Pinch analysis, also known as process integration, is used to systematically link process streams to reduce energy demand.

Pinch analysis is a system-oriented method with the aim of determining the theoretically minimum possible energy demand for heating and cooling of all processes. The focus here is on holistic optimization under the constraint of minimum investment and operating costs.

A prerequisite for pinch analysis is the presence of **heating AND cooling demand** for one or more processes in the plant. Ideally, the demands are present at the same time, but if not, the use of storage is also possible.

**A pinch analysis is divided into the following steps:**

- recording and analysis of all process flows
- generation of compound curves and determination of the pinch point
- process integration by means of heat exchangers, storage tanks and heat pumps
- verification of technical and economic feasibility

Interestingly, the first step represents the greatest effort in pinch analysis at 60 - 70%. This is mainly due to the fact that data acquisition is difficult to standardize, and the process flows in the companies have to be analyzed individually. In some cases, it is also necessary to retrofit measurement technology so that the data basis for the actual pinch analysis is sufficiently accurate.

In a nutshell: "To save energy and costs!"

In industry, the supply of process heating and cooling accounts for approx. 2/3 of energy consumption. And this causes high costs. In most cases, however, the savings potential is correspondingly high, and this is precisely where pinch analysis comes in. Pinch analysis is a methodology for **determining the maximum energy savings potential** by linking process flows energetically. Hence the alternative name process integration or heat integration for pinch analysis.

In the energetic analysis of an industrial process, different stages can be defined. An energetic optimization should always be done from the inside to the outside, because the outer stages can hardly influence the energy demand of the inner ones. If, for example, the core process already requires an unnecessarily large amount of energy, this cannot be reduced by the energy supply, but merely provided as efficiently as possible.

**Priorities for optimization: **

- core processes
- heat exchanger network
- energy storages
- energy transformation
- utilities / energy supply

Pinch analysis focuses on points 2 to 4 with its methodology. The optimization of the core processes (area of system simulation) is just as little part of pinch analysis as the energy supply (area of structural optimization). Whereby energy conversion and energy supply have certain intersections and here the boundary is not to be drawn quite so clearly.

In principle, the core processes define the energetic demand, and the energy supply defines the energetic costs for the pinch analysis. The energetic savings potential for not yet optimized operations is often in the range of 10 - 40%.

Typical **questions that can be answered with a pinch analysis** are:

- What is the minimum energy requirement of the processes?
- How efficient is the energy supply for the processes?
- How large is the potential for waste heat recovery?
- Is the use of heat pumps, combined heat and power plants and storage systems worthwhile?
- Where is the economic optimum in terms of investment and operating costs?
- How can this optimum be achieved?

If these or similar issues have ever arisen at your company, then pinch analysis may be the right methodology for you.

The best way to explain the pinch analysis procedure is to give an example. Therefore, we will look at the process of milk pasteurization in the following. By the way, this beautiful example comes from the PinCH course at HSLU, which I highly recommend.

For pasteurization the raw milk must be heated from 15°C to 95°C and then cooled to 5°C. For simplicity, we assume that the process is continuous. We therefore have a simultaneous heating and cooling requirement, the prerequisite for any heat integration.

For the analysis of the process streams, we also need the heat capacity rate in addition to the temperatures. This is simply the product of the mass flow and the specific heat capacity of the process stream. For our example we assume a mass flow of 2 kg/s and a heat capacity of 4 kJ/kg.K.

This results in a necessary heat flow for the cold process stream of

$$\dot{Q}_{\rm H} = \dot{m}c_p(T_{\rm out}-T_{\rm in}) = 640\,{\rm kW}$$

And for the hot process stream analogously a necessary cooling power of

$$\dot{Q}_{\rm C} = 2 \cdot 4 \cdot (5 - 95)\,{\rm kW} = - 720\,{\rm kW}$$

Thus, for the simple case where no heat recovery is used, a heating supply (hot utility) with a capacity of 640 kW and a cooling supply (cold utility) with a capacity of 720 kW are required.

For the evaluation and process integration of the flows, it is useful to represent them in a temperature-heat flow diagram (T-Q diagram). For the simple case of pasteurization without heat recovery, the following picture results:

On the left, the hot process stream to be cooled is shown in red, and on the right, the cold process stream to be heated is shown in blue. The necessary heat flow can be read directly on the x-axis and the temperature change on the y-axis.

The slope of the curves is inversely proportional to the** heat capacity rate** \(\sim 1/{\dot{m}c_p}\), i.e. the flatter the curves are, the more heat is required for the temperature change. In case of a phase change (e.g. evaporation and condensation) the curves would be horizontal. In our example, the heat capacity flows for both processes are the same and accordingly the slope of both curves is identical.

Integration or linking of the process streams can be done via various apparatuses, with heat exchangers being the simplest and the basis of any pinch analysis. Other possibilities are thermal storage and heat pumps.

A heat exchanger always transfers heat from the warmer to the colder process stream. If the two process curves in the T-Q diagram are now shifted horizontally against each other, they will partially overlap on the x-axis. It is important to ensure that the cold curve always remains below the hot curve.

In the diagram, you can now directly read the **possible heat recovery** and **temperature difference** for heat transfer. In the example, the curve has been shifted so that a temperature difference of 20 K results, and this for the entire heat transfer range, since the slope of the curves is the same. The theoretically maximum possible heat recovery would result for a temperature difference of 0 K.

The theoretical maximum of the pinch analysis thus states that a total of 640 kW can be recovered and accordingly only a cooling capacity of 80 kW would be required. Unfortunately, this is not possible in practice, since infinitely large heat exchangers are required for this.

But where is the pinch point in this analysis? The **pinch point** is the point in the diagram with the smallest distance between the hot and cold process curves. So in our case there is no pinch point at all, but a pinch region due to the same slope. In the following, however, we will also get to know a real pinch point.

For more complex processes or a large number of different processes, all hot and cold streams can be combined into a composite curve. These composite curves reflect the total cooling and heating requirements.

The streams are combined according to the **superposition principle**. The principle is explained here using a simple example with two cold streams. However, it can also be extended to any number of streams. The streams are combined by adding the heat flows in the **same temperature interval**. The resulting curve thus becomes flatter in this temperature range, reflecting the increased heat demand. The remaining curve segments remain unchanged. All segments together form the composite curve.

The two compound curves of a system can now be moved against each other again until they touch. The point of contact is the so-called **pinch point**, in some simple cases a pinch region also results for compound curves as in the previous example.

Based on the composite curves in the **T-Q diagram**, some **basic statements** can be made about the system at hand.

- To the left of the pinch point there is a heat surplus, i.e. there is more "transferable" heat in the total warm process stream than is needed to heat the cold stream.
- The excess heat to the left of the pinch point cannot be used by heat transfer but must be cooled by means of external cold utilities.
- To the right of the pinch point, on the other hand, there is a heat deficit, i.e. more heat is required than can be provided by the hot stream.
- The remaining heat demand of the cold composite curve must be heated accordingly by means of external heat utilities.
- The overlapping area of the curves reflects the maximum possible heat recovery.

When planning the heat exchanger network to integrate the process streams, the following rules result from this.

**The 3 main rules of pinch analysis:**

- external heat supply only above the pinch (because the subsystem above the pinch has a heat deficit).
- external heat rejection only below the pinch (because the subsystem below the pinch has a heat surplus).
- no heat transfer across the pinch (otherwise this heat is missing above the pinch and increases the heat deficit).

These rules also help in the analysis of an existing network. If you find that one of these rules (e.g. transferring heat across the pinch point) is violated, this should be questioned.

It is not necessarily wrong if the pinch rules are disregarded in practice. There are often technical limitations that make this necessary. The pinch analysis only provides the theoretically possible potential for heat integration.

However, in practice there are also numerous cases in which a great deal of energy and money can be saved by taking the pinch rules into account. A simple comparison of the minimum heating and cooling requirements from the pinch analysis with the actual energy consumption of the plant shows the possible savings potential here. In order to estimate the reasonably usable potential, an economic, technical analysis should be carried out following the process flow analysis.

In the above examples, the **minimum temperature difference** \(\Delta T_{\rm min}\) at the pinch point has either been set arbitrarily or the maximum potential has been determined at the difference of 0 K.

In reality, however, the minimum temperature difference \(\Delta T_{\rm min}\) is determined by the **costs of the heat exchangers**. The smaller the temperature difference, the larger the heat exchangers have to be and the implementation is correspondingly expensive.

If you consider not only the energy in the pinch analysis, but also the costs for the heat exchangers and heat supply, you speak of so-called super-targeting. **Super-targeting** provides the optimal \(\Delta T_{\rm min}\) such that the total costs for investment and operation are minimal.

Even with simple systems, super-targeting can be very costly, so that the use of software quickly pays off. For this purpose, we use PinCH from the HSLU, which offers a complete tool chain ( acquisition of the process streams, design of the heat exchanger network, economic efficiency consideration) for the pinch analysis.

The minimum temperature difference \(\Delta T_{\rm min}\) has a direct influence on the heat recovery potential and the need for external energy supply.

- The smaller \(\Delta T_{\rm min}\) the higher the potential for heat recovery. This means lower operating costs in energy supply, but higher investment costs.
- The larger \(\Delta T_{\rm min}\) the lower the potential for heat recovery. This means high operating costs in energy supply, but low investment costs

In addition to these economic constraints, there are a large number of** technical conditions** that must be checked and complied with:

- Location: what is the distance between the process streams? Is there enough space to install heat exchangers?
- Process requirements: Are there regulations in process control, e.g. for sensitive or pharmaceutical products?
- Safety: Can process streams react with each other in case of leakage?
- Flexibility: Are start-up and shut-down processes guaranteed? How variable can the production process still be run?

This list is certainly not exhaustive and shows that, in addition to the systematic approach to pinch analysis in individual cases, engineering know-how is always necessary for meaningful plant optimization.