Optimising heat recovery in a heat exchanger network
Maintaining equal heat capacity flow rates for heat sink and source provides maximum heat recovery from an exchanger network.
MADHURA REWATKAR, RAHUL PATIL and AJAY GUPTA
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Heat exchanger (HX) networks are an integral part of a process unit. There are streams in a process which need to be heated for effecting separation of components or conversion in a reactor. Similarly, there are streams which need to be cooled before storage in tanks. The heating and cooling of streams is done through heat exchange with either utilities like steam for heating or water for cooling or between the cold and hot process streams.
The objective of a design engineer should be to minimise the requirement of utilities (minimising operating cost) as well as achieving the heat exchange with minimum heat exchanger area (minimising capital expenditure). There is extensive work available on designing optimum heat exchanger networks (HEN). However, it is always useful for a practice engineer to have some handy rules by means of which he/she can make quick checks and decisions regarding optimum utilisation of HENs. This article presents one such simple scientific principle for optimising heat recovery in HENs.
We all know that the basic driving force for heat exchange between hot and cold streams is the temperature difference between them. A higher temperature difference will require a lower heat exchanger area for the same amount of heat transfer, or conversely will facilitate more heat exchange for a specified area. Now for a complex HEN, the temperature difference between streams keeps on changing along the heat transfer path. For a poorly designed HEN, there could be points where the temperature difference between hot and cold streams becomes very low, making heat transfer extremely difficult. These points are referred to as pinch points in classical pinch analysis. So, for optimum heat exchange, one should try to maintain temperature profiles of hot and cold streams which do not converge towards each other.
We will explain this through the example of a single heat exchanger and then expand the principle to multiple heat exchangers in a network. Let us compare temperature profiles in a co-current and counter-current heat exchanger (see Figure 1).
We can see that the temperature profiles in a counter-current heat exchanger are comparatively parallel as against those of a co-current heat exchanger where the temperature profiles converge towards the outlet. This results in a higher mean temperature difference between the hot and cold streams in a counter-current configuration, resulting in a more efficient heat exchange as compared to co-current flow.
This is illustrated in Figures 2 and 3.
Figure 2 shows hot and cold streams exchanging heat, first in the co-current direction and later in the counter-current direction. The corresponding temperatures along the length of the heat exchangers are shown in Figure 3. We can understand from Figure 3 that the driving force âˆ’ the temperature difference between the hot and cold streams along the length of the heat exchanger âˆ’ is continuously reducing for co-current operation while hot fluid gets cold and cold fluid gets heated. At the entrance of the heat exchanger, the temperature difference is large (134.8°C) and it becomes least (21.1°C) at the outlet of the heat exchanger. For counter-current operation however, the temperature difference at the entrance of the heat exchanger is 100.4°C and it reduces to 46.9°C at the exit of the heat exchanger. So the reduction in counter-current operation is much less compared to co-current operation. This results in a smaller mean temperature difference for co-current operation compared to that of counter-current operation.
Table 1 provides the results for co-current and counter-current operations of a heat exchanger with a heat transfer area of 1025 m2. We can see it confirms that the mean temperature difference (MTD) is 69.2°C in counter-current flow and is more, by about 5°C, compared to the MTD of 63.9°C in co-current flow. This results in 1 Gcal/hr more heat transfer between hot and cold streams for counter-current operation compared to co-current operation.
For multiple HENs, we should always opt for a counter-current configuration: the coolest and hottest streams should enter the network at opposite ends. We also need to keep the hot and cold temperature profiles as parallel as possible throughout the path of heat transfer from one end to the other. Now for a heat exchanger the slope of the temperature profile in a temperature-enthalpy (T-H) diagram is nothing but the inverse of the heat capacity flow rate (1/mCp) of the process stream. Thus, one should strive to maintain 1/mCp (hot) and 1/mCp (cold) as close as possible for maximum heat transfer while keeping the minimum heat transfer area (see Figure 4).
The above concept is illustrated by considering an example where streams need to be split to keep the heat capacities of cold and hot streams exchanging heat in a heat exchanger. Stream splitting is required for cases where there is a large difference between the heat capacities of hot and cold streams; equating heat capacities is not possible with a single heat exchanger.
This article presents and highlights a simple idea to split streams in an effective way. Here, the stream having a lower heat capacity flow rate (mCp), let us call it stream A, is made to pass entirely through the heat exchanger, whereas the other stream (B), having a higher heat capacity flow rate, is split and a fraction (B1) with equal heat capacity is used to exchange heat in the first heat exchanger. Stream A is then passed through another exchanger and a fraction (B2) of stream B exchanges heat with it in heat exchanger 2. This exercise can be repeated with more exchangers until we exhaust the stream B value. This strategy and its usefulness is illustrated by means of the following case studies.
Case study 1
Figure 5 shows a base case where a counter-current heat exchanger comprises one hot (523.2 t/h) and one cold fluid (1470.6 t/h). The targeted temperatures of hot and cold fluid are attained with a total heat transfer area of 2043 m2. Here, the heat capacity flow rate value of the hot fluid is low compared to that of the cold fluid (see Table 2). The heat capacity flow rate value of the cold stream is about 2.6 times greater than that of the hot stream.
Table 2 clearly illustrates that the heat capacity flow rate of the cold stream is about 2.6 times greater than the hot stream. This results in very dissimilar temperature differences at the two ends of the T-H diagram. The temperature difference of 100.4°C at the right-hand end of the T-H diagram is significantly higher than 47°C at the left-hand end. To demonstrate the above mentioned concept, we have completely passed the hot stream through one or more heat exchangers, and the cold stream is divided into multiple streams such that the split stream from it matches the heat capacity flow rate with the hot stream as closely as possible. Two such configurations are explained in detail in the following.
Case study 2
Since the mCp value of a hot stream is lower than that of a cold stream, the entire hot stream was passed through the heat exchanger HX1. Then the cold fluid is split into HX1 and HX2. The mCp values of the hot and cold streams are kept equal in HX1. About 550 t/h of total cold fluid is required to accomplish the same. The remaining cold fluid is passed through HX2 which is added in series with HX1. The hot stream coming from HX1 is input to HX2. So the hot stream is in series and the cold stream is in parallel for case 2 (see Figure 7).
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