Hot 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 ... 

Waste heat (WH) boilers are essentially indirect (nonfired) steam generators that recover the heat energy present in hot gases of combustion (e.g., from a gas turbine) or from hot process stream gases. 

The hot process streams leaving a reactor or a distillation column are frequently used to preheat the feedstreams. 

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. 

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). 

Hottest hot utility Intermediate hot utilities Hot 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 heat residual of each hot process stream/utility exiting each temperature interval k is modeled via the continuous variables, Ritk and Rk. ... 

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). 

This example, which corresponds to the motivating example of Gundersen and Grossmann (1990) below the pinch point, features three hot process streams, two cold streams, and a cold utility with data shown in Table 8.4. 

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 ... 

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. 

Remark 2 Note that each hot process stream has a postulated structure of a process-process match in series with the utility match. The cold stream Cl, however, has a postulated structure with five process-process matches and then a hot utility match in series. 

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. 

BODM No. 2 (Figure 2). This modification illustrates an application of Rule 2a to guide the shift of a cooler on a given hot process stream. As shown in Figure 2, the evolutionary changes involve (a) shifting C. downward to the... 

From Figure 4.45 and Table 4.21, the minimum hot utility for a specified A7mm of 20°C is qu = 3050kW. From Figure 4.46 and Table 4.22, the minimum hot utility for a specified A7mm of 10°C is r/n = 2450 kW. Minimum cold utility required Similarly, below a hot stream temperature of 90°C, there is no cold process stream available to cool the hot process streams. Thus, a cold utility must be used to remove this heat. The corresponding heat is called the minimum cold utility requirement. Table 4.21 shows that the minimum cold utility is 2825 kW. 

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