Upon deciding on process reaction-separation system design, the optimization of major design variables such as reactor conversion, selectivity, recycle inert concentration, etc., minimization of process waste, minimization of utility waste via heat integration, process modifications for the sake of more heat integration has been explored and the plant utility system is configured, the material and energy balance can now be roughly fixed and hence the hot and cold streams which contribute to the heat exchanger network can be identified. The task is then becomes to design the heat exchanger network. In a little elaboration define the HEN streams matching, duty of each heat exchanger inlet and outlet temperatures of each heat exchanger and with given overall heat transfer coefficients calculate the area of each heat exchanger.

**Heat Exchangers Network (HEN) Synthesis**

In the rest of this chapter we will be only defining the topology, duty and temperatures information of the synthesized HEN.

**The Pinch Design Method**

The best design for an energy efficient heat exchange network will often result in a tradeoff between the equipment and operating cost. This is dependent on the choice of the ΔT_min for the process. The lower the ΔT_min chosen, the lower the energy costs, but conversely the higher the heat exchanger capital costs, as lower temperature driving forces in the network will result in the need for greater area.

A large ΔT_min on the other hand will mean increased energy costs due to less overall heat recovery, but the required capital cost will be less. This is true most of the time but not all of the time. Designers may find that a very large ΔT_min might lead to high levels of heat duties available to be handled by process to process heat exchangers and process to utilities ones resulting in high surface area needs and consequently both capital cost and energy cost will be increased.

Early in this chapter we introduced how to set energy targets for the process before considering the HEN design because in the early days of pinch technology this technique was important to help make the trade-off between the HEN capital cost and operating cost quickly and without any heavy calculations. However, nowadays lot of software is available to make a preliminary synthesis of any large size HEN and estimate its capital cost directly and then automatically make the trade-off between the operating cost and the capital cost for the HEN in order to determine the optimal ΔT_min for the HEN to be designed.

Now let us first estimate the minimum number of units in a HEN (N_units) using the following formula: [2]

Nunits = S – 1

Where,

S = number of streams (hot and cold) including utilities

It is important to keep in mind that using the above formula for minimum number of units calculation will only be giving an estimate and in some cases designers can come up with less number of units due to some perfect matches in temperature range and load among hot and cold process streams, for instance.

Having calculated an estimate to HEN minimum number of units we can then use the composite curves again used before to determine the energy targets for a given value of ΔT_min to determine another estimate to the minimum heat transfer area required to achieve the desired energy targets ahead of HEN design.

To calculate the network area from the composite curves, utility streams must be included with the process streams in the composite curves to obtain the balanced composite curves. The resulting balanced composite curves should have no residual demand for utilities. Then, the balanced composite curves are divided into vertical enthalpy intervals to calculate the total minimum area targets assuming constant overall heat transfer coefficient and pure vertical counter current heat transfer [4].

Now we will start the design of the HEN using the well-known pinch design method. A good initialization of this design is to assume that no individual heat exchanger will have a temperature difference smaller than ΔT_min calculated from the targeting phase and there must be no heat transfer across the pinch by process to process heat transfer or/and inappropriate use of utilities.

These rules are important for the HEN design to achieve the energy target, given that no individual exchanger should have a temperature difference smaller than ΔT_min. To comply with these two guidelines the design problem needs to be divided at the pinch and using the grid diagram as shown earlier in this course manual.

*Pinch Design Method*

*Pinch Design Method*

The graph below shows the stream data of a very simple HEN problem drawn on a grid diagram [1,2,3], where the pinch temperature is shown on both the hot and the cold sides using a minimum approach temperature, ΔT_min=10ºC.

The Grid Diagram for the Step-by-Step HEN Design

The example given in this chapter for the illustration of the pinch design method for heat exchangers network design is very simple. Before going through the design of the network for this simple example step-by-step, some important rules in pinch design method need to be mentioned to enable the reader solve more complicated problems.

### Start at the Pinch

The pinch is the most constrained region of the problem. At the pinch, ΔTmin exists

between all the hot and cold streams. As a result, the number of feasible matches in this

region is severely restricted. Quite often there are essential matches to be made. If such matches are not made, the result will be either using a temperature differences smaller than ΔT_min or we have to buy more utilities due to heat transfer across the pinch.

Since the pinch point divides the problem into two sub-problems we are going to solve first the above pinch sub-problem. We need as we said to start at the pinch. There are some rules for matches to be both feasible and efficient for the designated ΔT_min. With feasible we mean that the hot stream shall always have a ΔT_min over the matched cold stream.

We will be elaborating more about feasibility later in this section.

With efficient we mean that a hot stream shall be matched above the pinch at the pinch in a way that he/she reaches its target temperature at the pinch. Hence, we reach the target heating utility calculated beforehand as we shown earlier in part I. Otherwise, we will be forced to buy cold utility above the pinch!! Resulting in more heating and cooling utilities than the ones originally calculated during the energy targeting step.

In order to be able to achieve this requirement, during matching above the pinch we have to have enough number of cold streams above the pinch at the pinch to enable each hot stream above the pinch at the pinch reaches its pinch temperature via matching with a cold process stream. Otherwise, we end up using cold utility above the pinch. If the number of hot stream above the pinch at the pinch is less than the number of cold streams in such situation we can consider splitting cold streams to enable us keep the following two rules intact above the pinch at the pinch.

This rule in pinch design method will be further elaborated in this section.

But for now we need to keep in mind the following two rules for streams matching above the pinch at the pinch:

Number of hot streams above the pinch at the pinch shall be less than or equal to number of cold streams; and

Upon matching hot and cold streams, hot stream CP(FCp) should be less than or equal to the cold stream matched with it (lighter in load) to avoid infeasibility in matching at some point and again to avoid using cold utility above the pinch at the pinch that results in consuming more than originally calculated energy target.

For streams matching below the pinch at the pinch the reverse is true:

Number of cold streams at the pinch shall be less than or equal to number of hot streams; and Upon matching hot and cold streams, cold stream CP(FCp) should be less than or equal to the hot stream matched with it (lighter in load) to avoid infeasibility in matching at some point and again to avoid using cold utility above the pinch at the pinch that results in consuming more than originally needed energy target.

**The CP Inequality for Individual Matches**

In summary, for hot and cold streams matching above the pinch at the if a hot steam with CP(FCp) greater than a CP(FCp) of a cold stream, moving away from the pinch, the temperature difference must increase. At the pinch the, the match starts with a temperature difference equal to selected ΔTmin.

The relative slopes of the temperature-enthalpy profiles of the two streams mean that the temperature differences become smaller while we are moving away from the pinch, which is infeasible. Hence, we should not consider such match. On the other hand if we match this hot stream with another cold stream having a greater CP, in such case the relative slopes of the temperature-enthalpy profiles now cause the temperature differences to become larger moving away from the pinch, which is feasible. Thus, starting with ΔTmin at the pinch, for temperature difference to increase while moving away from the pinch, we have to have this inequality achieved.

CPH <= CPC (Above the pinch for streams at the pinch)

Below the pinch at the pinch the rules are reversed. If a cold stream is matched with a hot that has a smaller CP, in such case steeper slope will result, then the temperature differences become smaller which is infeasible. If the same cold stream is matched with a hot stream with a larger CP different situation will arise. A less steep slope will be obtained resulting in temperature differences that become larger which is feasible. Thus, starting with ΔT_min at the pinch, for temperature difference to increase while we are moving away from the pinch we have to have the following inequality achieved.

CPH >= CPC (below the pinch for streams at the pinch).

Again, in very simple words, below the pinch at the pinch the CP (FCp) of the cold stream shall be less than (lighter in load) or equal the hot stream matched with to enable it reach its pinch target temperature without aid of hot utility below the pinch. Otherwise, the matching will be infeasible and to avoid infeasibility we have to use hot utility below the pinch to enable the cold stream reach its pinch target temperature that results in both heating and cooling utilities increase than originally obtained in the energy targeting step.

**The CP Table**

Identification of the essential matches in the pinch region can be clarified using what we call CP table [5]. In a CP table as is shown in the graphs below, the CP values of the hot and the cold streams at the pinch are listed in descending order.

It is important to note here that the CP inequality constraint applies only when a match is made between two streams that are both at the pinch. Away from the pinch, temperature differences increase and it is no longer essential to obey the CP inequalities.

In conclusion there are some essential matches at the pinch or the region of minimum choice (ROMC) that need to be made around the pinch or the ROMC.

The next task is to design a network that exhibit minimum number of units. In other words, we need to decide how big the matched heat loads would be to minimize the HEN number of units.

**The “tick-off” Heuristic**

Once the matches around the pinch have been chosen to satisfy the criteria for minimum energy, the design should be continued in such a way to keep capital cost to a minimum. One important criterion in the capital cost is the number of units since more heat exchangers mean more skids, instrumentation, space, concrete and so on.

Keeping the number of units at a minimum can be achieved using the “tick-off” heuristic [1,2,3]. To tick off a stream, individual units are made as large as possible. In other words, the smaller of the two heat duties on the streams being matched shall be taken completely.

Cooling water must not be used above the pinch to avoid unwarranted excessive use of utilities, therefore, if there are hot streams above the pinch where the duties are not specified by pinch matches, additional process-to-process matches for more heat recovery shall be explored. Same talking is correct for heating utilities application below the pinch.

**Streams Splitting**

Stream splitting is sometimes necessary to overcome the CP (FCp) constraints mentioned above and/or to avoid using cold utility above the pinch or hot utility below the pinch.

Cooling utilities should not be used above the pinch. It means that all hot streams must be cooled to pinch temperature by heat recovery.

If we have a number of hot streams greater than the number of cold streams (Three hot streams and two cold streams for instance) a problem will then arise. Since regardless of the CP (FCp) values of the streams, there will be one of the hot streams that will not to be cooled to pinch temperature without some violation of the ΔTmin constraint. This problem can only be resolved by splitting a cold stream into two parallel branches. Thus, in addition to the CP criterion, there is a stream number criterion above the pinch such that

Sh<=Sc (above the pinch)

Where:

Sh = number of hot streams at the pinch

Sc = number of cold streams at the pinch

If there had been more cold streams than hot streams in the design above the pinch, this would not have created a problem, since hot utility can be used above the pinch.

Let us now consider the sub-problem below the pinch. Here hot utility must not be used below the pinch. That’ means that all cold streams must be heated to pinch temperature by heat recovery.

Again, for below the pinch, if we have the number of cold streams greater than the number of hot streams (3 cold streams and two hot streams, for instance) regardless of the CP (FCp) values, one of the cold streams cannot be heated to pinch temperature without some violation of the ΔTmin constraint.

The problem can be solved by splitting a hot stream into two parallel branches. In such a case, each cold stream will have a partner with which to match and be capable of heating it to pinch temperature. Thus, there is also a stream number criterion below the pinch such that

Sh<= Sc (below pinch)

If we have more hot streams than cold streams below the pinch, this would not be a problem, since cold utility can be used below the pinch.

It is instructive to mention here that it is not only the stream number that creates the need to split streams at the pinch but also the streams CP (FCp) inequality.

Sometimes the CP (FCp) inequality criteria for the streams above the pinch “at the pinch” and below the pinch “at the pinch” cannot be met at the pinch without a stream split. It is important to emphasize here the need to satisfy both criteria; the stream population and the CP (FCp) inequality.

The number of hot streams above the pinch at the pinch needs to be greater than or equal to the number of cold streams above the pinch at the pinch. If this is not the case then we need to split a hot stream to achieve this guideline.

At the same time, the CP(FCp) of the hot stream above the pinch at the pinch shall be less than or equal to the CP(FCp) of the cold stream above the pinch at the pinch in order to be able to match them in a heat exchanger. If this is not the case, the cold stream needs to be split into two.

On the other hand, the number of cold streams below the pinch at the pinch needs to be smaller than or equal to the number of hot streams above the pinch at the pinch. If this is not the case, then we need to split a hot stream to achieve this guideline.

At the same time, the CP (FCp) of the hot stream below the pinch at the pinch shall be greater than or equal to the CP (FCp) of the cold stream below the pinch at the pinch in order to be able to match them in a heat exchanger. If this is not the case, the cold stream needs to be split into two lighter loads cold streams.

Before closing the pinch design method (PDM) description with its rules and heuristics let us summarize the methodology in a step-by-step fashion.

In summary, the design procedure known as the pinch design method can be summarized as follows:

Divide the problem at the pinch into two separate problems.

The design for the separate problems is started at the region of minimum choice known as the pinch point and then moving away.

Temperature feasibility requires constraints on the CP(FCp) values to be satisfied for matches between streams “at the pinch” for the two problems above the pinch and below the pinch.

The loads on individual heat exchangers are determined using the tick-off heuristic to minimize the number of units.

Away from the pinch there is usually more freedom in the choice of matches. In this case, the designer can choose on the basis of his/her process knowledge.

Having described the pinch design methodology, let us come back now to the numerical example.

The pinch point has divided the problem into two sub-problems one above the pinch and another below the pinch. The division lies at 310ºC on the hot streams side and 300ºC on the cold streams side.

The problem minimum approach temperature used is ΔT_min=10ºC, and the minimum heating and cooling utilities are 2876 kW and 50 kW, respectively.

Using the minimum number of units formula mentioned before we can estimate the network minimum number of units to be 5 units. Now, we will synthesize a feasible HEN that realizes these two targets of specified utilities consumption and number of units.

We will start the design above the pinch at the pinch. Since we have only one possibility at the pinch, we will check the CP (FCp) matching rule. Since H2 has CP (FCp) equal to 5 while C1 has a CP (FCp) equal to 20, the rule is satisfied and we can match H2 and C1. Upon matching H2-C1 we need to tick-off one of the streams to minimize the number of units, and the stream with lower heat load will be ticked-off which is stream H2. The heat exchanger load can now be calculated simply using Q= FCp (Ts-Tt) formula to render Q = 350 kW. The H2 stream has now been cooled to its pinch target temperature of 310ºC and the cold stream C1 has been heated from its pinch temperature at 300ºC to 317.5ºC.

It is instructive to mention hear that H1 and C2 streams can be called “near” pinch streams and in some commercial software another near pinch line will be drawn at 330ºC-320ºC. In such case, two pinch regions will be arising and three sub-problems will be produced. One above the 330ºC-320ºC near pinch; one below the 310ºC-300ºC pinch and a third in between. Handling situations like that is not difficult but less systematic than one pinch point situation [5].

**The Grid Diagram for the Step-by-Step HEN Design**

Away from the pinch there is no systematic technique to complete the HEN. The designer can use his/her common sense to complete the design to each a feasible network, with exact utilities requirements and with minimum number of units.

It is clear that H1 and C2 can also be a good match since H1 can be ticked-off completely, leading to a HEN with the desired minimum number of units estimated earlier for the this example.

The minimum approach temperature between the two streams is not violated,

greater than or equal to the specified ΔT_min=10ºC, is equal to 12.5ºC.

Stream H1 has a heat load of 1900 kW and hence the process to process heat exchange

between H1-C1 match is equal to 1900 kW which is the duty of this heat exchanger.

The Grid Diagram for the Step-by-Step HEN Design