*2.3. Step 3: Construct the Grid Diagram (GD)*

The nominal maximum energy recovery (MER) network is designed using the pinch design method by Linnhoff and Flower [25] and drawn on the grid diagram (GD) shown in Figure 2. Based on the feasibility criteria proposed by Linnhoff and Hindmarsh [27], streams matching above the pinch have to meet the criterion of CPCOLD ≥ CPHOT and streams matching below the pinch have to meet the criterion of CPHOT ≥ CPCOLD, at the pinch location. Equations (1) and (2) are used to determine the enthalpy balances for hot and cold streams.

$$\mathbf{Q\_{HE,hot}} = \mathbf{FCp\_{hot}} \cdot (\mathbf{T\_{hot,in}} - \mathbf{T\_{hot,out}}) \tag{1}$$

$$\mathbf{Q\_{HE,cold}} = \mathbf{FCp\_{cold}} \cdot (\mathbf{T\_{cold,in}} - \mathbf{T\_{cold,out}}) \tag{2}$$

**Figure 2.** Maximum energy recovery (MER) heat exchanger network (HEN) design for the nominal case.

#### *2.4. Step 4: Manage Fluctuating Ts (Ts Disturbances) in HEN to Achieve MER*

The steps to manage fluctuating TS in HEN to achieve Tt and MER can be defined in three stages. The first stage describes the effect of increasing or decreasing TS on the hot and cold streams energy requirement. The second stage provides the fundamental theory of the plus-minus principle. The final stage explains the effect of TS fluctuation on utilities based on the plus-minus principle. Heuristics are proposed for each disturbance scenario that necessitates bypass placement and valve opening, as well as the correct heat exchanger sizing to maximise utility savings.

### 2.4.1. Effect of Increasing or Decreasing TS on Hot and Cold Streams

Figure 3 shows the effect of increasing or decreasing TS for a hot stream. The target temperature, Tt is assumed to be maintained. An example of this situation is a fluctuating reactor exit temperature. Before the stream enters the next unit operation, the Tt should be maintained at the setpoint value. From Figure 3, it can be seen that increasing TS for hot stream results in an increase in enthalpy, ΔH, while decreasing TS results in a decrease in ΔH.

**Figure 3.** Effect of increasing or decreasing supply temperature (TS) on a hot stream.

On the other hand, Figure 4 shows the effect of increasing or decreasing TS on a cold stream. From the figure, it can be seen that an increase in TS results in an increase in ΔH while a decrease in TS results in a decrease in ΔH. The target temperature, Tt is also assumed to be maintained. An example of this situation is a feed stream coming from a storage tank experiencing temperature fluctuations due to changes in ambient conditions as a result of weather changes in a four-season country.

**Figure 4.** Effect of increasing or decreasing TS on a cold stream.

#### 2.4.2. The Plus-Minus Principle Concept

Figure 5 shows the effect of plus-minus principle on composite curves (CC), as explained by Linnhoff and Vredeveld [22]. Above the pinch, increasing the enthalpy of a hot stream and decreasing the enthalpy of a cold stream decreases the minimum hot utility target, QH,min. Doing the reverse above the pinch increases QH,min. Below the pinch, increasing the enthalpy of a cold stream and decreasing the enthalpy of a hot stream decreases the minimum cold utility target, QC,min. Doing the reverse below the pinch increases QC,min.

**Figure 5.** The plus-minus principle (amended from [22]).

#### 2.4.3. Control Mechanism Decision by Using the Plus-Minus Principle

The plus-minus principle can be used to describe the effect of disturbances on HEN operation, and how HEN can be controlled. As shown in Step 4(i), the increase or decrease in supply temperature, TS of the hot or cold stream results in an increase in either QH or QC; or a decrease in QH or QC. For effective control of Tt, utility units such as heaters and coolers have been widely used in process plants. Utility heaters/coolers are typically placed after a series of heat exchangers to supplement stream heating or cooling. A bypass, on the other hand, functions as a mechanism for controlling process stream parameters including for disturbance rejection.

A bypass placed on the hot stream side can be described using Equation (3) while a bypass placed on the cold stream side can be described using Equation (4) [28]. Th <sup>t</sup> represents the target temperature of the heat exchanger at hot the stream side, T<sup>c</sup> <sup>t</sup> represents the target temperature of the heat exchanger at a cold stream side; T<sup>h</sup> <sup>o</sup> represents the outlet temperature of the heat exchanger at hot stream side, T<sup>c</sup> o

represents the outlet temperature of the heat exchanger at a cold stream side; T<sup>h</sup> <sup>s</sup> represents the supply temperature of the heat exchanger at hot stream side, T<sup>c</sup> <sup>s</sup> represents the supply temperature of heat exchanger at a cold stream side; ub represents the bypass fraction; u<sup>h</sup> represents the stream fraction at hot stream side, u<sup>c</sup> represents the stream fraction at cold stream side. Application of Equations (1) and (2) is explained next, in the context of heuristics development.

$$\mathbf{T}\_{\mathbf{t}}^{\mathbf{h}} = \left(\mathbf{1} - \mathbf{u}^{\mathbf{h}}\right) \mathbf{T}\_{\mathbf{o}}^{\mathbf{h}} + \mathbf{u}^{\mathbf{b}} \mathbf{T}\_{\mathbf{s}}^{\mathbf{h}} \tag{3}$$

$$\mathbf{T}\_{\rm t}^{\rm c} = (\mathbf{1} - \mathbf{u}^{\rm c}) \mathbf{T}\_{\rm o}^{\rm c} + \mathbf{u}^{\rm b} \mathbf{T}\_{\rm s}^{\rm c} \tag{4}$$

New heuristics have been introduced in this work as guides for the appropriate placement of a bypass and sizing of the heat exchanger that can reduce hot and cold utilities in cases with recurring Ts disturbances. Each proposed heuristic shall refer to the plus-minus principle of process changes. Applicability of the heuristics is explained using a case study.

Below the pinch:

**Observation 1.** Decreasing TS for a hot or cold stream below the pinch results in decreasing QC. The first observation states that decreasing Ts for a hot or cold stream located below the pinch results in QC decreasing. For example, the TS of cold stream C1 decreases from 40 ◦C to 35 ◦C. As shown in Figure 4, decreasing TS on cold stream C1 increases C1 enthalpy by 15 MW. Based on the plus-minus principle, since stream C1 is located below the pinch, it can be used to recover more energy. This results in a reduction of CU2 cold utility from 180 MW to 165 MW, which is desirable. In order to control the target temperature of stream C1 at 220 ◦C, the C1 flowrate entering HE5 is selected as a manipulated variable. The duty of HE5 is increased from 20 MW to 35 MW to allow more heat to be exchanged. To be able to do this, HE5 should be designed with a bigger area to accommodate up to 35 MW heat duty.

**Observation 2.** Below the pinch, the point where QC equals zero is the limit for hot or cold stream TS to decrease. Further decrease in Ts leads to a penalty in QH.

It is observed that there exists a limit for TS to decrease for the hot or cold stream below the pinch, i.e., at the point of zero Qc. Any additional decrease in TS for hot or cold stream leads to a penalty of QH. Figure 6a,b illustrate Observation 2 involving the disturbance scenario for HE4. It can be seen for the case that when Ts of stream H2 decrease, the enthalpy decrease exceeds the MER of cold stream C1, leading to a penalty of hot utility (see Figure 6b). This situation is also illustrated using the plus-minus principle shown in Figure 7. Moreover, decreasing TS for the hot stream at the pinch point or where the heat exchanger inlet has ΔT = ΔTmin also incurs a penalty at the other side stream. However, in this case, cold stream C1 does not end at the pinch and the difference of temperature between TS,H2 and Tt,C1 is 25 ◦C, which is more than Tmin.

**Figure 6.** *Cont.*

**Figure 6.** (**a**) HEN design with nominal TS for hot stream H2; (**b**) HEN design with TS decrease by 5 ◦C for hot stream H2.

**Observation 3.** Increasing TS for a hot or cold stream below the pinch results in increasing QC.

Based on this third observation, increasing TS for a hot or cold stream located below the pinch causes QC to increase. To illustrate this, consider an increase in TS for the cold stream C1 from 40 ◦C to 45 ◦C due to a disturbance. Figure 4 shows that the increase in TS for the C1 resulted in the enthalpy for C1 decreasing by 15 MW. Since the Ts of stream C1 is located below the pinch, based on the plus-minus principle, the increase in Ts resulted in an increase in CU2 from 180 MW to 195 MW as shown in Figure 8. For this scenario, the bypass stream is selected as the manipulated variable as this deviation means the heat duty of heat exchanger HE5 is not high enough to keep the Tt at 220 ◦C. Equation (2) is used to calculate the bypass fraction for the bypass placed on the cold streamside. In this scenario, supply temperature, T<sup>c</sup> <sup>s</sup> of HE5 at the cold stream side is 45 ◦C. The decreasing of the heat duty of

HE 5 from 20 MW to 5MW caused the target temperature of HE5 at cold stream side, T<sup>c</sup> <sup>t</sup> increased to 46.667 ◦C. As the outlet temperature, T<sup>c</sup> <sup>o</sup> of HE5 with maximum duty at cold stream C1 is 56.667 ◦C, the bypass is placed on the cold stream side. Now the valve is opened at a bypass fraction, u<sup>b</sup> HE5 of 0.857. The bypass is calculated by rearranging Equation (2). As the heat duty of heat exchanger HE5 is not high enough to achieve the final target temperature of H3, the cold utility of cooler C2 is increased to absorb the remaining heat.

Tc <sup>t</sup> = 46.667 ◦C; Tc <sup>o</sup> = 56.667 ◦C; T<sup>c</sup> <sup>s</sup> = 45 ◦C Rearranged Equation (2) to gain the value of u<sup>b</sup> and uc, Tc <sup>t</sup> = - <sup>1</sup> − ub Tc <sup>o</sup> + ubTc s ub = 0.857; u<sup>c</sup> = 0.143

**Figure 8.** HEN design with TS increased for cold stream below the pinch.

**Observation 4.** Below the pinch, size the heat exchanger to achieve the maximum energy recovery target when TS decreases, and the cooler to achieve the higher utility when Ts increases.

Observation 4 states that the heat exchanger size below the pinch should be designed to achieve the maximum energy recovery when TS decreases and the cooler size should be designed to achieve the higher utility when Ts increases. Previously, the impact of the increase or decrease of Ts on cold stream C1 was shown. In the case of decreasing Ts, more heat is allowed to be exchanged. It is preferable to design HE5 with a bigger area to accommodate up to at 35 MW heat duty instead of 20 MW heat duty for the nominal case. CU2 cold utility should also be designed with the duty of 195 MW instead of the nominal case with the duty of 180 MW in order to absorb the remaining heat when Ts increases. Figure 9a–c illustrate this situation by using the plus-minus principle. The bypass stream is used to control the duty of HE5 during the disturbances as shown in Figure 10a–c, while the CU2 cold utility is used to absorb the remaining heat.

Above the pinch:

**Observation 5.** Increasing TS for a hot or cold stream above the pinch results in decreasing QH.

Observation 5 states that, increasing TS for hot or cold stream located below the pinch results in QH decreasing. For example, TS of hot stream H1 increases from 310 ◦C to 315 ◦C. As shown in Figure 3, the increasing TS on hot stream H1 increases H1 enthalpy by 15 MW. Based on the plus-minus principle, since stream H1 is located above the pinch, it can be used to recover more energy. This would result in a reduction of HU1 hot utility from 130 MW to 115 MW, which is desirable (as shown in Figure 11. In order to control the target temperature of stream H1 at 270 ◦C, the H1 flowrate entering HE2 is selected as a manipulated variable. The duty of HE2 is increased from 120 MW to 135 MW to allow more heat to be exchanged. In order to attain it, HE2 should be designed with a bigger area to accommodate up to 135 MW heat duty.

(b)

**Figure 9.** *Cont.*

(c)

**Figure 9.** (**a**) The plus-minus principle with TS decreased by 5 ◦C for C1; (**b**) the plus-minus principle of nominal TS for C1; (**c**) The plus-minus principle with TS increased by 5 ◦C for C1.

**Figure 10.** *Cont.*

**Figure 10.** (**a**) HEN design with TS decreased by 5 ◦C for C1. HE5 is designed with a bigger area to accommodate up to 35 MW heat duty; (**b**) HEN design with nominal TS for C1. HE5 is designed with a bigger area and heat duty at 20 MW; (**c**) HEN design with TS increased by 5 ◦C for C1. HE5 is designed with a bigger size and heat duty at 5 MW.

(c)

**Observation 6.** Above the pinch, the point where QH equals zero is the limit for hot or cold stream TS to increase. Further increases in TS lead to a penalty of QC.

As explained in Observation 2, the same situation can also occur above the pinch. There is a limit for TS to increase for hot or cold streams above the pinch, i.e., at the point of zero QH. Further increases in TS for the hot or cold stream lead to a penalty of QC. Besides that, increasing TS for the hot stream at the pinch or where the heat exchanger inlet has ΔT = ΔTmin also leads to a penalty at the other side stream. Figure 12 shows that TS increases for cold stream C3 from 240 ◦C to 245 ◦C. The nominal value of TS on cold stream C3 and the outlet temperature of HE1 on the hot stream side is at the pinch temperature. The ΔT of HE1 decrease to 5 ◦C, which is less than the original ΔTmin of 10 ◦C. This cause the enthalpy of cold stream C3 reduced to 385 MW. HE1 with the duty of 100 MW

led the hot utility HU2 minimised to 285 MW (see Figure 12). This situation is also illustrated by the plus-minus principle shown in Figure 13a,b. Figure 13a shows the nominal temperature of stream C3 matching with stream H3 with ΔTmin of 10 ◦C. Figure 13b shows that, increasing of TS on cold stream results in ΔT less than ΔTmin.

**Figure 11.** HEN design with increasing TS for the hot stream H1 above the pinch.

**Figure 12.** HEN design with increasing TS for cold stream at the pinch.

**Observation 7.** Decreasing TS for a hot or cold stream above the pinch results in increasing QH. As stated in observation 7, decreasing TS for hot or cold stream located above the pinch causes QH to increase. To illustrate this, consider a decrease in TS for the hot stream H1 from 310 ◦C to 305 ◦C. Figure 3 shows that the decrease in TS for the H1 resulted in the enthalpy for H1 to decrease by 15 MW. Since the TS of stream H1 is located above the pinch, based on the plus-minus principle, the decrease in TS resulted in an increase in hot utility HU1 from 130 MW to 145 MW as shown in Figure 14. For this scenario, the bypass stream is selected as a manipulated variable as this deviation means the heat duty of heat exchanger HE2 is not high enough to keep the target temperature at 270 ◦C. Equation (1) is used to calculate the bypass fraction for the bypass placed on the hot streamside. In this scenario, the supply temperature, T<sup>h</sup> <sup>s</sup> of HE2 at the hot stream side is 305 ◦C. The decrease in heat duty of HE2 from 120 MW to 105 MW caused the target temperature of heat exchanger HE2 at hot stream side, Th <sup>t</sup> to decrease to 270 ◦C. As the outlet temperature, Th <sup>o</sup> of HE2 with maximum duty at hot stream H1 is 260 ◦C, the bypass is placed on the hot stream side. Then, the valve is opened at a bypass fraction, ub HE2 of 0.286. The bypass is calculated by rearranging Equation (1). As the heat duty of heat exchanger HE2 is not high enough to achieve the final target temperature of C2, the hot utility of heater HU1 is increased in order to satisfy the remaining heat.

Th <sup>t</sup> = 270 ◦C; T<sup>h</sup> <sup>o</sup> = 260 ◦C; Th <sup>s</sup> = 305 ◦C Rearranged Equation (1) to gain the value of u<sup>b</sup> and uc, Th <sup>t</sup> = - <sup>1</sup> − ub Th <sup>o</sup> + ubTh s ub = 0.222; u<sup>h</sup> = 0.778

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**Figure 13.** (**a**) The plus-minus principle of nominal TS for cold stream at the pinch with Tmin = 10 ◦C; (**b**) The plus-minus principle of infeasible matching with increasing TS for the cold stream at the pinch.

**Figure 14.** HEN design with TS decreased for hot stream H1 above the pinch.

**Observation 8.** Above the pinch, size the heat exchanger to achieve the maximum energy recovery when TS increase, and the heater to achieve the minimum utility when TS decrease.

Observation 8 states that the heat exchanger size above the pinch should be designed to achieve the maximum energy recovery when TS increases, and the heater size should be designed to achieve the higher utility when TS decreases. Previously, the impact of increase or decrease in Ts on hot stream H1 was shown. In the case of increasing Ts, more heat is allowed to be exchanged. It is preferable to design HE2 with a bigger area to accommodate up to 135 MW heat duty instead of 120 MW for the nominal case. HU1 hot utility should also be designed with the bigger capacity of 145 MW heat duty instead of the nominal case of 130 MW, in order to cater for the remaining heat when TS decreases. Figure 15a–c illustrate this situation by using the plus-minus principle. The bypass stream is used to control the duty of HE2 when a disturbance occurs as shown in Figure 16a–c, while HU1 hot utility is used is to satisfy the remaining heat.

(a)

**Figure 15.** *Cont.*

(c)

**Figure 15.** (**a**) The plus-minus principle with increasing TS by 5 ◦C for H1; (**b**) The PLUS-MINUS principle for nominal TS for H1 considering maximum size of HE and a bypass; (**c**) The plus-minus principle with decreasing TS by 5 ◦C for H1 considering maximum size of HE and a bypass.

(b)

**Figure 16.** (**a**) HEN design with TS increase by 5 ◦C for H1. HE2 is designed with a bigger area to accommodate up to 135 MW heat duty; (**b**) HEN design for nominal TS for H1. HE2 is designed with a bigger area and 120 MW heat duty; (**c**) HEN design with TS decrease by 5 ◦C for H1. HE2 is designed with bigger area and 105 MW heat duty.

Based on Observations 1 to 8, two heuristics are proposed for HEN design cases above and below the pinch to allow for flexibility and controllability in achieving maximum energy recovery:

	- a. A bypass should be placed at the disturbed stream if the TS value increases or decreases on either above or below the pinch and if ΔT = 0.
	- b. A bypass should be placed on the other side of the disturbed stream if the TS value is touching the pinch point, and if ΔT = 0 or the enthalpy is less than the enthalpy of another side of the disturbed stream.
	- a. Size a heat exchanger to cater to the highest amount of energy to be exchanged, considering all disturbances scenario.
	- b. Size a utility heat exchanger to cater to the highest amount of utility needed, considering all disturbances scenario.

After all the heuristics have been applied to the HEN design to cater for all the possible scenarios, there are some issues that must be checked:

(1) After adjusting heat exchanger duties, temperature feasibility test should be done for all the affected streams. If temperature infeasibility occurs, designers should consider redistributing the duty to the utilities.

(2) The bypass fraction should be calculated for all possible cases considering the biggest heat exchanger size.

Table 2 summarises the effects of cold and hot streams' supply temperature disturbances on hot and cold utilities as explained in the heuristics.


