Engineering Application of Exergy Analysis - circe - Universidad de ...

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where xi,j is the molar fraction of component j in flow i, bch,j is the specific exergy of component j and R is the constant of gases. The second part of the equation refers to the difference between the exergy of the different components of a mixture isolated, and the exergy of the components all mixed together. Szargut reference state [2] has been used for the calculation of chemical exergy. After calculating the exergy of all flows, it is possible to obtain the irreversibility of each component (Ik). It should be noted that, in this paper, irreversibility will also include losses (external irreversibilities). I = B − B , (4) ∑ ∑ k i i inputs outputs In order to put in perspective the values of exergy and irreversibility obtained, two non-dimensional parameters have been defined. First, several efficiencies calculated by dividing the exergy of the outputs of the system into the main input (exergy of gases leaving the converter): Bi η i = B , (5) 1 Besides, irreversibility of components is made non-dimensional by dividing it also into the exergy of flow 1: I k ϕ k = , (6) B 1 2.4. Parameters for characterizing the whole cycle. Exergy flows, irreversibility and non-dimensional parameters defined in the previous section vary with time, and thus they are suitable for a detailed study of a given recovery cycle. However, in order to summarize the results of a cycle and to compare it with others, integral indicators characterizing the whole cycle are needed. Accordingly, the exergy of a flow i over a cycle (kJ) is defined as: Bcycle, i = ∫ Bi() t ⋅dt , (7) cycle Besides, the irreversibility in a component k over a cycle (kJ) is defined as: Icycle, k = ∫ Ik() t ⋅dt , (8) cycle Finally, the non-dimensional parameters η and φ can also be calculated for the whole cycle: η ϕ cycle, i cycle, k cycle,1 1 cycle () B i t dt B ∫ ⋅ cycle, i cycle = = , (9) B B t ⋅ dt ∫ ∫ cycle,1 1 cycle () () Ik t ⋅ dt Icycle, k cycle = = , (10) B B t ⋅ dt 3. Results ∫ () The model described above is being applied for the study of the operation of the gas and steam recovery system by using information (detailed in Fig. 1 and at the beginning of section 2.2), which is stored by the plant information system every 16 seconds. In this section, the most important results corresponding to an example of a gas recovery cycle are presented. First, evolution of both exergy and irreversibility is presented, and then the cycle is summarized by the integral cycle indicators. 3.1. Exergy and irreversibility versus time. Figure 2 shows the evolution of the exergy of flue gases leaving the BOF during a cycle. It can be seen how this amount increases during the first half of the cycle and decreases later, with smooth variations according to the blowing pattern of oxygen inside the converter. B[1] (kW) 350000 300000 250000 200000 150000 100000 50000 0 0 200 400 600 800 1000 1200 Time (s) Fig. 2. Exergy of gases leaving the converter. http://www.ecos2010.ch 4 14-17th june 2010, Lausanne, Switzerland
The exergy of gas which is recovered in the gasholder is shown in Fig. 3. In this figure and in the following ones, two families of points are plot: the absolute value (left axis) and the relative value (according to 5 or 6) in the right axis. Due to quality requirements of gas to be stored (e. g. minimum amount of CO), gas recovery only takes place during part of the cycle. It should be noted that the exergy of this gas represents between 50 and more than 80% of exergy of flow 1. B[10] (kW) 300000 250000 200000 150000 100000 50000 0 B[10] (kW) eta[10] (‐) 0 200 400 600 800 1000 1200 Time (s) Fig. 3. Exergy of recovered gas. B[9] (kW) 250000 200000 150000 100000 50000 0 B[9] (kW) phi_flare (‐) 0 200 400 600 800 1000 1200 Fig. 4. Exergy of flared gas. Time (s) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 The part of the gas which is flared is represented in Fig. 4. This amount represents more than 50% of flow 1 before the recovery but falls at the end of the cycle. This result indicates that it is very interesting to extend the duration of the recovery as much as possible and to flare gas only when this is the only possibility. As explained previously, the system not only recovers gas, but also produces steam. Figure 5 shows the evolution of exergy of steam used in several steel treatments (flow 104). This amounts eta [10] (‐) phi_flare (‐) around 12 MW, which corresponds to less than 10% of the exergy of converter gas. B[104] (kW) 14000 12000 10000 8000 6000 4000 2000 0 B[104] (kW) eta[104] (‐) 0 200 400 600 800 1000 1200 Time (s) Fig. 5. Exergy of steam to steel treatments. 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 Exergy of steam exported to the steam net of steelworks is presented in Fig. 6. First, the system exports 1.5 MW of steam, which are progressively reduced and afterwards more than 2 MW are imported (negative value). These amounts are less than 2% of the exergy of flow 1. B[135] (kW) 2000 1500 1000 500 0 ‐500 ‐1000 ‐1500 ‐2000 ‐2500 ‐3000 B[135] (kW) eta[135] (‐) 0 200 400 600 800 1000 1200 Time (s) Fig. 6. Exergy of steam exchanged with the net. 0.06 0.04 0.02 0 ‐0.02 ‐0.04 ‐0.06 ‐0.08 ‐0.1 Results presented above have shown the variation of the exergy of several flows leaving the system. However, a key advantage of the use of exergy is that it allows one to consider also losses of energy quality (irreversibilities) taking place inside the different component. Figure 7 represents the exergy destroyed in the combustion process. The low value of this variable (around 2%) can be explained by considering two points. First, only a fraction of the CO contained in the gas is burned (the other part contributes strongly to the chemical exergy of gas which is either stored or flared, as it can be seen in Fig. 3 http://www.ecos2010.ch 5 14-17th june 2010, Lausanne, Switzerland eta[104] (‐) eta[135] (‐)
Page 1 and 2: Engineering Application of Exergy A
Page 3: part of the steam can be vented (fl
Page 7 and 8: Table 2. Integral cycle indicators

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