INTRODUCTION:
The term “Pinch Technology” was introduced by Linnhoff and Vredeveld to represent a new set of thermodynamically based methods that guarantee optimum energy requirements in design of heat exchanger networks. The application of Pinch technology to study industrial process is called Pinch Analysis.
Applying first and second Laws of thermodynamics is essential in Pinch Analysis method. The first law of thermodynamics enables us to use the energy equations in order to calculate the enthalpy change in the streams passing through heat exchangers and the second law decides the direction of heat flow because according to second law heat may only flow in the direction from hot to cold regions but there conditions in heat transfer in heat exchanger like:
1) No temperature crossover should be done: since in a heat exchanger, a hot stream can’t be cool down below the cold stream inlet temperature nor the cold stream can be heated up above the hot stream temperature.
2) In reality the hot stream can be cooled down to a temperature defined by the ‘temperature approach’ of the heat exchanger. The temperature approach is the minimum allowable temperature difference (DTmin) in the stream temperature profiles. The temperature level at which DTmin is observed in the process is referred to as “pinch point”.
Pinch Analysis
There are 8 steps in pinch analysis which are:

Steps of Pinch Analysis

Identification of the Hot, Cold and Utility Streams in the Process

Thermal Data Extraction for Process & Utility Streams

Selection of Initial DTmin value

Construction of Composite Curves and Grand Composite Curve

Estimation of Minimum Energy Cost Targets

Estimation of Heat Exchanger Network ( HEN ) Capital Cost Targets

Estimation of Optimum DTmin Value by Energy-Capital Trade Off

Design of Heat Exchanger Network

1. Identification of the Hot, Cold and Utility Streams in the Process
* ‘Hot Streams’: Hot streams that are required to be cooled down.
* ‘Cold Streams’: Cold streams that are required to be heated up.
* ‘Utility Streams’ are used to heat or cool process streams, when heat exchange between process streams is not practical or economic.
2. Thermal Data Extraction for Process & Utility Streams
For each hot, cold and utility stream identified, the following thermal data is extracted:
* Supply temperature (TS oC) : the temperature at which the stream is available.
* Target temperature (TT oC) : the temperature the stream must be taken to.
* Heat capacity flow rate (CP kW/ oC) : the product of flow rate (m) in kg/sec and specific heat (Cp kJ/kg 0C).
CP = m x Cp
* Enthalpy Change (dH) associated with a stream passing through the exchanger is given by the First Law of Thermodynamics:
First Law energy equation: d H = Q ± W
In a heat exchanger, no mechanical work is being performed:
W = 0 (zero)
The above equation simplifies to: d H = Q, where Q represents the heat supply or demand associated with the stream. It is given by the relationship: Q= CP x (TS – TT).
Enthalpy Change, dH = CP x (TS – TT)
3. Selection of Initial DTmin value
As discussed before and according to second law of thermodynamics no temperature crossover can be done. Thus the temperature of the hot and cold streams at any point in the exchanger must always have a minimum temperature difference (DTmin).
In mathematical terms, at any point in the exchanger
Hot stream Temp. ( TH ) – ( TC ) Cold stream Temp. >= DTmin
For a given value of Q, if smaller values of DTmin are chosen, the area requirements rise. If a higher value of DTmin is selected the heat exchange between the exchangers will decrease and the use of utilities will increase. Thus, the selection of DTmin value has an imprtants and significant implications for both capital and energy costs.
This table shows a typical DTmin of some industrial processes:

No

Industrial Sector

Experience DTmin Values

1

Oil Refining

20-40°C

2

Petrochemical

10-20°C

3

Chemical

10-20°C

4

Low Temperature Processes

3-5°C

4. Construction of Composite Curves and Grand Composite Curve
* COMPOSITE CURVES: Composite curves consist of temperature (T) – enthalpy (H) profiles of heat availability in the process (the hot composite curve) and heat demands in the process (the cold composite curve) together in a graphical representation.
To construct the composite curve, a stream with a constant heat capacity (CP) is represented on a T – H diagram by a straight line running from stream supply temperature to stream target temperature. When there are a number of hot and cold streams, the construction of hot and cold composite curves simply involves the addition of the enthalpy changes of the streams in the respective temperature intervals.

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For heat exchange to occur, the hot stream cooling curve must lie above the cold stream-heating curve. This point of minimum temperature difference represents a bottleneck in heat recovery and is commonly referred to as the “Pinch” which is DTmin. Increasing the DTmin value results in shifting the curves horizontally apart resulting in lower process to process heat exchange and higher utility requirements.
In summary, the composite curves provide overall energy targets but do not clearly indicate how much energy must be supplied by different utility levels. The utility mix is determined by the Grand Composite Curve.
GRAND COMPOSITE CURVE (GCC):
In selecting utilities to be used, determining utility temperatures, and deciding on utility requirements the Composite curve doesn’t provide so much information, that’s why Grand Composite Curve (GCC) is used. The GCC (Figure 3) shows the variation of heat supply and demand within the process.Using this diagramthe designer canfind which utilities are to be used. The aim is to maximize the use of the cheaper utility levels and minimize the use of the expensive utility levels. Low-pressure steam and cooling water are preferred instead of high-pressure steam and refrigeration, respectively.
To construct GCC the information required comes directly from the Problem Table Algorithm. The method involves shifting (along the temperature [Y] axis) of the hot composite curve down by ½ DTmin and that of cold composite curve up by ½ DTmin. The vertical axis on the shifted composite curves shows processinterval temperature. In other words, the curves are shifted by subtracting part of the allowable temperature approach from the hot stream temperatures and adding the remaining part of the allowable temperature approach to the cold stream temperatures. The result is a scale based upon process temperature having an allowance for temperature approach (DTmin). The Grand Composite Curve is then constructed from the enthalpy (horizontal) differences between the shifted composite curves at different temperatures. On the GCC, the horizontal distance separating the curve from the vertical axis at the top of the temperature scale shows the overall hot utility consumption of the process.
The utility can be divided into many temperatures. The GCC indicates that we can supply the hot utility over two temperature levels TH1 (HP steam) and TH2 (LP steam). Recall that, when placing utilities in the GCC, intervals, and not actual utility temperatures, should be used. The total minimum hot utility requirement remains the same: QHmin = H1 (HP steam) + H2 (LP steam). Similarly, QCmin = C1 (Refrigerant) +C2 (CW). The points TH2 and TC2 where the H2 and C2 levels touch the grand composite curve are called the “Utility Pinches.” The shaded green pockets represent the process-to-process heat exchange.
5. Estimation of Minimum Energy Cost Targets
Once the DTmin is chosen, minimum hot and cold utility requirements can be evaluated from the composite curves.
If the unit cost of each utility is known, the total energy cost can be calculated using the energy equation given below.
6. Estimation of Heat Exchanger Network (HEN) Capital Cost Targets
The capital cost of a heat exchanger network is dependent upon three factors:
1. The number of exchangers.
2. The overall network area.
3. The distribution of area between the exchangers.
* AREA TARGETING:
To calculate the HEN minimum total area Amin ,divide the composite curve into a set of adjoining enthalpy intervals such that within each interval, the hot and cold composite curves do not change slope. The total area of the HEN (Amin) is given by the formula below, where i denotes the ith enthalpy and interval j denotes the jth stream and dTLM denotes LMTD in the ith interval.
NUMBER OF UNITS TARGETING:
For the minimum number of heat exchanger units (Nmin) required for MER (minimum energy requirement or maximum energy recovery). The minimum number of units (NminMER) is the sum of the targets evaluated both above and below the pinch separately.
NminMER=[Nh+Nc+Nu-1]AP +[Nh+Nc+Nu-1]BP
Where :

Nh = Number of hot streams

Nc=Number of cold streams

Nu = Number of utility streams

AP / BP : Above / Below Pinch

HEN TOTAL CAPITAL COST TARGETING:
HEN capital cost (CHEN) is the capital cost is annualized using an annualization factor that takes into account interest payments on borrowed capital. The equation used for calculating the total capital cost and exchanger cost law is given below.
C($) HEN=[Nmin{a+b(Amin/Nmin)c}]AP +[Nmin{a+b(Amin/Nmin)c}]BP
Where a, b, and c are constants in exchanger cost law
For the Exchanger Cost Equation shown above, typical values for a carbon steel shell and tube exchanger would be a = 16,000, b = 3,200, and c = 0.7.
7. Estimation of Optimum DTmin Value by Energy-Capital Trade Off
To select an optimum DTmin value, plot the total annual cost which is the sum of total annual energy and capital cost versus values of DTmin.
After plotting three important key features can be concluede:
1. If DTmin increases, the energy costs will increase but capital costs will decrease.
2. If DTmin decreases,t he energy costs will decrease but capital costs will increase.
3. Theoptimum DTmin is where the total annual cost of energy and capital costs is minimized.
8. Design of Heat Exchanger Network
In designing the heat exchanger network it is essential to know which hot stream match which cold stream. Every match brings one stream to it target temperature. As mentioned before the pinch point divides the network into two separate regions, and each region is designed separeatley.When the heat recovery is maximized the remaining thermal needs must be supplied by the utilities.
The graphical method of representing flow streams and heat recovery matches is called a ‘grid diagram’ .
All the cold (blue lines) and hot (red line) streams are represented by horizontal lines. The entrance and exit temperatures are shown at either end. The vertical line in the middle represents the pinch temperature. The circles represent heat exchangers. Unconnected circles represent exchangers using utility heating and cooling.
To design the network and construct the grid diagram we use the “CP Inequality Rule” which states that the heat capacity flow-rate (CP) of the stream leaving the pinch needs to be greater than the CP of stream approaching the pinch, or CPout ≥ CPin
So above the pinch: CPhot ≤ CPcold
And Below the pinch: CPhot ≥ CPcold
After making all the possible matches above and under the pinch separately, the two designs are then brought together and usually refined to further minimize the capital cost. After the network has been designed according to the pinch rules, it can be further subjected to energy optimization.