Andrea Toffolo
email: andrea.toffolo@unipd.it

The synthesis of cost optimal heat exchanger networks with unconstrained topology

Keywords: synthesis optimization, heat exchanger networks, graph theory

The optimization of heat exchanger network (HEN) synthesis still remains an open problem because of the complexity of the space comprising all the possible solutions, and most of the proposed methods introduce simplifying assumptions that mainly affect the topological features of the candidate solutions considered and thus artificially limit the boundaries of the search space. This work is devoted to the pursuit of cost-optimal HENs with unconstrained topology, exploiting the advantages deriving from two graph representations of a HEN. One representation is used by an evolutionary algorithm to manage HEN topology and the other is used by a NLP algorithm to manage heat load distribution among the exchangers. The proposed two-level hybrid optimization method is applied to four test cases taken from the literature about HEN synthesis, among which the well-known Aromatics Plant problem.

INTRODUCTION

The problem of heat exchanger network (HEN) synthesis is widely studied in the field of process integration, due to its importance in determining the amount of the internal energy recovery, and thus the savings in primary energy consumption. The most recent publications about applications of process integration (see, e.g., [START_REF] Bulasara | Revamp study of crude distillation unit heat exchanger network: Energy integration potential of delayed coking unit free hot streams[END_REF][START_REF] Chen | A resource-task network approach for optimal shortterm/periodic scheduling and heat integration in multipurpose batch plants[END_REF][START_REF] Higa | Thermal integration of multiple effect evaporator in sugar plant[END_REF][START_REF] Bandyopadhyay | Targeting for cogeneration potential through total site integration[END_REF][START_REF] Tokos | Energy saving opportunities in heat integrated beverage plant retrofit[END_REF]) and various aspects of HEN synthesis (see, e.g., [START_REF] Foo | Minimum units targeting and network evolution for batch heat exchanger network[END_REF][START_REF] Salama | Optimal assignment of multiple utilities in heat exchange networks[END_REF][START_REF] Nordman | Use of advanced composite curves for assessing costeffective HEN retrofit I: Theory and concepts[END_REF][START_REF] Nordman | Use of advanced composite curves for assessing costeffective HEN retrofit II: Case studies[END_REF][START_REF] Sikos | Reliability, availability and maintenance optimisation of heat exchanger networks[END_REF]) confirm the interest of the research community in this field, the ultimate aim of which is cleaner production.

In particular, in the HEN synthesis problem a challenging compromise between the reduction of the requirements from external hot and cold utilities and the increase in the number and in the heat transfer surface of heat exchanger units has to be found in assessing minimum total costs. The difficulty of this task is due to the vastness of the search space that has to be considered. In fact, the number of combinations resulting from stream splitting and remixing, stream matching and the distribution of heat loads among the exchangers is enormous even for a small number of hot and cold streams.

In their comprehensive review of this research field [START_REF] Furman | A critical review and annotated bibliography for heat exchanger network synthesis in the 20th century[END_REF], Furman and Sahinidis conclude that important issues are still to be addressed in spite of the latest new or improved techniques:

4/34 -heuristic-based methods do not seem to provide a worst-case performance guarantee;

-efficient optimization algorithms and robust formulations should be used to deal with the combinatorial complexity of the problem and the presence of local optima;

-restrictive simplifying assumptions preclude the path towards the global optimal solution of a complete formulation of the problem.

In particular, the latter issue is the main motivation to this paper, since most of the HEN synthesis strategies proposed in the literature limit in advance the types and the number of elementary topological features that are considered in the optimization process.

On the contrary, this work presents a new optimization algorithm for the synthesis of HENs, which allows networks with unconstrained topology to be defined.

This means that neither network topology is bounded (e.g. the number of stream matches is not limited) nor its features are decided in advance (e.g. the maximum number of branches per split stream and the maximum number of heat exchangers arranged in a branch are not fixed). If the purpose is to let network topology be really unconstrained, then it cannot be handled by deterministic algorithms, which are usually associated with the definition of a superstructure embedding the subset of all the considered solutions. As a consequence, an evolutionary algorithm is used here to manage HEN topology, and this is made possible by establishing a suitable codification of the structure of a candidate solution, so that it can be handled by genetic operators. In fact, the key to dealing with unconstrained topologies relies in the representation of HEN structure. A suitable representation should be able to codify any feasible topology and to codify it bi-univocally (i.e. there should be a one-to-one correspondence between a network and its representation). According to these basic requirements, for example, a

The synthesis of cost optimal heat exchanger networks with unconstrained topology -Andrea Toffolo 5/34 matrix representation of stream matches is disregarded, because it is not univocal and it cannot codify, for instance, two stream matches on a given stream branch. A very simple and effective graph-based representation is suggested in this work, focusing on heat exchanger sides, their junctions and the matches among them. Then this representation is further transformed into another graph-based one that focuses on the enthalpy flows circulating in the network and is suitable for the optimization of the heat load distribution among the exchangers of a given HEN topology.

In the following sections the problem of HEN synthesis optimization is defined, a brief survey is given about the methods proposed in the literature to solve it and some details of the proposed algorithm are introduced; finally, the latter is applied to four test cases taken from the literature, one of them being the well-known Aromatics Plant problem.

FORMULATION OF THE HEN SYNTHESIS PROBLEM

Grass-root HEN synthesis problem is generally formulated as:

"design from scratch a network of heat exchangers with minimum total (investment and operating) costs given 1. a set of hot streams to be cooled, with their inlet and outlet temperatures, heat capacity flow rates and film coefficients;

2. a set of cold streams to be heated, with their inlet and outlet temperatures, heat capacity flow rates and film coefficients;

3. a set of cost laws for the heat exchangers and for the use of auxiliary heat sources or sinks (the external utilities)."

6/34

As in most of the problems proposed in the literature, the objective function used in this work evaluates the annualized total costs (to be minimized) according to the following expression:

( )

∑ ∑ ∑ + + + = C H EX j n j j CU CU n j j HU HU n j m j j EX s j EX f t Q c Q c S C C C , , , , , , (1)
in which the same type of cost law is used for all the heat exchangers (coolers and heaters included), that is the sum of a fixed component (C f,EX ) and a surface-dependent component (C s,EX S m ). Heat exchanger surfaces are calculated assuming a counter-current heat transfer:

( )

LM j EX j T U Q S ∆ = , ( 2
)
in which the heat transfer coefficient is:

( ) 1 / 1 / 1 - + = c h h h U (3)
The exponent m in Eq. 1 is usually in the range between 0.6 and 1. If m=1 and C f,EX is low, HEN optimal design will be quite independent from the number of heat exchanger units, whereas, if m<1 and C f,EX is relatively high, small units will be penalized and designs featuring a lower number of units will be promoted. Finally, if both C f,EX and C s,EX can be neglected, the search is driven towards a maximum energy recovery (MER) design that minimizes the transfer from/to external utilities.

APPROACHES AND ALGORITHMS FOR HEN SYNTHESIS

The approaches suggested in the literature for optimized HEN synthesis can be divided into two main categories [START_REF] Furman | A critical review and annotated bibliography for heat exchanger network synthesis in the 20th century[END_REF]: sequential and simultaneous.

Sequential approaches use some heuristics to decompose a priori the optimization problems into a chain of sub-problems requiring a much lower

The synthesis of cost optimal heat exchanger networks with unconstrained topology -Andrea Toffolo 7/34 computational burden. The sub-problems are solved in a given sequence, so that the solution of a sub-problem is used as a constraint for the following ones. A typical decomposition consists in:

1. minimizing the need of (i.e. the cost due to) external utilities;

2. minimizing the number of HEN units;

3. minimizing heat exchanger surfaces.

Design guidelines and heuristic rules (e.g., the Pinch Design Method [START_REF] Linnhoff | The Pinch Design Method for heat exchanger networks[END_REF]) or mathematical programming techniques (see, e.g., [START_REF] Floudas | Automatic synthesis of optimum heat exchanger network configurations[END_REF]) are applied to solve the subproblems and to obtain the final HEN design. However, this kind of approach is not suitable to guarantee the optimal solution, since it considers the cost of external utilities as the most dominating and therefore it is biased towards MER designs.

Simultaneous approaches exploit other simplifying assumptions to reduce the computational complexity. In general, a HEN superstructure is defined, i.e. a complex topology that embeds all the possible network configurations and all the possible stream matches that the designer chooses to consider. The optimal HEN design, the topology of which can only be a simplified version of the superstructure, is searched by applying mixed-integer non-linear programming (MINLP) techniques, integer decision variables governing network topology (e.g., presence/absence of heat exchangers, stream splitting) and real decision variables governing exchanger heat loads. The superstructure proposed by Yee et al. [START_REF] Yee | Simultaneous optimization models for heat integrations -I. Area and energy targeting and modeling of multi-stream exchangers[END_REF] is the most popular in the literature about HEN synthesis.

Network topology is subdivided into stages with no actual physical meaning (Figure 1), in which each stream of one type (hot/cold) is split into a number of branches that is equal to the number of streams of the other type and heat exchangers are allowed to transfer heat from any stream of one type to any stream of the other type, but only once.

No bypass stream is allowed, and the split streams are re-mixed isothermally at the end

The synthesis of cost optimal heat exchanger networks with unconstrained topology -Andrea Toffolo 8/34 of each stage. This elementary structure is repeated for a fixed number of times, which is not greater than the maximum number of cold or hot streams, and one utility heat exchanger is placed at the outlet of each stream.

In simultaneous approaches, non-deterministic algorithms are mostly used to search for the optimal HEN configuration and heat loads. In fact, Furman and Sahinidis [START_REF] Furman | Computational complexity of heat exchanger network synthesis[END_REF] demonstrated that the HEN synthesis problem belongs to a particularly difficult class of optimization problems (it is NP-hard in the strong sense) for which a computationally efficient (i.e. polynomial) exact solution algorithm does not exist. This has opened the path to the use of evolutionary algorithms and meta-heuristic methods (e.g., tabu search), which do not guarantee that the true optimum is found but have proved to explore effectively the complex search space of the problem finding the most promising regions. However, these techniques are applied in general to restricted formulations of the HEN synthesis problem, as it is shown in the following four examples.

The evolutionary strategy suggested by Gross et al. [START_REF] Groβ | Optimization of heat exchanger networks by means of evolution strategies[END_REF] tries to codify the candidate optimal networks into a graph representation that can be handled by evolutionary operators. Graph nodes represent network components (heat exchangers, splitters and mixers) and graph edges represent the connections among the components.

The maximum number of nodes is fixed and the different candidate network topologies are obtained by switching the nodes from an active to a non-active state (or vice versa) and rearranging the connections accordingly. However, if nodes cannot be switched from one component type to another as well by the evolutionary algorithm, this representation is actually equivalent to a superstructure defined in advance.

In the method proposed by Lewin [START_REF] Lewin | A generalized method for HEN synthesis using stochastic optimization -II. Synthesis of cost-optimal networks[END_REF] a genetic algorithm manages topology optimization, integer variables being involved to represent possible stream matches. The 9/34 order of stream matches is taken into account using the concept of "level": only a restricted combination of stream matches is permitted within each level, and structural complexity is governed by the chosen maximum number of levels. Actually, under these hypotheses the resulting possible configurations are only a subset of those embedded in the stagewise superstructure proposed by Yee and al. [START_REF] Yee | Simultaneous optimization models for heat integrations -I. Area and energy targeting and modeling of multi-stream exchangers[END_REF].

Lin and Miller [START_REF] Lin | Solving heat exchanger network synthesis problems with Tabu search[END_REF] apply tabu search, a meta-heuristic approach that is suitable for combinatorial optimization problems, to the stagewise superstructure by Yee et al.

[14] exclusively. Tabu search consists in a memory-based neighbor search approach which guides the process using a list of the tabu (forbidden) moves to keep track of search history.

Pariyani et al. [START_REF] Pariyani | Design of heat exchanger networks using randomized algorithm[END_REF] use a random search algorithm, the structure of a candidate optimal network being defined by limiting the number of heat exchangers in each stream to a maximum and by assigning randomly the matches. Only one stream per network can be split in two branches only (with isothermal mixing). The only variant from the other topologies mentioned in this section is that a branch of a split stream may pass through more than one heat exchanger.

Finally, it is worth noting that very recent publications about evolutionary methods for HEN synthesis still restrict a priori the topology of the candidate solution considered:

• Ravagnani et al. [START_REF] Ravagnani | Heat exchanger network synthesis and optimisation using genetic algorithm[END_REF] use an ordered list of stream matches to represent HEN topology. Stream splitting, which cannot be taken into account in such a representation, is decided in an earlier step in which the problem is heuristically divided into sub-problems and sub-networks;

• Jezowski et al. [START_REF] Jezowski | On application of stochastic optimization techniques to designing heat exchanger-and water networks[END_REF] define a superstructure of the possible stream matches for the solution of HEN retrofit problems; 10/34

• Dipama et al. [START_REF] Dipama | Synthesis of heat exchanger networks using genetic algorithms[END_REF] use a level-based representation similar to the one proposed by Lewin [START_REF] Lewin | A generalized method for HEN synthesis using stochastic optimization -II. Synthesis of cost-optimal networks[END_REF] and do not consider stream splitting;

• Yerramsetty and Murty [START_REF] Yerramsetty | Synthesis of cost-optimal heat exchanger networks using differential evolution[END_REF] define a stagewise topology in which the number of stages and the number of branches into which a stream can be split within one stage are limited. Moreover, each branch can have a maximum of one exchanger in a particular stage.

• Ponce-Ortega et al. [START_REF] Ponce-Ortega | Synthesis of multipass heat exchanger networks using genetic algorithms[END_REF] and Luo et al. [START_REF] Luo | A hybrid genetic algorithm for synthesis of heat exchanger networks[END_REF] use the stagewise superstructure suggested by Yee et al. [START_REF] Yee | Simultaneous optimization models for heat integrations -I. Area and energy targeting and modeling of multi-stream exchangers[END_REF];

• Khorasany and Fesanghary [START_REF] Khorasany | A novel approach for synthesis of cost-optimal heat exchanger networks[END_REF] use the level-based representation by Lewin [START_REF] Lewin | A generalized method for HEN synthesis using stochastic optimization -II. Synthesis of cost-optimal networks[END_REF].

THE PROPOSED ALGORITHM FOR HEN SYNTHESIS OPTIMIZATION

The algorithm proposed in this work for the optimization of HEN synthesis is organized in two levels, as shown in Figure 2. The optimization is driven by the upper level algorithm, which is an evolutionary algorithm that generates new candidate HEN topologies by applying genetic operators to a graph-based representation of the HEN.

The lower level algorithm is a sequential quadratic programming (SQP) algorithm that evaluates the objective function for the topologies generated by the upper level algorithm, minimizing the annualized total costs (Eq. 1) of a given topology. The essentials of both algorithms are discussed in the following.

The Upper Level Algorithm and the Representation Graph

The upper level algorithm follows the steps of an elitist evolutionary strategy starting from a set of network topologies ("old population" in Figure 2). In the reproduction phase, a reproduction pool is formed by randomly choosing some of these 11/34 topologies and an "offspring population" is generated by applying a mutation operator to each of the topologies in the pool. These operators, which are described below, randomly modify the "old" topology to generate an "offspring" topology that is similar, but not identical, to the original one (as it is shown in Figure 2). After the minimum total costs of the topologies in the offspring population have been evaluated by the lower level algorithm, the topologies of both the old and offspring populations are sorted in the selection phase, and those having the higher minimum total costs are discarded. The remaining topologies form the "new population" that replaces the old one in the next iteration ("generation") of the upper level algorithm.

The directed graph that is used in the upper level algorithm to deal with HEN topology is called the Representation Graph (RG). All RG edges represent a heat exchanger side, except for stream inlet edges (stream outlet edges represent heater cold sides or cooler hot sides). RG vertices represent the junctions among inlets and outlets of heat exchanger sides, so they represent splitters and mixers when a vertex is shared by more than two edges. Edge direction is the same of the flow within a stream. The pairing between heat exchanger sides is taken into account by assigning an integer to each RG edge, except for stream inlet and outlet edges. Figure 3 shows the RG of a simple HEN.

This representation is very flexible and suitable to handle topologies of any level of complexity without limitations or constraints on the number of stream matches and on the number of branches after stream splitting. The only forbidden topologies are:

-loops and auto-loops (mass recirculations within a stream);

-by-passes (branches that do not contain a heat exchanger side);

-any other heaters or coolers besides those on stream outlet edges,

The synthesis of cost optimal heat exchanger networks with unconstrained topology -Andrea Toffolo 12/34 because it is easy to demonstrate that, problem data being equal, these features would make the distance between the hot and cold composite curves narrower, increasing heat exchanger surfaces and, as a consequence, HEN total costs.

The mutation operators applied in the reproduction phase to generate offspring topologies from the old ones are three and their effects are shown in Figure 4:

M1) adds a heat exchanger, i.e. adds a side to a hot stream, a side to a cold stream and links the two (probability = 50%); M2) deletes an existing heat exchanger (35%); M3) swaps the links between the hot and cold sides of two existing heat exchangers (15%).

In order to guarantee that network topology does not evolve according to a small number of features fixed in advance, a heat exchanger side can be added to a stream in three different ways (with equal probability):

-two vertices of the RG are selected at random and a new edge (i.e. the new heat exchanger side) is added to connect them (see the first two rows in Figure 5); -an existing edge of the RG is split in two edges, one of the two (at random) being the one that represents the new heat exchanger side (see the third row in It is also worth noting that when a heat exchanger side is deleted from a stream the resulting network topology may feature streams with unfeasible intermediate sources or

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The synthesis of cost optimal heat exchanger networks with unconstrained topology -Andrea Toffolo 13/34 sinks. In order to avoid this, the two vertices of the removed edge must be merged into one if one of the two vertices has a degree equal to 1 after the removal. The need for this precaution is illustrated in the last two rows in Figure 5.

The Lower Level Algorithm and the Evaluation Graph

The lower level SQP algorithm searches for the minimum C t (Eq. 1) of a given HEN topology exploiting some ideas already proposed in [START_REF] Mehta | An optimization approach for evolutionary synthesis of heat exchanger networks[END_REF] and further developed in this work. Another graph describing HEN topology, the Evaluation Graph (EG), is built from the RG according to the following rules (see Figure 6):

-a vertex, representing the heat exchanger side, is added in the middle of each RG edge (except for stream inlet edges);

-new edges are added to connect the pairs of heat exchanger sides, from the hot side to the cold side;

-heater cold sides and cooler hot sides are connected, according to the direction of heat transfer, to a new vertex ("E" in Figure 6) representing external utilities.

This special representation allows EG edges, considered with their direction, to be associated with the enthalpy flows inside the HEN. This is very important in order to exploit a property of the EG graph that significantly simplifies the formulation of the nonlinear optimization problem. Let H 0j be the enthalpy flows of a candidate solution to the optimization problem (i.e. they satisfy the enthalpy balances at EG vertices and comply with problem data). Then, according to graph theory [START_REF] Deo | Graph theory and applications to engineering and computer science[END_REF], the enthalpy flows H j of any other candidate solution can be expressed as:

∑ = + = nc k k jk j j H H H 1 0 α (4)
14/34 in which each k H is an appropriate enthalpy flow circulating in the k-th cycle of a set of the nc independent cycles of the EG (see the example in Figure 6) and the coefficients α jk are equal to:

-0 if the j-th EG edge does not belong to the k-th independent cycle; -+1 if the j-th EG edge belongs to the k-th independent cycle and its direction is the same chosen for k H ;

--1 if the j-th EG edge belongs to the k-th independent cycle and its direction is opposite to that chosen for k H .

The number of independent cycles in the EG (nc) is equal to the number of EG edges minus the number of EG vertices plus 1 [START_REF] Deo | Graph theory and applications to engineering and computer science[END_REF]. As it appears from the example in Figure 6, EG cycles basically result from either stream matches or stream splitters.

Taking advantage of this fundamental property of the EG, the k H are used as the decision variables of the optimization problem, and the H 0j (which can be considered as the enthalpy flows of the initial solution) are evaluated by imposing that all heat exchanger loads are equal to zero (except for heaters and coolers, so that all T e are reached relying on the external utilities only) and mass flow rates are equally partitioned at splitters.

The constraints the objective function is subject to are:

-the heat loads of all heat exchangers matching two streams (i.e. the enthalpy flows of the edges connecting hot sides to cold sides) must be greater than or equal zero;

-the heat loads of heaters and coolers (i.e. the enthalpy flows of the edges entering or exiting the "E" vertex) must be greater than or equal to zero;

15/34 -the enthalpy flows in all EG edges representing a physical stream or one of its branches must be greater than or equal to zero, in order to avoid mass recirculations among stream branches;

-the temperature differences at both ends of each heat exchanger must be greater than a minimum value ∆T min assumed as a technological limit.

It is worth noting that in this formulation enthalpy balances are automatically satisfied thanks to EG property expressed in Eq. 4. Accordingly, no equality constraints have to be imposed, contrary to the case in which mass flow rates and temperature were chosen as decision variables.

THE TEST CASES

In this section, the presented method is applied to four test cases taken from the literature about HEN synthesis. These cases are selected in order to set a comparison with as many solutions as possible that are proposed in the works by other authors as best results of the methods they suggest.

The 4SP problem

This is a very simple problem with only two hot and two cold streams (see problem data in Table 1), yet it can be used to show effectively that the networks with unconstrained topologies are superior to those derived from superstructures. In fact, the cost optimal network found by the proposed algorithm (which was run for 100 generations using a population of 50 individuals) has a topological feature that is not considered in the usual superstructures, that is a series of two heat exchangers in a branch of stream H1 (Figure 7). The comparison in Table 2 shows that total cost of the 16/34 network shown in Figure 7 is lower than the two other solutions taken from the literature, because of a better trade-off between the number of units and the sum of unit surfaces (exponent m in Eq. 1 is equal to 1 and costs due to cold utility requirement are the same for all the solutions).

The 6SP problem

This problem features 5 hot streams and just one cold stream (see problem data in Table 3), but the distinctive attribute of this test case is that the hot streams cannot be split (and, therefore, the genetic operators manipulating these streams are modified accordingly). The cost optimal network found by the proposed algorithm (which was run for 100 generations using a population of 100 individuals) is shown in Figure 8. As a result of the constraint on hot stream structure, the cold stream has a quite complex and unusual topology. The comparison in Table 4 reveals that the total cost of the network shown in Figure 8 is lower than that of two other solutions taken from the literature. It is worth noting that the exponent m in the objective function (equal to 0.6) promotes heat exchanger units with larger duties, and this is the reason why the costoptimal HEN found is not a MER design, although heat transfer across the pinch point (380-370K) occurs only in one exchanger (the one matching H3 and one of the branches of the cold stream). Two solutions having lower total costs can be found in [START_REF] Furman | Computational complexity of heat exchanger network synthesis[END_REF] and [START_REF] Groβ | Optimization of heat exchanger networks by means of evolution strategies[END_REF] and they too are reported in Table 4 (571,698$/y and 572,476$/y, respectively), but the constraint ∆T min =10K (Table 3) is not included in those formulations of the 6SP

problem. If the constraint on ∆T min is removed, the proposed algorithm is still able to find a network (Figure 9) the total costs of which are lower (570930$/y, see Table 4).

The Aromatics Plant problem

17/34

The Aromatics Plant problem proposed by Linnhoff and Ahmad [START_REF] Linnhoff | Cost optimum heat exchanger networks -1. Minimum energy and capital using simple models for capital cost[END_REF] (see problem data in Table 5) has been widely studied in the literature. One of the most challenging features is that the hot utility (oil) has to be cooled to a temperature (250°C) which is lower than the final temperatures of two of the cold streams (C1 and C5, which must be heated up to 300°C).

The proposed algorithm was run for 200 generations using a population of 200 individuals (only 40,000 HEN topologies were examined) and the best solution found is shown in Figure 10. It features a large number of units (n EX =15), since the objective function has a linear dependence from heat exchanger surfaces. Note that network topology cannot be derived from the stagewise superstructure proposed in [START_REF] Yee | Simultaneous optimization models for heat integrations -I. Area and energy targeting and modeling of multi-stream exchangers[END_REF], because one of the branches of stream H4 is matched to two cold streams (C1 and C2). The comparison with other solutions from the literature, proposed in Table 6, shows that the HEN in Figure 10 is cheaper than the other solutions because of the apparently lower hot and cold utility requirements.

Another solution to the same problem, the minimum total costs of which are very close to the optimal value found (2,920,272$/y instead of 2,920,130$/y), is shown in Figure 11. This network has fewer units than the optimal one (12 instead of 15), but its external utility requirements are higher. Near optimal solutions are important because they may feature design variations that could be preferable if other criteria, such as control, were to be considered.

The 10SP1 problem

The last test case features 5 hot and 5 cold streams (see problem data in Table 7).

The cost optimal network found by the proposed algorithm (which was run for 200 generations using a population of 200 individuals) is shown in Figure 12. The 18/34 comparison in Table 8 shows that this network is the cheapest among the solutions proposed in the literature, although the margin for improvement is narrow. In fact, fixed costs of heat exchanger units are not considered in the problem (so the number of units does not affect total costs) and all the solutions have the same cold utility requirements.

The only chance to lowering total costs is, therefore, to reduce the surface-dependent costs of the heat exchanger units, keeping in mind that the exponent m (equal to 0.6) penalizes units with small duties.

CONCLUSIONS AND FUTURE WORK

This work presented a two-level hybrid optimization methodology for the synthesis of HENs. The advantages of HEN representation by means of directed graphs were fully exploited in order to:

-deal with HEN topologies of any level of complexity, avoiding the use of superstructures and other limiting assumptions;

-simplify the formulation of the nonlinear optimization problem about the minimization of the total costs for a given HEN topology by considering the enthalpy flows circulating in a set of graph independent cycles as decision variables.

A promising result was obtained on a well-known test case taken from the literature. Further developments will be aimed at taking into account multiple objectives in HEN synthesis optimization and at extending the analysis of HEN costs by considering pressure drop effects and other details about heat exchanger design.

The synthesis of cost optimal heat exchanger networks with unconstrained topology -Andrea Toffolo The synthesis of cost optimal heat exchanger networks with unconstrained topology -Andrea Toffolo 28/34

Figure 5

 5 Figure 5);

Figure 1 -

 1 Figure 1 -An example of the stagewise superstructure suggested in [14] for a network with two hot and three cold streams.

Figure 2 -

 2 Figure 2 -Scheme of the proposed two-level hybrid algorithm.

Figure 3 -

 3 Figure 3 -A simple HEN and its RG.

Figure 4 -

 4 Figure 4 -Examples of the effects of the three mutation operators on network topology.

Figure 5 -

 5 Figure 5 -Insertion and deletion of heat exchanger sides in the RG.

Figure 6 -

 6 Figure6-The EG of the simple HEN in Figure3and its independent cycles.

Figure 7 -

 7 Figure 7 -The solution to the 4SP problem found by the proposed algorithm (temperatures [K] in normal font and heat exchanger loads [kW] in italics).

Figure 8 -

 8 Figure 8 -The solution to the 6SP problem found by the proposed algorithm (temperatures [K] in normal font and heat exchanger loads [kW] in italics).

Figure 9 -

 9 Figure 9 -The solution to the 6SP problem found by the proposed algorithm without the constraint on ∆T min (temperatures [K] in normal font and heat exchanger loads [kW] in italics).

Figure 10 -

 10 Figure 10 -The solution to the Aromatics Plant problem found by the proposed algorithm (temperatures [°C] in normal font and heat exchanger loads [kW] in italics).

Figure 11 -

 11 Figure 11 -A near optimal solution to the Aromatics Plant problem found by the proposed algorithm (temperatures [°C] in normal font and heat exchanger loads [kW] in italics).

Figure 12 -

 12 Figure 12 -The solution to the 10SP1 problem found by the proposed algorithm (temperatures [K]in normal font and heat exchanger loads [kW] in italics).

27 / 34 Figure 7 -

 27347 Figure 7 -The solution to the 4SP problem found by the proposed algorithm (temperatures [K] in normal font and heat exchanger loads [kW] in italics).

Figure 8 -

 8 Figure 8 -The solution to the 6SP problem found by the proposed algorithm (temperatures [K] in normal font and heat exchanger loads [kW] in italics).

Figure 9 -

 9 Figure 9 -The solution to the 6SP problem found by the proposed algorithm without the constraint on ∆T min (temperatures [K] in normal font and heat exchanger loads [kW] in italics).

Figure 10 -

 10 Figure 10 -The solution to the Aromatics Plant problem found by the proposed algorithm (temperatures [°C] in normal font and heat exchanger loads [kW] in italics).

Table 1 -

 1 4SP problem data[START_REF] Zamora | A global MINLP optimization algorithm for the synthesis of heat exchanger networks with no stream splits[END_REF].

Table 2 -

 2 A comparison among the solutions to the 4SP problem.

Table 3 -

 3 6SP problem data[START_REF] Lewin | A generalized method for HEN synthesis using stochastic optimization -II. Synthesis of cost-optimal networks[END_REF].

Table 4 -

 4 A comparison among the solutions to the 6SP problem.

Table 5 -

 5 Aromatics Plant problem data[START_REF] Linnhoff | Cost optimum heat exchanger networks -1. Minimum energy and capital using simple models for capital cost[END_REF].

Table 6 -

 6 A comparison among the solutions to the Aromatics Plant problem.

Table 7 -

 7 10SP1 problem data[START_REF] Flower | Synthesis of heat exchanger networks: II. Evolutionary generation of networks with various criteria of optimality[END_REF].

Table 8 -

 8 A comparison among the solutions to the 10SP1 problem.

Table 5 -

 5 Aromatics Plant problem data [31]. C EX [$/y] = 2000+70 S c HU [$/kWy] = 60 (oil cost); c CU [$/kWy] = 6 (water cost);

	Stream	T i [°C] T e [°C] FC P	h
	H1	327	40	100 0.50
	H2	220	160	160 0.40
	H3	220	60	60 0.14
	H4	160	45	400 0.30
	C1	100	300	100 0.35
	C2	35	164	70 0.70
	C3	85	138	350 0.50
	C4	60	170	60 0.14
	C5	140	300	200 0.60
	Hot oil	330	250	-0.50
	Water	15	30	-0.50
	∆T min [K] = 10 ;

Table 6 -

 6 A comparison among the solutions to the Aromatics Plant problem.

	Method	n EX ΣQ HU ΣQ CU	C t
			[MW] [MW] [k$/y]
	Ref. [32]	14	26.2 33.9	2970
	Ref. [33]	12	25.9 33.6	2970
	Ref. [31]	13	25.3 33.0	2960
	Ref. [17]	11	25.7 33.4	2946
	Ref. [23]	15	25.9 33.6	2942
	Ref. [25]	14	23.6 31.3	2922
	This work	15	23.7 31.4	2920

ACCEPTED MANUSCRIPT

The synthesis of cost optimal heat exchanger networks with unconstrained topology -Andrea Toffolo 19/34

The synthesis of cost optimal heat exchanger networks with unconstrained topology -Andrea Toffolo 23/34 Figure 1 -An example of the stagewise superstructure suggested in [START_REF] Yee | Simultaneous optimization models for heat integrations -I. Area and energy targeting and modeling of multi-stream exchangers[END_REF] for a network with two hot and three cold streams. The synthesis of cost optimal heat exchanger networks with unconstrained topology -Andrea Toffolo 31/34


prof Celidonio Dispenza

Ing Giorgio Dispenza
email: dispenza@unipa.it

prof La Vincenzo

Rocca

Giuseppe Panno

EXERGY RECOVERY IN REGASIFICATION FACILITIES -COLD UTILIZATION: A MODULAR UNIT

Keywords: LNG Regasification -cold utilization, Carbon dioxide as secondary refrigerant, Exergy and Economic Analysis, Safety of LNG Regasifiers

The paper deals with the problem of cold recovery for direct utilization both in the site of regasification facility and far from it.

A modular LNG regasification unit is proposed having the regasification capacity of 2 billion standard cubic meters/year of gas. The modular plant is based on use of a Power Cycle working with Ethane or Ethylene which allows operation of cold energy transfer, contained in LNG to be regasified, in a range of temperatures suitable for multipurpose use of cold, reducing regasification process irreversibility. Some electric energy is produced by the Power Cycle, but the own mission of modular unit proposed is addressed to deliver cold suitable for industrial and commercial use in the proper

Introduction

The recovery of physical exergy of cold available during the regasification of LNG in a Regasification Plant is of capital interest. Cold contained in LNG has a great environmental impact, usually on the sea near the regasification site.

A suitable option [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part One[END_REF][START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part Two[END_REF][START_REF] Dispenza | CHP plants for production of electrical energy during regasification of LNG recovering exergy of cold[END_REF] can be the production of electric energy recovering energy available as cold, using a cryogenic stream of LNG during regasification as cold source in an improved CHP Plant (Combined Heat and Power). In papers [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part One[END_REF][START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part Two[END_REF] main problems arising by feasibility study of a venture of this kind of Regasification facility have been extensively analyzed by Authors.

In past years some studies [START_REF] Buffiere | La recuperation des frigories du LNG et l'ajustement du gaz au terminal de Fos sur Mer, on LNG[END_REF][START_REF] Mcdermott | Liquefied Natural Gas Technology[END_REF][START_REF] Medici | The natural gas industry[END_REF][START_REF] Katz | Handbook of natural gas engineering[END_REF][START_REF] Haywood | Analysis of engineering cycles[END_REF][START_REF] Dispenza | Recupero e utilizzazione del freddo nella rigassificazione del GNL, La Termotecnica[END_REF] have been carried out on the possibility of cold energy recovery in cold technology application facilities (e.g.: air liquefaction producing Nitrogen, Oxygen, Argon, deep freeze warehouse and cold storage warehouse, freezing process of foods etc.). The commercial application of cold near a regasification site has limitation and, usually, there the demand of cold is low, but due to expected wide future exploitation of LNG regasification in the World, possible applications far from the regasification site deserve a thorough analysis. This paper deals with the problem of cold exergy recovery for direct cold utilization both in the site of regasification facility and far from it. A modular LNG regasification unit is proposed having the regasification capacity of 2 10 9 standard cubic meters/year. Some results of a research carried out at DREAM-University of Palermo are reported. The research developed includes both cryogenic applications and industrial use of cold at very low temperature inside the regasification site and cold utilization by end users far from the regasification site in deep freezing facilities and for space conditioning in the commercial sector (e.g.: Supermarkets and Hypermarkets) 2 .

The regasification process

The Italian natural gas transmission system works with main pipelines at a pressure rating up to more than 70 bar, then the LNG regasified has to be sent in the transport pipeline at a pressure of the same order of magnitude. In principle it is possible (see Fig. 1, path AB'D'D) to pump natural gas at this pressure (D'D) after regasification at a low pressure (AB'B''B'''D'), but this option isn't applied in Europe.

When the regasification is carried out at low pressures and, then, the gas is compressed at the pressure required by pipelines, the pumping power (W NG ) is very high. Instead, if the LNG is pumped in liquid phase, at a pressure lying in the pressure rating range required by pipelines (hypercritical pressures) there is convenience because the pumping power (W LNG ) is lower (see Fig. 1, path ABCD).

The ratio W NG /W LNG is higher than 20 [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part One[END_REF]. Moreover, with regasification at hypercritical pressures, the heat exchange by the LNG side is very good and heat transfer equipment is more reliable. The process proposed works at hypercritical pressures (pressure in the LNG regasification loop lies in the range 75÷80 bar) [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part One[END_REF].

A typical composition of LNG considered in the feasibility analysis of DREAM is that reported in Table 1 in which are included also main thermo-physical properties and both the higher and lower heating values 3 of natural gas obtained after the regasification process. This kind of composition is quite usual for LNG processed in a regasification site.

The transport of natural gas by pipeline from gas field to the town or industrial sites in most cases is impossible, so there is need to transport LNG by ship. At the terminal of arrival a regasification process of LNG, which is processed and liquefied near wellhead, returns it back to gas state before its transport in the pipeline network. Sometimes LNG contains other hydrocarbon products which are added during the process of liquefaction to transport these products with LNG at the regasification facility, then some components added will be separated before transport of gas to market by pipeline.

In this case the LNG composition is different from that reported in Table 1 and the plants used are cryogenic facilities which in some cases become so complex that are seeming to a part of a modern oil refinery or a petrochemical plant 4 .

Delivery of cold recovering exergy of cold during regasification of LNG

Fig. 2 shows a process sheet of a modular multipurpose regasification facility, proposed by the Authors, to recover LNG physical exergy for cold utilization. 3 calorific values 4 a process of this kind was managed at Panigaglia, italy in a regasification site belonging to ENI Group

The process includes both possibility to use cold at lower temperatures for industrial use and cold at higher temperatures for other use. The plant proposed [START_REF] Dispenza | Recupero e utilizzazione del freddo nella rigassificazione del GNL, La Termotecnica[END_REF] is modular and has a regasification capacity of 2 10 9 Stm 3 /y when working 24 hour a day all a year around (270 days 5 ).

A facility of such kind requires an intermediate Power Cycle working with a suitable fluid such as Ethane or Ethylene, the cycle can produce 3 MW of electric power. Cold at very low temperatures is delivered by LNG in the condenser, while in the vapor generator cold is delivered in a secondary fluid which transfer cold to end users. This plant structure allows operation of cold exergy transfer, contained in LNG to be regasified, in a range of temperatures suitable for multipurpose use of cold, reducing regasification process irreversibility. Some electric energy is produced by the Power Cycle, but the own mission of modular unit proposed is addressed to deliver cold suitable for industrial and commercial use in the proper temperature range.

Ethane can be used currently in a facility addressed only to regasify LNG, while Ethylene can be used in a facility where this product is available.

In the process represented in Fig. 2, which is that using Ethane, cold can be produced at lower temperatures suitable for industrial applications (-80°C/-90°C÷-40°C) in the Heat Exchangers CU, CU1 and at higher temperatures (-35°C up to 0°C) in the Kettle type evaporators KE1, KE2, KE3 and in the Heat Exchanger CU2. Open 5 270 days correspond to a seasonal characteristic period of year during which there is a high gas demand.

In a typical modern Terminal having a regasification capacity of 8 10 9 Stm 3 /y it can have four modular Units or a mix of CHP Units [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part One[END_REF] and this kind of facility. The 270 days period of plant exploitation is conservative, considering that the growing demand of natural gas for electric energy generation gives a wide perspective on the possibility to consider a higher plant utilization factor.

Rack units will be used to manage the matching of duty. R. and D. on this subject now is in progress at DREAM, University of Palermo.

In Fig. 3 it is shown a drawing of a Spiral Wound Heat Exchanger as those selected for the CU, CU1 and CU2 units (Ethane in CU and LNG in CU1 and CU2 travel by the tube side and the secondary fluid by the shell side). Note that the Ethane condenser is also a heat exchanger of this kind6 : LNG travels from tube side and Ethane from the shell side 7 .

In Fig. 4 it is shown a drawing of a Kettle type evaporator as that selected for the KE1, KE2 and KE3 units (secondary fluid travels by the tube side and Ethane by the shell side).

The main design criteria are the following:

there is need to manage cold for some process different from cryogenic applications at a suitable temperature lying in a range allowing the use of available secondary fluids, -the above criterion calls for use of a suitable power plant which is heated by heat released by secondary fluids carrying cold far from the regasification site (at end users), -a part of cold available during the regasification process of LNG can be used inside the same regasification site area (e.g.: air liquefaction producing Nitrogen, Oxygen, Argon, deep freeze industrial warehouse and cold storage warehouse, etc).

The main operating parameters of the power plant thermodynamic cycle (pressures an temperatures) shall be selected on the basis of the following criteria, considering that the working fluid changes phase during the cycle evolution:

the lower pressure shall be higher than external atmospheric pressure to avoid air infiltration in the plant: in the feasibility analysis it was selected as 1.3 bar, -the higher pressure shall be selected at a value allowing to have a temperature near -40°C, in dependence of working fluid selected.

In the paper results are presented for two working fluids:

-Ethane: lower pressure 1.3 bar (t sat =-83.85 °C), higher pressure 7.8 bar (t sat =-39.91 °C), -Ethylene: lower pressure 1.3 bar (t sat =-99.45 °C), higher pressure 14.0 bar (t sat =-41.22 °C).

The pinch temperature difference in the condenser between the working fluid and LNG (at the exit of the device) is in both cases 10 K.

The power cycle working with ethylene is little different from that working with Ethane.

Modular Unit working with Ethane

The process is represented in Fig. The electric power generated by the modular unit working with Ethane is 3 MW and the net efficiency (at busbar8 ) is 13.6%.

There are three set of Open Rack heat exchangers. Their operation is required in continuous operation of LNG regasification facility, when cold duty of a given device (CU, CU1, CU2, KE1, KE2, KE3) is insufficient to cover the whole need of heat for the regasification process.

Modular Unit working with Ethylene

The process is represented in Fig. The electric power generated by the modular unit cycle working with Ethylene is 3.1 MW and the net efficiency (at busbar) is 18.0%.

There are three set of Open Rack heat exchangers. Their operation is required in continuous operation of LNG regasification facility when cold duty of a given device (CU, CU1, CU2, KE1, KE2, KE3) is insufficient to cover the whole need of heat for the regasification process.

Use of cold inside the regasification facility

In past years studies [START_REF] Buffiere | La recuperation des frigories du LNG et l'ajustement du gaz au terminal de Fos sur Mer, on LNG[END_REF] have been carried out on the possibility of cold exergy recovery inside a regasification area (e.g.: air liquefaction producing Nitrogen, Oxygen, Argon, liquid Carbon dioxide and dry ice, etc.).

Cold available during regasification of LNG can be used at lowest temperatures to reduce energy need in the process of liquefaction of air, Nitrogen, Oxigen, Argon.

Another application can be the liquefaction of Carbon dioxide or the production of dry ice. It would be possible also desalination of sea water with a freezing process.

Cold application at lowest temperature offer a wide perspective on suitable options [START_REF] Mcdermott | Liquefied Natural Gas Technology[END_REF], [START_REF] Haywood | Analysis of engineering cycles[END_REF].

Use of cold outside the regasification facility

End use facilities, lying far away of the regasification terminal, require transfer of cold at a suitable distance from land-based regasification facilities. The relevant problems arising have capital weight due to lack of suitable secondary fluids. Among the secondary refrigerants available on the market almost isn't no one, compared to the old well known calcium chloride brine, which shows a remarkable better behavior. The reason is that when using such kinds of fluids heat transport is linked to sensible heat, then a large mass flow rate of liquid has to be circulated with special problems in the low temperature range where high viscosity increases the pumping power and many fluids can freeze.

Recently nanofluids and ice slurries have been proposed, but these seem no suitable for the kind of application analyzed. A reliable solution can be based, indeed, on the use of natural fluids such as Hydrocarbons (flammable) or Carbon dioxide; the feasibility study performed in this work demonstrated that the use of Carbon dioxide should be preferred.

The possible applications in refrigerating facilities, for recovery and utilization of physical exergy of LNG during regasification, could be, as an example, of two kind: one pertaining to a cluster of end users made of agro-food factories, where need there is of cold for the freezing process of foods and to maintain these at low temperature; another pertaining to users such as supermarkets and hypermarkets where need there is of cold for space air conditioning, for the refrigeration of display cases and cabinets in the sales area and for foodstuffs preparation and cold storage in cold storage rooms. This kind of application have been analyzed at DREAM for the modular plant working with Ethane.

The two clusters analyzed have a mean distance of 2 km from the regasification site.

A mean size regasification capacity in sites planned in the World is 8 billion Stm 3 /y.

A regasification facility such that proposed has a regasification capacity of 2 billion Stm 3 /y. The power required by the cluster including Agro Food Factories amounts to 9

MW of cold delivered at a mean temperature of -43 °C9 . The end use in the hypermarket pertains mainly to the process of space air conditioning and a quantity of cold is required in the refrigeration utilities. The whole amount of power required is 7.5

MW 10 : 7.0 MW for space conditioning and 0.5 MW of cold of which 150 kW are delivered as cold at -35 °C and the remaining part as cold at -15 °C.

The transfer of cold between the regasification facility and the clusters of Agro Food

Factories and the Hypermarket takes place by means of two pipelines into which travels 9 e.g.: cold delivered in CU1 10 e.g.: part of cold delivered in KE2 carbon dioxide: in the feeding pipeline in liquid phase and in the return pipeline in gaseous phase. Carbon dioxide is liquefied in the regasification facility recovering cold available in the regasification process (Unit CU1). This secondary fluid is pumped in liquid phase, this option allows a considerable saving of pumping power (e.g.: for the gaseous phase shall be more than 30 time higher in the Case Study of the Agro Foof Factories).

Carbon dioxide in liquid phase goes to the clusters of users and feeds evaporators of cold utilities, the gaseous phase returns back to the regasification facility where it is liquified and then pumped in the feeding pipeline.

Agro Food Factories

A process sheet of the condensation facility and of the liquid carbon dioxide pumping station lying in the regasification site 11 is reported in Fig. 6 indicate for sake of simplicity the whole adiabatic throttling process which takes place in all evaporators 12 .

The line 6-1 indicates the process which pertains to the pressure losses during the return of the gaseous phase.

The pipeline ahead of the end uses has a mean diameter of 8 inch (thickness 8.18 mm, pressure rating 40 bar, seamless steel API 5L).

The pipeline downstream of the end uses (return pipeline) has a mean diameter of 18 inch (thickness 11.13 mm, pressure rating 40 bar, seamless steel API 5L).

The insulation material is polyurethane foam, which has high thermal efficiency and is mechanically strong. The system is capable of working in a temperature range of -200

°C to 150 °C.

The condensation and pumping facility (in the regasification site) and the facility lying in the cluster will be monitored on-line by means of a master PC (cluster controller) which receives signals by the data acquisition and control peripherals (remote units, at the end uses). The main task of the supervision system will be to assure the right feeding of the evaporators at the end use.

Hypermarket

Fig. 8 shows a process sheet of the condensation facility and of the liquid carbon dioxide pumping station lying in the regasification site13 (exchanger KE2, receiver A' and carbon dioxide Liquid Pump). In the same Figure it is reported a schematic sheet of some end uses, the liquid carbon dioxide storage system (B') installed ahead of the end uses. In the receiver (C') goes the gaseous phase returning from the evaporators; from this device it goes (almost dry) in the return pipeline.

In Fig. 9 it is represented the process which takes place in the secondary line (which includes the carbon dioxide pipeline) on the p-h diagram.

The processes represented both for the end use at -35°C and for the end use at -15°C are seeming to those explained for the Fig. 7. Note that there is need here for a compressor (see Fig. 8) which pumps the gaseous phase coming out from the evaporators working at a lower temperature14 up to a pressure level suitable for mixing the gaseous phase with that coming out from the Air Treatment Units in the Hypermarket.

The pipeline lying ahead of the end users has a mean diameter of 6 inch (thickness 10.97 mm, pressure rating 80 bar, seamless steel API 5L).

The pipeline lying downstream of the end uses (return pipeline) has a mean diameter of 12 inch (thickness 17.48 mm, pressure rating 80 bar, seamless steel API 5L).

The insulation material is polyurethane foam, which has high thermal efficiency and is mechanically strong. The system is capable of working in a temperature range of -200 °C to 150 °C.

Thermodynamic analysis

Two series of numerical simulation are presented: one for a modular unit working with Ethane and another for a modular unit working with Ethylene 15 .

The numerical simulations have been performed with a software developed at DREAM in the context of the Programme "ORPA059444: Innovazione tecnologica di sistemi energetici e loro componenti; metodologie di progettazione, verifica e simulazione", University of Palermo, Italy, using as a main tool the Engineering Equation Solver of S.A.Klein and A.Alvarado, Professional version 7.934.

Exergy analysis of CHP modular unit working with Ethane

15 The feasibility analysis of DREAM pertains to a lot of hydrocarbons products. The use of Ethane seems appropriate for the application examined in LNG regasification sites. In the paper the analysis performed with Ethylene is also presented. This fluid can be used if easy available near the site. The results of exergy analysis demonstrated that efficiency based on the 2 nd Principle of Thermodynamics is a little higher than that for Ethane.

The performance simulation for the whole regasification facility, represented in Fig. 1, gives the main results reported in Fig. 10, 11, 12 for the Exergy analysis of each part of the process. Analyzing the CHP plant working with Ethane, the splitting detail items of exergy delivered in the Ethane condenser have been derived with an appropriate methodology.

The results obtained are reported in Fig. 12. The item P el is the part of LNG exergy which is recovered as electric power produced by the Power Cycle working with Ethane. This cycle has a mean overall efficiency of 13.3% and it produces a rated power of 3.0 MW.

Other items pertain to exergy delivered in heat exchangers CU and in Kettle type evaporators KE1, KE2, KE3, to exergy recovered as mechanical work for driving Ethane pump (booster group GT EP /EP, see Fig. 1), to exergy losses in each main device and exergy losses due to pressure losses along the Ethane-cycle loop.

Energy and Exergy efficiency parameters

The regasification facility is a cogeneration system which has the aim to produce electric power and cold in various temperature range and to regasify LNG.

In the plant working with Ethane cold is delivered to a secondary fluid or a cooling process in the heat exchangers CU, KE1, KE2, KE3 (see Fig. 1). At the same time

Ethane is heated and it vaporizes. Cold duties of each device composes the whole cold duty of this part of the regasification facility. The condenser of Ethane Cycle is cooled by the LNG which is to be regasified. Moreover completion of the LNG regasification takes place in heat exchangers CU1 and CU2. Cold released in the equipment is also utilized.

ACCEPTED MANUSCRIPT a) Energy Efficiency parameter (COP)

An appropriate Energy efficiency parameter for such complex kind of modular plant is a COP. It can be estimated as the percentage recovered of cold energy supplied to the system (in the condenser of the Ethane Cogeneration Plant and in the LNG heat exchangers CU1 and CU2):

COP Ethane Cogeneration Plant

The COP for this part of the modular plant is defined by the formula: 100 100

el CU KE1 KE2 KE3 EthCP condLNG condLNG P Q Q Q Q ER COP Q Q + + + + = × = × (1) el CU KE1 KE2 KE3 ER P Q Q Q Q = + + + + (2)
for the case study analyzed COP EthCP = 161%.

COP of the whole Regasification Facility

ACCEPTED MANUSCRIPT

The COP for the whole modular plant is defined by the formula: 100

CU1 CU2 Reg LNG LNG ER ExNG E E COP Q P + + + = × + (3)
for the case study analyzed COP Reg = 201%.

b) Exergy Efficiency

The Exergy efficiency ζ for the modular plant can be estimated as the percentage recovered of cold exergy supplied to the system (the exergy of the LNG stream to be regasified).

Exergy efficiency of Ethane Cogeneration Plant

It is defined by the formula:

+ + + + = × = × (4) 1 2 3 EL C U K E K E K E ExRE ExR ExR ExR ExR ExR = + + + + (5)
for the case study analysed ζ EthCP = 35%.

Exergy efficiency of whole Regasification Facility

It is defined by the formula:

1 2 Re 100 CU CU g ExR ExNG ExR ExR ExLNG ζ + + + = × (6)
for the case study analysed ζ Reg = 64%.

It is worth of mention that ζ would be a 42% if the same Regasification Plant of Figure 1 regasifies LNG at a pressure below that pseudo-critical, as proposed in eastern countries. Moreover, ζ would be a 48% for a simple regasification plant based on Open

Rack technology working at hypercritical pressure and a 32% when the same works at a pressure below that of the pseudo-critical state of LNG. Note that, the exergy "recovered" in both the last two cases is only that of the natural gas regasified.

Exergy analysis of CHP modular unit working with Ethylene

The performance simulation for the whole regasification facility, represented in Fig. 2, gives the main results reported in Fig. 13, 14, 15 for the Exergy analysis of each part of the process. Other items pertain to exergy delivered in heat exchangers CU and in Kettle type evaporators KE1, KE2, KE3, to exergy recovered as mechanical work for driving Ethylene pump (booster group GT EP /EP, see Fig. 5), to exergy losses in each main device and exergy losses due to pressure losses along the Ethylene-cycle loop.

Energy and Exergy efficiency

In the plant working with Ethylene cold is delivered to a secondary fluid or a cooling process in the heat exchangers CU, KE1, KE2, KE3 (see Fig. 5). At the same time Ethylene is heated and it vaporizes. The cold duty of each device composes the whole cold duty for this part of the regasification facility. The condenser of the Ethylene Cycle is cooled by the LNG which is to be regasified. Moreover the completion of the LNG regasification takes place in heat exchangers CU1 and CU2. The cold released in the equipment is also utilized.

a) Energy Efficiency parameter (COP)

The COP for such complex kind of modular plant can be estimated as the percentage recovered of the cold energy supplied to the system (in the condenser of the Ethylene Cogeneration Plant and in the LNG exchangers CU1 and CU2):

COP of Ethylene Cogeneration Plant

For the case study analyzed using the definition (1) it is obtained:

COP EthCP = 124%.

COP of the whole Regasification Facility

For the case study analyzed using the definition (3) it is obtained:

COP Reg = 183%.

b) Exergy Efficiency

The Exergy efficiency ζ for the modular plant can be estimated as the percentage recovered of the cold exergy supplied to the system (the exergy of the LNG stream to be regasified).

Exergy efficiency of Ethylene Cogeneration Plant

For the case study analyzed using the definition (4) it is obtained:

ζ EthCP = 44%.

Exergy efficiency of the whole Regasification Facility

For the case study analysed using the definition ( 6) it is obtained:

ζ Reg = 71%.
It is worth of mention that ζ would be a 43% if the same Regasification Plant of Figure 5 regasifies LNG at a pressure below that pseudo-critical, as proposed in eastern countries. Moreover, ζ would be a 52% for a simple regasification plant based on Open

Rack technology working at hypercritical pressure and a 36% when the same works at a pressure below that of the pseudo-critical state of LNG. The exergy "recovered" in both the last two cases is only that of the natural gas regasified.

Economic and Environmental analysis

An economic venture analysis has been carried out comparing some hypotheses of process management of modular unit proposed for the regasification of LNG:

considering some forecast for cost of money, inflation, etc17 , -considering some scenarios to account for price volatility of energy products, -considering selling price of electric energy produced in a regime of free market in the context of Electric Energy Stock Exchange in Italy [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part Two[END_REF],

considering for natural gas a mean selling price in Italy weighted using real quantities sold [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part Two[END_REF].

Venture analysis was carried out comparing a given alternative for the management of process using the modular unit, "Alternative 1", with a reference alternative which is based on the use of a regasification plant using OR (Open Rack Technology) having the same regasification capacity of the CHP Plant analyzed:

"Alternative 0".

The leading idea doing venture analysis is that:

-The use of modular unit allows the LNG regasification during plants exploitation producing some amount of electric energy and delivering cold suitable for industrial and commercial use in the proper temperature range.

-Thus, exploiting a modular unit, use of electric energy for pumping sea water to feed OR is avoided.

-Considering this hypothesis, regasification costs are included in a low range because, actually, only the incidence of regasification of LNG using the OR technology back-up system during the period of its operation is to be considered apart.

-The income to be considered is that of selling electric energy produced and cold delivered to end users and, moreover, the saving due to avoided expenditure of electric energy for pumping sea water to feed OR. Really, in the venture analysis the cost of regasification using modular unit proposed or OR technology, prudentially, are considered equal (although this leads to an overestimate of regasification cost using modular unit with the stated hypothesis).

In each analysis done, cash flows consider an initial capital investment equal to the whole cost expense to built and put in operation a modular unit. Analysis pertains to a comparison of performance of a modular unit proposed with an OR facility (considered as basis option) having the same regasification capacity as that of modular unit proposed. Prudentially, capital initial investment cost, thus, isn't that "differential" 18 but the whole cost to built and put in operation a modular plant. Really, it is very difficult that a regasification site will work for a long time at its maximum capacity, thus "differential" initial capital investment cost could be considered (one modular unit has a regasification capacity of 2 10 9 Stm 3 /y while a typical site of regasification 8 10 9

Stm 3 /y). Moreover, considering that a modular unit proposed represent a relative new technology, an additional capital investment cost was spread over the entire life period of venture in each year (25 years).

18 cost to built a modular unit minus cost to built an OR facility having the same regasification capacity; note that this last facility will be built to assure an emergency back-up system

In the venture analysis it is considered an escalation rate both for selling price of electricity and natural gas and for cost of LNG purchased, also an escalation rate was considered for man power and some other items [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part Two[END_REF].

Each venture analysis considers items composing cash flows both before tax and after tax. Tax rate [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part Two[END_REF] pertains to that of Italy, this, which, in the EU area, is lower only to that for Germany, amount to a whole 37.25% (this value has been stated in the analysis, although some financial incentive really can lower this value by a 10÷15%).

Present Worth before tax (PW bt ), Present Worth after tax (PW at ) and Present Worth of Revenue Requirements (PWNR) were derived [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part Two[END_REF]. Using cash flow items componsing PW at , Return On Investment (ROI at = [net casflow after tax -mean depreciacion charge]/[Capital Investment]) and Benefit Cost Ratio (BCR at , IP in Italy:

[PW at +Capital Investment]/ [Capital Investment]) were also derived. Time of return on investment was derived utilizing cumulated PWNR during the years up to reach the value of initial capital expenditure (note that this value is higher than those derived using PW bt or PW at ). Also, marginal costs of regasification were derived (both when using a modular unit or OR, prudentially, costs are assumed as equal). Marginal costs considered of electric energy produced and cold delivered to end users are those actual and those levelized on the entire venture life.

The economic analysis is based on a numerical simulations which has been performed with a software developed at DREAM. In the analysis some hypotheses of process management of the modular plant proposed for the regasification of LNG have been compared. The simulation was carried out 19 comparing a given alternative for the management of the process using the modular plant with a reference alternative which is based on the use of a regasification plant operating with Open Rack Technology. 20 The venture was considered in the analysis as a Project financing venture (all bond) and a reference cost of a loan, which will have a duration of 15 years was assumed with an interest rate of 8.00%.

Here main results of the economic analysis, considering nominal discount rate varying in the range 5-15%, for a modular unit working with Ethane are reported in Table 2. The sharing of the amount between the three type of production was assumed: as 20% for the gas production, 80% for the production of cold and electricity, sharing these costs among them and considering their respective incidence on the co-production.

The cost obtained for each item are the following: 0.07 c€/Nm 3 for gas, 0.99 c€/kWh for cold and 0.51 c€/kWh for electric energy.

Table 3 shows some results obtained fixing the selling price for electric energy at 7.00 c€/kWh and for a set of selling price for the cold. Time of return (by PW at ) lies in the range 4.5÷15.5 years when the selling price for cold lies in the range 3.50 ÷ 1.00 19 for criteria on which the methodology used is based see [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part Two[END_REF], see also Appendix 20 having the same regasification capacity of the modular unit analyzed c€/kWh. Then the results obtained show the profitability of these modular regasification plants.

In the analysis it has been derived a reference price for cold produced far from the regasication site with a conventional cooling plant based on refrigerating equipment available on the market. The primary energy saving estimated for the regasification facility, considering the avoided demand to produce the amount of cold recovered, is 39.46 ktoe/y and cold reject avoided amount to 336,960.00 MWh/y. The avoided emission of CO 2 is of 88.61 kt/y.

Safety aspects in the management of regasification process

The recovery of cold during LNG regasification in applications pertaining cold technology put a great challenge, bearing in mind that the regasification site area should be near the potential end users of cold. But, this occurrence seldom happens because LNG is characterized by fire and explosion hazards, which pose many safety challenges to project managers and operators. Safety regulations require that LNG terminals to be surrounded by exclusion zones to protect neighbouring communities in the event of a pool fire or flammable vapour cloud [START_REF] Alderman | Introduction to LNG Safety[END_REF]. Then it seems that availability of cold is proper for industrial use. Industrial facilities can be built inside the regasification terminal 21 .

21 e.g.: the agreement between "Gaz de France" and "L'Air Liquide" for the Terminal of Fos sur Mer -France addressed to the production of Nitrogen utilized by "Gaz de France" in the Terminal for gas adjustment

Cold should be utilized off the regasification site, but it is difficult to transfer cold at long distances due to unavailability of a suitable brine or safe fluids for such kind of application, this subject now requires R. and D. A possible option, proposed in this paper, can be the use of Carbon dioxide.

As far as it pertains to generation of electric energy and utilization of cold for the industrial use, the process will take place inside the regasification facility area, in the other cases the end users are far from the regasification area. Moreover, the layout of plants proposed considers properly the reliability of risk management during the process exploitation.

Conclusive remarks

The possible applications in refrigerating facilities for recovery and utilization of physical exergy during LNG regasification, here envisaged, is based on the use of a modular facility having a regasification capacity of 2 10 9 Stm 3 /y (as a mean: 1/4 of the mean single regasification capacity of sites planned in the World: 8 10 9 Stm 3 /y).

The results of a feasibility study of the venture proposed, starting from conceptual design and with an analysis both thermodynamic and economic demonstrated the suitability and the profitability of the application proposed. This seems very attractive due to expected wide future exploitation of LNG regasification in the World.

As a mean, land-based regasification facilities in program in the World have a regasification capacity of 8 10 9 Stm 3 /y. Then, coupling modular units both of the type i Π disbursements (annual Cash outflows for ad-valorem expense)

PW bt Net Present Worth of venture before tax:

(1 ) (1 )

i i i bt i i i i R O PW I r r Π + = - - + + ∑ ∑ (A-2) I initial investment r nominal discount rate
CF at Investment Cash flow after tax: ( ) (1 )

at i i i i CF R O T Π = - + - (A-3) ( ) i i i i i b b i T R O D r f V τ τ Π = --- - (A-4)
i i i i at i i i i i i R O T PW I r r r Π + = - - - + + + ∑ ∑ ∑ (A- (1 )(1 )
( ) ( ) ( ) B PWNR i i i i i b wi i b b i CF R O T D r V D r f V τ τ Π ⎡ ⎤ = - + -- + - + ⎣ ⎦ (A-8) B i D annual book depreciation charge wi V
whole amount of money on which must be paid interest at the end of year i PWNR Present Worth of Net Revenue:

( ) ( ) (1 ) (1 ) (1 ) (1 )
B i b w i i b b i i i i i i i i i i i i i D rV D r f V R O T PWNR r r r r τ τ Π ⎡ ⎤ + - + + ⎣ ⎦ = - - - + + + + ∑ ∑ ∑ ∑ (A-9)

TR Time of Return on Investment based on PWNR:

Time of return on investment reported in results of Venture Analysis was derived utilizing cumulated PWNR during the years up to reach the value of initial capital expenditure; note that this value is higher than those derived using PW bt or PW at .

[13] D.

  (exchanger CU1, receiver A and carbon dioxide Liquid Pump). In the same Figure it is reported a schematic sheet indicating some clusters of end users (CLi), the liquid carbon dioxide storage system (Bi) installed ahead of the end users in a Factory. The gaseous phase returning from the evaporators goes in the receiver (Ci). From this device installed in each Factory it goes (almost dry) in a common receiver (C installed in the cluster area) and then it goes in the return pipeline collecting all the gaseous carbon dioxide returning from the whole cluster of Factories In Fig.7it is represented the process which takes place in the secondary line (which includes the carbon dioxide pipeline) on the p-h diagram. The line 1-2 indicates the condensation process of the gaseous phase which returns from the Agro Food Factories.The evaporation process takes place in the evaporators (at the end use, line 5-6). The pumping of the liquid phase is indicated by the line 2-3 and line 3-4 indicates the amount of pressure losses in the lines in which the liquid phase travels. Line 4-5

Fig. 10 reports

 10 Fig. 10 reports results of Exergy analysis for the LNG regasifier.

Fig. 13

 13 Fig. 13 reports results of Exergy analysis for the LNG regasifier.

Fig. 14

 14 Fig.14shows a different detail of exergy analysis for the whole regasification plant,

Figure 16

 16 Figure 16 reports results obtained for Time of return (by PWNR analysis), while

  investment at beginning year i PW at Net Present Worth of venture after tax:

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .Fig. 10 .Fig. 11 .Fig. 12 .

 123456789101112 Fig. 1. Thermodynamic process during regasification of LNG Fig. 2. A proposed process sheet for cold recovery during regasification of LNG Fig. 3. A detail a of a spiral-wound heat exchanger (Courtesy of Linde AG) Fig. 4. A schematic drawing of a Kettle -type evaporator Fig. 5. The process of modular unit working with Ethylene for regasification of LNG Fig. 6. The system for transfer and utilization of cold in Agro Food Factories Fig. 7. The cooling cycle for transfer and utilization of cold in Agro Food Factories (R-744 Diagram courtesy of IIR) Fig. 8. The system for transfer and utilization of cold in a Hypermarket Fig. 9. The cooling cycle for transfer and utilization of cold in a Hypermarket (R-744 Diagram courtesy of IIR) Fig. 10. Results of exergy analysis for the LNG regasifier working with Ethane Fig. 11. Input Exergy in Ethane condenser, in CU1 and CU2 and exergy losses Fig. 12. Results of exergy analysis for the Ethane cycle Fig. 13. Results of exergy analysis for the LNG regasifier working with Ethylene Fig. 14. Input Exergy in Ethylene condenser, in CU1 and CU2 and exergy losses Fig. 15. Results of exergy analysis for the Ethylene cycle Fig. 16 -Time of return (by PWNR analysis) varying the nominal discount rate (Regasifier working with Ethane) Fig. 17 -Trend of PWbt, PWat, PWNR varying the nominal discount rate(Regasifier working with Ethane)

Fig 15 Figure

 15 Fig 15

Figure

  Figure(s)

Figure(s)

  Figure(s)

  Romano et a., "Italian Greenhouse gas inventory 1990-2003 -National Inventory report 2005"

	P el GT	Electric power generated in the Ethane/Ethylene Loop (kW) Gas turbine
	Published by APAT Italy 2005 P LNG Pumping power of LNG to be regasified (kW) KE1 Heat exchangers KE1
	PW bt KE2	Net Present Worth of venture before tax Heat exchangers KE2
	PW at KE3	Net Present Worth of venture after tax Heat exchangers KE3
	PWNR P	Present Worth of Net Revenue Pressure losses along in the Ethane/Ethylene loop
	Nomenclature Q condLNG Cold power delivered in Ethane/Ethylene condenser (kW) PS Pressure losses in the regasification facility
	BCR at Q CU PU	Benefit Cost Ratio Cold power delivered in CU (kW) Ethane/Ethylene pump
	CF bt Q KE1 Reg	Investment Cash flow before tax Cold power delivered in KE1 (kW) Regasification facility
	CF at Q KE2	Investment Cash flow after tax Cold power delivered in KE2 (kW)
	at Q KE3 CF	Levelized Cash flow after tax Cold power delivered in KE3 (kW)
	CFPWNR Financing Cash flow after tax Q LNG Cold power delivered by LNG to be regasified (kW)
	COP ROI at	Coefficient of performance Return On Investment
	E CU1 TR	Cold power delivered in CU1 (kW) Time of Return on Investment based on PWNR
	E CU2 ζ	Cold power delivered in CU2 (kW) Exergy efficiency
	Ex	Exergy (kW)
	ExD Subscripts	Exergy destroyed (kW)
	ExL CO	Exergy of cold delivered during the regasification process of LNG (kW) Ethane/Ethylene condenser
	ExLNG CTR	Exergy of LNG to be regasified (kW) Whole exergy in the regasification facility
	ExNG CU	Exergy of exit stream of NG regasified (kW) Heat exchangers CU
	ExR CU1	Exergy recovered (kW) Heat exchangers CU1
	LNG CU2	Liquefied Natural Gas Heat exchangers CU2
	NG EL	Natural Gas Electric power

  Exergy of LNG delivered in Ethane condenser, DeLNGcond=17,902 kW

	Figure(s) Figure(s) Figure(s) Figure(s) Figure(s)
			ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT
			Exergy of LNG at inlet, ExLNG=69,663 kW Exergy of LNG at inlet, ExLNG=69,663 kW
	54% ExGN 33,256.00 48% 37,366.00 ExGN 33,256.00 48% evcond 8,546.58 48% ExGN evcond 5,191.00 37%	DeLNGcond 17,902.00 26% DeLNG1 4,452.00 RecCU2 6% 6% 6% evCU 314.73 evCTR 11,598.74 Exergy of LNG at inlet, ExLNG=69,663 kW RecCTR 6,303.26 9% 17% RecCU1 2,541.00 3% evCU1 1,911.00 1,019.00 814.60 3% RecCU 1,347.00 8% evCU 101.20 1% RecKE1 657.10 4% evKE1 178.50 1% 1,153.00 RecKE2 6% evKE2 7% 6% evKE2 20% 4,629.00 865.60 13,834.00 RecCU1 RecKE2 DeLNGcond RecCU 1,496.00 2% RecKE1 Exergy of LNG at inlet, ExLNG=69,663 kW 11% 493.20 RecCTR 6,109.55 9% 4% evCTR evKE1 7,724.45 1% 11% 153.00
	Fig 10	ExGN 37,366.00 54% Plosses 933.80 7%	Plosses 1,289.47 7% evP_tpump 0% 8.82	plossesCHE 11,070.00 16% evgenel 197.30 1% plossesCHE 7,953.80 11% 0.005 73.47 Ptpumpnet	DeLNG2 2,983.00 4% evCU2 plossesCHE 11,070.00 16% 762.00 1% evgenel 2,221.00 3% evKE3 259.70 1% 187.60 1% 48.66 0% 16.69 11% evP_tpump RecKE3 203.50 1% Pel 2,894.00 16% 7,954.00 Ptpump net DeLNG1 8,250.00 12% DeLNG2 2,259.00 3% plossesCHE RecKE3 evCU1 3,621.00 5% 89.28 Pel RecCU2 1,654.00 2% 1% evKE3 3,092.00 22% evCU2 605.20 1% 111.20 0.80%
					0%
	Fig 14
	Fig 11 Fig 12 Fig 13

Exergy of LNG delivered in Ethylene condenser, DeLNGcond=19,868 kW

research developed at DREAM University of Palermo in the framework of the Program "ORPA059444: "Innovazione tecnologica di sistemi energetici e loro componenti; metodologie di progettazione, verifica e simulazione"

But it has a liquid receiver installed downstream.

The same concern holds for CU1 and CU2, this operation is suitable as the LNG change of phase occurs in the hypercritical region.

note that this parameter for the case analyzed is of less meaning because it is defined as the ratio of electric energy delivered at busbar and the heat supplied to the cycle, effectively delivered as cold to the end users.

For sake of simplicity pressure losses in the equipment aren't represented, note that these have been duly considered in the simulation.

see Fig.2, Kettle type evaporators KE2

Evaporators working at a lower pressure, which perform the duty to produce cold suitable for feeding the end uses at a mean temperature level of -35 °C.

The Dead State considered is restricted: this is a restricted form of equilibrium where only the conditions of mechanical and thermal equilibrium must be satisfied.

see[START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part Two[END_REF]: a sensitivity analysis of cash flows on Nominal Discount Rate (included in the range: 5÷15%) was performed

proposed by the Authors [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part One[END_REF][START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part Two[END_REF] and of modular units addressed to cold recovery, the modular plants proposed offer a wide perspective.

Appendix -Definitions pertaining the Venture Analysis

For sake of clearness need there is to define main parameters involved in Venture Analysis [START_REF] Dispenza | Exergy recovery during LNG regasification -Electric energy production: Part Two[END_REF].

Cash flow is defined as the movement of money both into the project (revenues) and out of the project (disbursements). Cash flows can be classified into: 1) Operational cash flows: Cash received or expended as a result of the company's core business activities, 2) Investment cash flows: Cash received or expended through capital expenditure, investments or acquisitions, 3) Financing cash flows: Cash received or expended as a result of financial activities, such as receiving or paying loans, issuing or repurchasing stock, and paying dividends.

Three kind of Cash flow are used in Venture Analysis done: 1) Investment Cash flow before tax, 2) Investment Cash flow after tax, 1) Financing Cash flow after tax: CF bt Investment Cash flow 22 before tax: