Cold process stream

Having determined the individual heating loads and cooling ctq)acities of all process streams for all temperature intervals, one can also obtain the collective loads (capacities) of the hot (cold) process streams. The collective load hot process streams within the zth interval is calculated by summing up the individual loads of the hot process streams that pass through that interval, i.e.. 

As has been mentioned earlier, within each temperature interval, it is ther modynamically as well as technically feasible to transfer beat from a hot process stream to a cold process stream. Moreover, it is feasible to pass heat from a hot process stream in an interval to any cold process stream in a lower interval. Hence, for the zth temperature interval, one can write the following heat-balance equation ... 

To illustrate the idea, we consider the temperature control of a gas furnace, which is used to heat up a cold process stream. The fuel gas flow rate is the manipulated variable, and its flow is subject to fluctuations due to upstream pressure variations. 

We will continue with the gas furnace to illustrate feedforward control. For simplicity, let s make the assumption that changes in the furnace temperature (T) can be effected by changes in the fuel gas flow rate (Ffuei) and the cold process stream flow rate (Fs). Other variables such as the process stream temperature are constant. 

In Section 10.1, the fuel gas flow rate is the manipulated variable (M) and cascade control is used to handle its fluctuations. Now, we consider also changes in the cold process stream flow rate as another disturbance (L). Let s presume further that we have derived diligently from heat and mass balances the corresponding transfer functions, GL and Gp, and we have the process model... 

In the chemical plant, the transformation of the feed streams (e.g., raw materials) into desired products and possible by-products takes place. In the heat recovery system, the hot and cold process streams of the chemical plant exchange heat so as to reduce the hot and cold utility requirements. In the utility plant, the required utilities (e.g., electricity and power to drive process units) are provided to the chemical plant while hot utilities e.g., steam at different pressure levels) are provided to the heat recovery system. Figure 7.1 shows the interactions among the three main components which are the hot and cold process streams for (i) and (ii), the electricity and power demands for (i) and (iii), and the hot utilities e.g., fuel, steam at different pressure levels, hot water) and cold utilities e.g., cooling water, refrigerants) for (ii) and (iii). 

The heat recovery system has as units heat exchangers, and its primary objective is to reduce energy requirements expressed as hot and cold utilities by appropriately exchanging heat between the hot and cold process streams. 

Given are a set of hot process streams, HP, to be cooled, and a set of cold process streams, CP, to be heated. Each hot and cold process stream has a specified heat capacity flowrate while their inlet and outlet temperatures can be specified exactly or given as inequalities. A set of hot utilities, HU, and a set of cold utilities, CU, along with their corresponding temperatures are also provided. 

This example is taken from Floudas and Ciric (1989) and consists of two hot process streams, two cold process streams, and has HRAT — 30°C. The inlet, outlet temperatures, and the flowrate heat capacities are shown in Table 8.1. If we consider a first-law analysis for this example and simply calculate the heat available in the hot process streams and the heat required by the cold process streams, we have... 

Therefore we have QH1 + QH2 = 350 kW available from the hot process streams while there is a demand of 725 kW for the cold process streams. Based on this analysis then, we may say that we need to purchase (725 - 350) = 375 kW of hot utilities. 

We will see, however, that this is not a correct analysis if a pinch point exists. In other words, the implicit assumption in the first law analysis is that we always have feasible heat exchange for the given HRAT = 30°C. To illustrate the potential bottleneck, let us consider the graphical representation of the hot and cold process streams in the T - Q diagram shown in Figure 8.1. 

Remark 1 The above guidelines assume that we have one hot and one cold utility each located at the top and bottom respectively of the temperature range. In the case, however, where there exist multiple hot and cold utilities then we first identify the hottest hot utility and the coldest cold utility and define the rest of the utilities as intermediate hot and intermediate cold utilities. Subsequently, we treat the intermediate hot and cold utilities as hot and cold process streams for purposes of the partitioning into temperature intervals. In other words, we have to apply the two aforementioned guidelines for both the hot and cold process streams and intermediate hot and cold utilities. Another pictorial representation of the four temperature intervals is shown in Figure 8.3 along with the hot and cold stream data. 

Remark 3 A hot process stream cannot transfer heat to a cold process stream that exists in a higher TI because of driving force violations. For instance, hot stream H1 cannot transfer heat to cold streams Cl, C2 at TI - 1. Similarly, hot stream H2 cannot transfer heat to cold stream C2 at all. Also, hot stream H2 can only transfer heat to cold stream C2 at TI - 4. 

Papoulias and Grossmann (1983) drew the analogy between the transshipment model and the HEN, which is shown in Table 8.2. Using this analogy, heat is considered as a commodity which is transferred form the hot process streams and hot utilities to the cold process streams and cold utilities via the temperature intervals. The partitioning procedure discussed in the previous section allows only for feasible transfer of heat in each temperature interval (see also the remarks of section 8.3.1.3). 

Coldest hot utility Intermediate cold utilities Cold process streams... 

Remark 2 Note that in the top temperature interval, there is no heat residual entering. The only heat flows entering are those of the hottest hot utility and of the hot process streams. Similarly in the bottom temperature interval there is no heat residual exiting. The only heat flows exiting are those of the cold utility and the cold process streams. 

CUk = j cold utility j is present in interval k, i hot process stream/utility, j cold process stream/utility, k temperature interval. 

The temperature interval partitioning along with the transshipment representation is shown in Figure 8.6. Note that in Figure 8.6, we also indicate the heat loads provided by the hot process streams at each temperature intervals as well as the heat loads needed by the cold process streams at each temperature interval. Note also that the optimization variables are QS, QW, Ri, R2, and R3. 

Given the information provided from the minimum utility cost target (i.e., loads of hot and cold utilities, location of pinch points, and hence subnetworks), determine for each subnetwork the minimum number of matches (i.e., pairs of hot and cold process streams, pairs of hot utilities and cold process streams, pairs of cold utilities and hot process streams, and pairs of hot-hot or cold-cold process streams exchanging heat), as well as the heat load of each match. 

The pictorial representation of a temperature interval k is shown in Figure 8.8, where we have a hot process stream H1, a hot utility 51 potentially exchanging heat with a cold process stream Cl that is, we have two potential matches (HI, Cl) and (51 - Cl). 

In the top temperature interval only the matches between the hot process streams and the cold process streams can take place. In the bottom interval we have the matches of Hi, H2, HZ with Cl and CW only since C2 does not participate in this TI. As a result we need to introduce 12 instead of 18 continuous variables Qijk. We need to introduce nine binary variables for the aforementioned potential matches. The MILP transshipment model P2 is ... 

A number of research groups suggested that in certain cases it is desirable to allow for matches between hot-to-hot, and cold-to-cold process streams (Grimes etai, 1982 Viswanathan and Evans, 1987 Dolan et al., 1989). It is worth noting that the MILP transshipment model of Papoulias and... 

In the first three Els we have heat transfer from stream to cold process streams. In the El - 6 we have heat transfer from hot process streams to cooling water. In El — 4, El - 5 we have heat transfer from hot process streams to cold process streams. 

This example is taken from Floudas et al. (1986) and features one hot, two cold process streams, one hot and one cold utility with data shown in Table 8.6. It is also given that HRAT = TIAT = EM AT = 10 K. 

Given is a process that consists of the following set of hot and cold process streams, hot and cold utilities ... 

One might classify several of these heat exchanger network synthesis algorithms into two broad classes. There are several algorithms which view the synthesis problem as one which selects the next hot process stream/cold process stream match to make. 

Rule 3. Reduce the number of units by deleting repeated matches between two hot and cold process streams in a given network. In particular, if a given network contains a local subnetwork in which a hot (cold) stream matches the same cold (hot) stream which it has matched before, delete one of these repeated matches. 

---