated steam), a constant mean heat capacity representing sensible and latent heating is used. Note that assuming constant heat capacities in these cases does not introduce inaccuracies in the model because these streams are constrained to be present in only one heat exchanger. The distillation model provides the coefficients of the linear heat capacity models and constant mean heat capacities. Table 2 compares the number of variables and constraints that the repair algorithm would encounter with and without applying the decomposition approach proposed in this work. With HEN decomposition, the maximum number of variables to be optimized is reduced from 21 to 16 variables. Similarly, the maximum

Refinery specification Budget and space limitations

Smaller areas would be impractical to install

number of constraints to be handled is reduced from 54 to 41 constraints. Table 2 also provides information about the HEN decomposition. The decomposition procedure identified that 5 utility heat exchangers and 3 utility streams could be moved to the secondary HEN. Table 3 shows the results for Case 1 (operational optimization) and Case 2 (retrofit). The demand for fired heating decreases by 5% and 10%, respectively, and cold utility demand decreases by 7% and 34%, respectively. It can be seen that in both cases, the optimizer found solutions with greater heat recovery, allowing an increase in the coil inlet temperature (i.e. as the crude oil enters the furnace) of 1.6 °C and 2.7 °C, respectively. In addition, the optimizer found solutions that allowed the coil outlet temperature

Table 2 Features of full and decomposed HENs. Item

Full HEN

Primary HEN

Secondary HEN

Optimization variables Equality constraints Inequality constraints

21a 13 41

16 5 36

5 8 10

Process streamsb Utility streams Process-to-process heat exchangers Utility heat exchangers Conventional splitters New type of mixers Simple unit operations

11 4 13 6 2 1 1

11 1 13 1 2 1 1

5 3 0 5 0 0 0

a Heat transfer areas of 19 heat exchangers and split fractions of 2 stream splitters b Process streams: 3 crude oil sections, 4 distillation products, 1 mixed product, 2 pump-arounds and 1 condenser

Table 3 Optimization results with the new methodology. Description

Furnace duty Cold utility demand Furnace coil inlet temperature (°C) Furnace coil outlet temperature (°C) Pump-around 1 duty (top) Pump-around 2 duty (bottom) Pump-around 1 flow rate (top) Pump-around 2 flow rate (bottom) Total stripping steam T95% temperature of top product (°C) T95% temperature of mixed product (°C) Fig. 6. Heat capacity model used for the crude oil stream.

Change compared to base case Case 1 Operational optimization

Case 2 Retrofit

5% 7% +1.6 2.7 +24% 13% +13% +5% 8% 1 +5

10% 34% +2.7 3.0 +14% 7% +13% 3% 6% 0 +6

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(i.e. column feed temperature) to be reduced by 2.7 °C and 3 °C, respectively. In both cases, the distillation column modeling approach ensured that product quality specifications were not

compromised by the colder column feed temperature and the additional heat recovery from the column: the key product specifications (the ASTM D86 temperature T95 for the top product and

Fig. 7. Proposed retrofit modifications. For confidentiality, streams without retrofit modifications are not shown in the grid diagram.

Fig. 8. Heat exchanger network results for operational optimization. Values are normalized to range from zero to one.

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mixed product) changed by only 1 °C and 6 °C, which is well within the allowable range specified by the refinery. In both cases, a reduction in the coil outlet temperature was facilitated by changes in intermediate and top cooling duties in the column and changes in stripping steam. The benefits after optimization were, unsurprisingly, significantly greater for Case 2, where HEN retrofit changes were permitted. The lower furnace duty observed for the retrofit case, compared to the operational optimization case, is due mainly to a higher coil inlet temperature. The additional heat transfer area and improved HEN configuration in the retrofit case increases heat recovery and thus the coil inlet temperature. Table 3 also shows that the duty of Pump-around 1 is increased while the duty of Pump-around 2 is decreased. However, the total pump-around duty in both studies is very similar to the base case. Similarly, for both studies the flow rate of Pump-around 1 was increased and the total stripping steam was reduced. Fig. 7 illustrates the structural modifications identified in the retrofit study. The new methodology proposed just a few structural modifications to achieve a 10% reduction in furnace duty. Only two heat exchangers require additional area, namely exchangers 5 and

615

10. Additional heat transfer area is added to the maximum extent, 1300 m2. The additional heat transfer area required in these exchangers is similar to the existing heat transfer area; this implies that a new, similar shell, could be installed in parallel to the existing shell. Exchanger 5 is the only exchanger to be relocated; it is only ‘swapped’ with exchanger 4. The solution also included two new exchangers with a calculated area equal to zero. These exchangers are discarded from the design. No new stream splitters were installed and no existing splitters were removed from the HEN. Figs. 8 and 9 show the variation of the optimal heat exchanger variables for operational optimization and retrofit. Fig. 10 shows the optimized split fractions of stream splitters. For confidentiality, the results are normalized to the range [0,1]. The values for each set of variables have been normalized as xnorm = (x-xmin)/ (xmax-xmin). For both studies, the optimization algorithm proposed to utilize fully the installed heat transfer areas of all exchangers, including exchangers 1 and 8. For retrofit, it can be seen that the additional area of exchangers 5 and 10 is mainly used to compensate for the loss in temperature driving force; that is, Ft
LMTD is reduced for these exchangers. Ft is the exchanger temperature

Fig. 9. Heat exchanger network results for retrofit optimization. Values are normalized to range from zero to one.

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4. Conclusions

Fig. 10. Stream splitter results.

Table 4 Optimization results obtained in a previous study using i-HeatTM. Description

Furnace duty Furnace coil inlet temperature (°C) Furnace coil outlet temperature (°C) Pump-around 1 duty (top) Pump-around 2 duty (bottom) Additional heat transfer area (m2) Exchangers with additional area Relocated exchangers

Change compared to base case Operational optimization

Retrofit

2% 2.0 3.0 0% 2% – – –

9% +3.0 3.0 0% 2% 2500 2 1

correction factor. Regarding stream split fractions, the split fractions were kept close to the base case values except for splitter 2 in the retrofit study. For both studies, changing the split fraction of splitter 2 helped to increase the heat transferred in exchanger 8. The results obtained with the new methodology were compared with results from a previous study carried out by Process Integration Ltd (PIL). A summary of these results is presented in Table 4. PIL’s procedure started with manually and iteratively changing the operating conditions of the column to reduce the furnace coil outlet temperature. Then, the heat exchanger network with the new stream data was optimized using i-HeatTM, which is a state-of-the-art commercial software for HEN design, simulation and optimization developed by PIL. For both operational optimization and retrofit studies, the new methodology (Table 3) achieved greater reductions in the furnace duty than the previous study (Table 4). For the retrofit study, a similar reduction in the furnace duty was obtained. Similar retrofit modifications were also identified. However, the previous study recommends almost double the area than that of the new methodology, which suggests that a significantly higher capital investment may be required. In the studies developed with the new methodology, a significant reduction in furnace duty and cold utility requirements was identified. This reduction is directly related to fuel oil and cooling water consumption, steam generation and thus operating costs. For operational optimization, results can be readily implemented on-site at no cost as capital investment is not needed. With HEN retrofits, greater savings can be achieved, compared to operational optimization, by investing capital to perform only a few structural modifications to the heat exchanger network.

This paper presents a new procedure for practicable retrofit and operational optimization of existing heat exchanger networks, with particular focus on crude oil preheat trains. One main feature of this procedure is the specification of heat exchangers in terms of area, rather than duty. This consideration facilitates the monitoring of existing heat transfer area, and the optimization of additional area to a limited number of heat exchangers for reduced cost and downtime. Another innovation is the decomposition and simplification of the repair algorithm responsible for respecting HEN operational constraints. This decomposition is useful for large-scale networks as it reduces the number of variables and constraints to be considered within each sub-problem during optimization. Another important contribution of this work is its ability to consider features particularly relevant to crude oil preheat trains, such as temperature-dependent heat capacities, flow rate-dependent heat transfer coefficients, mixing of two product streams and splitting of process streams. The method has been developed while paying considerable attention to practical limitations in industry and to the practicality of proposed changes. The usual constraints relating to exchanger minimum approach temperature are imposed; in addition, constraints are defined to limit the number of new heat exchangers and stream splitters and to limit the amount of area to be added to individual exchangers or to the HEN overall. The new methodology was compared with a previous industrial study carried out using software i-HeatTM. For operational optimization, the new approach achieved a reduction in the furnace duty of 5%, compared to a 2% reduction achieved by the benchmark study. For retrofit, a similar reduction in the furnace duty was achieved with similar retrofit modifications. However, the new approach requires about half the additional area of that of the benchmark study. These results indicate that the new approach proposes solutions with lower furnace operating costs, with no or less capital investment, compared to state-of-the-art commercial HEN optimization software.

Acknowledgements This work was supported by Innovate UK via a Knowledge Transfer Partnership [No. KTP009567, 2014] between The University of Manchester and Process Integration Limited.

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