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Fig. 8. a. Grid diagram of designed Heat Exchanger Networks for the case with branching of stream fragments, with marked loops according to the Pinch technology rule for loops in parts above and below the Pinch point; b. Grid diagram of designed Heat Exchanger Networks for both cases with marked loops and paths that are going through the Pinch point (after usage of rule for loops in sections above and below the Pinch point).

Figure 8 a. Grid diagram of designed Heat Exchanger Networks for the case with branching of stream fragments, with marked loops according to the Pinch technology rule for loops in parts above and below the Pinch point; b. Grid diagram of designed Heat Exchanger Networks for both cases with marked loops and paths that are going through the Pinch point (after usage of rule for loops in sections above and below the Pinch point).

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The Heat Process Integration with Pinch technology is divided into two separate parts — targeting with super-targeting and design of a solution. Super-targeting determines the minimal values for heat de- mand and minimal allowed temperature difference in heat exchangers. The second part is design of Heat Exchanger Network as applicable solution. A number of studies explore methods and techniques for design of Heat Exchanger Networks based on data from Pinch analysis. Some of them use different optimization methods and give complex solutions. This paper presents a modified technique for Heat Exchanger Network design. This technique uses a combination of Problem Table Algorithm (PTA) and Pinch Design Method (PDM). The main idea for this technique is the design of sub-networks of heat exchangers for every enthalpy interval determined by the breaking points on the hot and cold composite curves. All these sub-networks were connected into one Heat Exchanger Network in the same order as enthalpy intervals exist in composite curves’ graphs. The created Heat Exchanger Network was simplified with the basic rules for network relaxing in Pinch technology. The results of this technique were Heat Exchanger Networks that have high-energy recovery, and it got the optimal solution, or it was close to it. This technique is easy to apply, but in some cases, the primary Heat Exchanger Network's designs could have a very complex composition. aculty of Technical Sciences, International Balkan University, Tasko Karadza 11a, 1000 Skopje, Macedonia Aleksandar Anastasovski> Enthalpy Table Algorithm for design of Heat Exchanger Network as optimal solution in Pinch technology Keywords: Pinch technology HEN design Composite curve segments Grid diagram
The Heat Process Integration with Pinch technology is divided into two separate parts — targeting with super-targeting and design of a solution. Super-targeting determines the minimal values for heat de- mand and minimal allowed temperature difference in heat exchangers. The second part is design of Heat Exchanger Network as applicable solution. A number of studies explore methods and techniques for design of Heat Exchanger Networks based on data from Pinch analysis. Some of them use different optimization methods and give complex solutions. This paper presents a modified technique for Heat Exchanger Network design. This technique uses a combination of Problem Table Algorithm (PTA) and Pinch Design Method (PDM). The main idea for this technique is the design of sub-networks of heat exchangers for every enthalpy interval determined by the breaking points on the hot and cold composite curves. All these sub-networks were connected into one Heat Exchanger Network in the same order as enthalpy intervals exist in composite curves’ graphs. The created Heat Exchanger Network was simplified with the basic rules for network relaxing in Pinch technology. The results of this technique were Heat Exchanger Networks that have high-energy recovery, and it got the optimal solution, or it was close to it. This technique is easy to apply, but in some cases, the primary Heat Exchanger Network's designs could have a very complex composition. aculty of Technical Sciences, International Balkan University, Tasko Karadza 11a, 1000 Skopje, Macedonia Aleksandar Anastasovski> Enthalpy Table Algorithm for design of Heat Exchanger Network as optimal solution in Pinch technology Keywords: Pinch technology HEN design Composite curve segments Grid diagram
Fig. 1. Solving of paths and loops after Heat Exchanger Network design with Pinch Design Method; a — determined path in the network; b — possible solution of the path; c — determined loop between heat exchangers paired with the same streams; d — solution of the loop from c; e — determined loop between heat exchangers connected on various streams; f — solution of the loop from e. (x is minimal heat load or some value with which there is no violation on AT,,;, and temperature crossing). Designs of Heat Exchanger Networks could have many stream's splits. That could be unacceptable for some production plants because of extra costs in pipe work and valves as well as control of production parameters. This can be minimized by using cyclic matching | 13]. In fact, the cycling matching determines splits that do not violate ATmin and temperature crossing through the heat transfer in the heat exchangers. This paper suggests other directions for design of Heat Exchanger Networks than the Pinch Design Method. This new technique does not use temperature intervals, but enthalpy in- tervals from a heat cascade. The main idea for this technique is based on the assumption that every enthalpy interval determined by the breaking points of hot and cold composite curves represents an independent Heat Exchanger Network with balanced heat de- mand. Those Heat Exchanger Networks (sub-networks of final so- lution) connect all the stream's fragments present in the certain enthalpy interval. The values for enthalpies in the heat cascade determine new temperature intervals for Hot and Cold Composite Curves (Fig. 2). Every new determined temperature interval con- tains fragments of hot or cold streams. All those stream’'s fragments form a simple case for Heat Exchanger Network design. Every sub- network has its place in the final solution according to the order of enthalpy intervals in the heat cascade. All designed heat exchangers for all fragmentations were connected together in a series as a final
Fig. 1. Solving of paths and loops after Heat Exchanger Network design with Pinch Design Method; a — determined path in the network; b — possible solution of the path; c — determined loop between heat exchangers paired with the same streams; d — solution of the loop from c; e — determined loop between heat exchangers connected on various streams; f — solution of the loop from e. (x is minimal heat load or some value with which there is no violation on AT,,;, and temperature crossing). Designs of Heat Exchanger Networks could have many stream's splits. That could be unacceptable for some production plants because of extra costs in pipe work and valves as well as control of production parameters. This can be minimized by using cyclic matching | 13]. In fact, the cycling matching determines splits that do not violate ATmin and temperature crossing through the heat transfer in the heat exchangers. This paper suggests other directions for design of Heat Exchanger Networks than the Pinch Design Method. This new technique does not use temperature intervals, but enthalpy in- tervals from a heat cascade. The main idea for this technique is based on the assumption that every enthalpy interval determined by the breaking points of hot and cold composite curves represents an independent Heat Exchanger Network with balanced heat de- mand. Those Heat Exchanger Networks (sub-networks of final so- lution) connect all the stream's fragments present in the certain enthalpy interval. The values for enthalpies in the heat cascade determine new temperature intervals for Hot and Cold Composite Curves (Fig. 2). Every new determined temperature interval con- tains fragments of hot or cold streams. All those stream’'s fragments form a simple case for Heat Exchanger Network design. Every sub- network has its place in the final solution according to the order of enthalpy intervals in the heat cascade. All designed heat exchangers for all fragmentations were connected together in a series as a final
Stream data used in the example for explanation the design of Heat Exchanger Network with Enthalpy Table Algorithm. Table 1 Table 2 Determined temperature intervals in detected enthalpy intervals (bold values are missing temperatures, calculated with interpolation).
Stream data used in the example for explanation the design of Heat Exchanger Network with Enthalpy Table Algorithm. Table 1 Table 2 Determined temperature intervals in detected enthalpy intervals (bold values are missing temperatures, calculated with interpolation).
temperature point on the Hot Composite Curve. The same way was used in opposite cases with the known breaking point of hot composite curves to determine the temperatures on the cold composite curve. Interpolation and determining of unknown tem- peratures are explained in the section that explains applying this technique.
temperature point on the Hot Composite Curve. The same way was used in opposite cases with the known breaking point of hot composite curves to determine the temperatures on the cold composite curve. Interpolation and determining of unknown tem- peratures are explained in the section that explains applying this technique.
Fig. 2. Hot and cold composite curves with their breaking points (data from stream: given as an example). The data for the simple theoretical example are given in Table 1. The Pinch analysis of the streams’ data were made by using the Problem Table Algorithm and super-targeting without any changes of these techniques, so that part of the calculations are the same for the new technique (Enthalpy Table Algorithm) and the Pinch Design Method. As it was said before, the Pinch Design Method separates the problem of the Heat Exchanger Network design into two separate problems. The design of the Heat Exchanger Network above and below the Pinch point are two problems that remain to be solved separately. In this example, the problem is separated into n problems above the Pinch point and k problems below the Pinch point. The number of n problems is equal to the number of enthalpy intervals above the Pinch point formed by the breaking points on composite curves based on streams' supply and target tempera- tures. Furthermore, the number of enthalpy intervals or the num- ber of problems above the Pinch point is equal to the number of the breaking points with different values and without the Pinch point. Similarly, the number of k problems below the Pinch point corre- sponds with the number of enthalpy intervals below the Pinch point, formed by the breaking points of the Cold Composite Curve and the Hot Composite Curve together (Fig. 2). The total number of problems is the sum of all enthalpy intervals determined by the supply and targeting temperatures of selected streams (Equation (2)). The temperature values for the segments were determined by the breaking points of curves. In any case, if there is a breaking point for the Cold Composite Curve at a certain value of enthalpy, the Hot Composite Curve may not contain the breaking point for the same enthalpy. Because of that, the temperature for the Hot Composite Curve needs to be found with interpolation. Interpola- tion was made as a linear function between two end points (breaking points) of composite curve segments, determined by the temperature's difference and the enthalpy's difference in the certain enthalpy interval. The breaking point of the Cold Composite Curve has the same value for enthalpy in a heat cascade as the
Fig. 2. Hot and cold composite curves with their breaking points (data from stream: given as an example). The data for the simple theoretical example are given in Table 1. The Pinch analysis of the streams’ data were made by using the Problem Table Algorithm and super-targeting without any changes of these techniques, so that part of the calculations are the same for the new technique (Enthalpy Table Algorithm) and the Pinch Design Method. As it was said before, the Pinch Design Method separates the problem of the Heat Exchanger Network design into two separate problems. The design of the Heat Exchanger Network above and below the Pinch point are two problems that remain to be solved separately. In this example, the problem is separated into n problems above the Pinch point and k problems below the Pinch point. The number of n problems is equal to the number of enthalpy intervals above the Pinch point formed by the breaking points on composite curves based on streams' supply and target tempera- tures. Furthermore, the number of enthalpy intervals or the num- ber of problems above the Pinch point is equal to the number of the breaking points with different values and without the Pinch point. Similarly, the number of k problems below the Pinch point corre- sponds with the number of enthalpy intervals below the Pinch point, formed by the breaking points of the Cold Composite Curve and the Hot Composite Curve together (Fig. 2). The total number of problems is the sum of all enthalpy intervals determined by the supply and targeting temperatures of selected streams (Equation (2)). The temperature values for the segments were determined by the breaking points of curves. In any case, if there is a breaking point for the Cold Composite Curve at a certain value of enthalpy, the Hot Composite Curve may not contain the breaking point for the same enthalpy. Because of that, the temperature for the Hot Composite Curve needs to be found with interpolation. Interpola- tion was made as a linear function between two end points (breaking points) of composite curve segments, determined by the temperature's difference and the enthalpy's difference in the certain enthalpy interval. The breaking point of the Cold Composite Curve has the same value for enthalpy in a heat cascade as the
Heat capacity flow rates of energy streams present in temperature intervals. Table 3
Heat capacity flow rates of energy streams present in temperature intervals. Table 3
Process integration parameter values calculated with Pinch analysis. Table 4 missing temperatures (Equation (3)). Every enthalpy interval con- tains a temperature interval for hot streams and a temperature interval for cold streams. So, one enthalpy interval determines two different temperature intervals. The values of enthalpies in a heat cascade for the first enthalpy interval always start with a zero value. The first temperature value at zero enthalpy for cold streams has the supply value of cold utility. The first temperature for hot streams in the first enthalpy interval has the value of the lowest supply temperature of hot streams. The next breaking point of the Hot or Cold Composite Curve gives a known temperature for hot or cold streams. If that temperature is coming from a cold stream's supply or target temperatures, the hot stream's temperature is unknown. In that situation, the first temperature for the cold streams (cold utility supply temperature) and the second temper- ature (the breaking point of the Cold Composite Curve) make the value of heat that they demand. That heat has the same value for hot streams in that enthalpy interval. According to the First Law of Thermodynamics (Equations (3)—(5)), the unknown temperature can be calculated. The value of calculated heat corresponds with the enthalpy difference in the heat cascade. So, the second value for enthalpy would be the cumulative addition of heat to the starting enthalpy with value equal to zero. The procedure occurs in the same manner for all enthalpy intervals. The value of heat was calculated from known temperatures and the sum of the heat ca- pacity flow rates of the streams present in that enthalpy interval (Equation (5)). Temperature and enthalpy intervals are very important for the next step.
Process integration parameter values calculated with Pinch analysis. Table 4 missing temperatures (Equation (3)). Every enthalpy interval con- tains a temperature interval for hot streams and a temperature interval for cold streams. So, one enthalpy interval determines two different temperature intervals. The values of enthalpies in a heat cascade for the first enthalpy interval always start with a zero value. The first temperature value at zero enthalpy for cold streams has the supply value of cold utility. The first temperature for hot streams in the first enthalpy interval has the value of the lowest supply temperature of hot streams. The next breaking point of the Hot or Cold Composite Curve gives a known temperature for hot or cold streams. If that temperature is coming from a cold stream's supply or target temperatures, the hot stream's temperature is unknown. In that situation, the first temperature for the cold streams (cold utility supply temperature) and the second temper- ature (the breaking point of the Cold Composite Curve) make the value of heat that they demand. That heat has the same value for hot streams in that enthalpy interval. According to the First Law of Thermodynamics (Equations (3)—(5)), the unknown temperature can be calculated. The value of calculated heat corresponds with the enthalpy difference in the heat cascade. So, the second value for enthalpy would be the cumulative addition of heat to the starting enthalpy with value equal to zero. The procedure occurs in the same manner for all enthalpy intervals. The value of heat was calculated from known temperatures and the sum of the heat ca- pacity flow rates of the streams present in that enthalpy interval (Equation (5)). Temperature and enthalpy intervals are very important for the next step.
Fig. 3. Composite curves form enthalpy intervals, limited with vertical lines that go through the breaking points. Intersections between vertical lines and composite curve segments determine interpolated temperatures for every enthalpy interval (@ — known temperature points, ll — unknown (interpolated) temperature points).
Fig. 3. Composite curves form enthalpy intervals, limited with vertical lines that go through the breaking points. Intersections between vertical lines and composite curve segments determine interpolated temperatures for every enthalpy interval (@ — known temperature points, ll — unknown (interpolated) temperature points).
Fig. 4. The criterion for serial connection of heat exchangers in the same stream when the direction of Heat Exchanger Network design is from the right-side end to the left-side end; a — grid diagram of sub-network design with an already paired one hot stream with the part of the cold stream. There need to be chosen the way of connection for the next heat exchanger to impair the residue of cold stream and the rest hot stream (-————— non-paired streams or parts of streams); b — case with the criterion that must be satisfied for serial connection of new heat exchanger (HE2) in the cold stream; c — case in which has a violation of the criteria for serial connection of heat exchanger; d — solution of sub- network in case that satisfy the criterion for serial connection; e — solution for sub-network in case of violation of the criteria for serial connection — stream branching.
Fig. 4. The criterion for serial connection of heat exchangers in the same stream when the direction of Heat Exchanger Network design is from the right-side end to the left-side end; a — grid diagram of sub-network design with an already paired one hot stream with the part of the cold stream. There need to be chosen the way of connection for the next heat exchanger to impair the residue of cold stream and the rest hot stream (-————— non-paired streams or parts of streams); b — case with the criterion that must be satisfied for serial connection of new heat exchanger (HE2) in the cold stream; c — case in which has a violation of the criteria for serial connection of heat exchanger; d — solution of sub- network in case that satisfy the criterion for serial connection; e — solution for sub-network in case of violation of the criteria for serial connection — stream branching.
Heat content of energy stream's fragments presented in certain temperature intervals. Table 5
Heat content of energy stream's fragments presented in certain temperature intervals. Table 5
Fig. 5. The criterion for serial connection of heat exchangers in the same stream when the direction of Heat Exchanger Network design is from the right-side end to the left-side end; a — grid diagram of sub-network design with the already paired one cold stream with the part of the hot stream. There need to be chosen the way of connection for the next heat exchanger to impair the residue of hot stream and the rest cold stream (-—-———— non-paired streams or parts of streams); b — case with the criterion that must be satisfied for serial connection of new heat exchanger (HE2) in the hot stream; c — case in which has a violation of the criteria for serial connection of heat exchanger; d — solution of sub- network in case that satisfy the criterion for serial connection; e — solution for sub-network in case of violation of the criteria for serial connection — stream branching. Step 3 is forming a heat load's table (Table 5), based on heat capacity flow rates and temperature differences for each deter- mined temperature interval for the hot and cold streams (Table 3). In both Tables 3 and 5 there were calculated the temperature dif- ferences for every hot and cold temperature interval. Those values were used for calculation of the stream's fragment heat content (Equations (6) and (7)). The enthalpy of the stream's fragment is the product of multiplication between the temperature difference for hot or cold streams and the stream's heat capacity flow rate (Equation (5)). The enthalpies of the fragments are written in col- umns for all four streams. Tables 3 and 5 are divided into two parts, above and below the bolded line. These two parts represent places above and below the Pinch point. In fact, the bold line is the Pinch point and there is no heat load. The last column gives the heat values of its balances between the stream's fractions in the enthalpy interval. The heat balance values are related to the pre- vious assumption for a complete heat transfer of energy from hot streams to cold streams. All balances are zero, except for the top and bottom ones. The heat values in those positions are values of the heating and cooling demand. The hot streams are marked as negative values because they give heat. The sum of all negative and positive values in one balanced enthalpy interval is always zero.
Fig. 5. The criterion for serial connection of heat exchangers in the same stream when the direction of Heat Exchanger Network design is from the right-side end to the left-side end; a — grid diagram of sub-network design with the already paired one cold stream with the part of the hot stream. There need to be chosen the way of connection for the next heat exchanger to impair the residue of hot stream and the rest cold stream (-—-———— non-paired streams or parts of streams); b — case with the criterion that must be satisfied for serial connection of new heat exchanger (HE2) in the hot stream; c — case in which has a violation of the criteria for serial connection of heat exchanger; d — solution of sub- network in case that satisfy the criterion for serial connection; e — solution for sub-network in case of violation of the criteria for serial connection — stream branching. Step 3 is forming a heat load's table (Table 5), based on heat capacity flow rates and temperature differences for each deter- mined temperature interval for the hot and cold streams (Table 3). In both Tables 3 and 5 there were calculated the temperature dif- ferences for every hot and cold temperature interval. Those values were used for calculation of the stream's fragment heat content (Equations (6) and (7)). The enthalpy of the stream's fragment is the product of multiplication between the temperature difference for hot or cold streams and the stream's heat capacity flow rate (Equation (5)). The enthalpies of the fragments are written in col- umns for all four streams. Tables 3 and 5 are divided into two parts, above and below the bolded line. These two parts represent places above and below the Pinch point. In fact, the bold line is the Pinch point and there is no heat load. The last column gives the heat values of its balances between the stream's fractions in the enthalpy interval. The heat balance values are related to the pre- vious assumption for a complete heat transfer of energy from hot streams to cold streams. All balances are zero, except for the top and bottom ones. The heat values in those positions are values of the heating and cooling demand. The hot streams are marked as negative values because they give heat. The sum of all negative and positive values in one balanced enthalpy interval is always zero.
Fig. 6. The direction of Heat Exchanger Network (sub-network) design in case of unbalanced enthalpy intervals; a — left to right direction of design was used in case of cold utility demand; b — right to left direction of design was used in case of hot utility demand.
Fig. 6. The direction of Heat Exchanger Network (sub-network) design in case of unbalanced enthalpy intervals; a — left to right direction of design was used in case of cold utility demand; b — right to left direction of design was used in case of hot utility demand.
Fig. 7. Grid diagram with designs of heat exchanger's networks in separate enthalpy intervals (heat exchangers are connected in series for the same streams into the heat exchanger sub-network, and ordered as the order of enthalpy intervals in the composite curve diagram); b. Grid diagram with designs of heat exchanger's networks in separate enthalpy intervals (heat exchangers are connected with branching of streams into the heat exchanger sub-network, and ordered as the order of enthalpy intervals in the composite curve diagram).
Fig. 7. Grid diagram with designs of heat exchanger's networks in separate enthalpy intervals (heat exchangers are connected in series for the same streams into the heat exchanger sub-network, and ordered as the order of enthalpy intervals in the composite curve diagram); b. Grid diagram with designs of heat exchanger's networks in separate enthalpy intervals (heat exchangers are connected with branching of streams into the heat exchanger sub-network, and ordered as the order of enthalpy intervals in the composite curve diagram).
Fig. 9. Heat Exchanger Network after using of rule for loops through the Pinch point. All designs of heat exchanger's networks designed for all othe enthalpy intervals are presented in Fig. 7a and b. Fig. 7a present: The heat capacity flow of branches in the stream's fragment is determined with Equation (4). Only the value of mass flow will be changed. According to that, heat capacity flow of the stream's fragment is the sum of all heat capacity flows of branches in the stream's fragment (Equation (20))
Fig. 9. Heat Exchanger Network after using of rule for loops through the Pinch point. All designs of heat exchanger's networks designed for all othe enthalpy intervals are presented in Fig. 7a and b. Fig. 7a present: The heat capacity flow of branches in the stream's fragment is determined with Equation (4). Only the value of mass flow will be changed. According to that, heat capacity flow of the stream's fragment is the sum of all heat capacity flows of branches in the stream's fragment (Equation (20))
The results of supertargeting of analyzed case study and values of parameters in designed solutions compared with parameters of designed solutions by using Pinch Design Method and the suggested method (columns with % represent the percent of each parameter for case study results according to the minimal values of these parameters).
The results of supertargeting of analyzed case study and values of parameters in designed solutions compared with parameters of designed solutions by using Pinch Design Method and the suggested method (columns with % represent the percent of each parameter for case study results according to the minimal values of these parameters).
The data of selected process streams for the case study. Table 6
The data of selected process streams for the case study. Table 6
Table of calculated unknown temperatures for all enthalpy intervals and heat capacity flows for stream's fragments in every enthalpy interval (bold numbers are temperatures calculated with interpolation).
Table of calculated unknown temperatures for all enthalpy intervals and heat capacity flows for stream's fragments in every enthalpy interval (bold numbers are temperatures calculated with interpolation).
Table of temperature differences and stream's fragments presence in already determined enthalpy intervals.
Table of temperature differences and stream's fragments presence in already determined enthalpy intervals.
Fig. 10. a. Designs of sub-networks above the Pinch point (enthalpy intervals 3—5) and common relaxed sub-network for enthalpy intervals 6—11; b. Designed sub-networks fo! enthalpy intervals 6—11.
Fig. 10. a. Designs of sub-networks above the Pinch point (enthalpy intervals 3—5) and common relaxed sub-network for enthalpy intervals 6—11; b. Designed sub-networks fo! enthalpy intervals 6—11.
Fig. 11. a. Primary design of Heat Exchanger Network — designs of sub-networks below the Pinch point connected with relaxed sub-networks above the Pinch point; b. The fin. relaxed design of Heat Exchanger Network for the case study.
Fig. 11. a. Primary design of Heat Exchanger Network — designs of sub-networks below the Pinch point connected with relaxed sub-networks above the Pinch point; b. The fin. relaxed design of Heat Exchanger Network for the case study.
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