Decomposition stages

Under BW temperature conditions, this first-stage decomposition reaction proceeds to 100% completion, producing carbonate alkalinity and carbon dioxide. Thus, 1 ppm of bicarbonate initially produces 0.44 ppm of carbon dioxide. 

This second-stage decomposition reaction (carbonate hydrolysis) proceeds to approximately 80% completion at 150 psig, producing hydroxide alkalinity and carbon dioxide and providing a further 0.35 ppm carbon dioxide (80% of 0.44 ppm). Consequently, the total production of carbon dioxide from 1 ppm of bicarbonate alkalinity is 0.79 ppm at 150 psig. 

The intermediate formed in the two-stage decomposition of ZnS04 to ZnO has been variously reported as Zn502(S04)3 [781,798] and Zn30(S04)2 [784,799] reported values of E (Table 15) show little consistency. Decomposition has been described [799] as a topochemical reaction and the reverse process is slow if the ZnO (product) is not finely divided. 

McPherson, J. B. et al., J. Agric. Food Chem., 1956, 4, 42-49 Overheating during removal of solvent by distillation from a pilot batch of methyl parathion led to explosive decomposition, and the course of the 2-stage decomposition was studied. A 1.5 g sample immersed at 270°C decomposes after an induction period of 54 s and the residue later deflagrates, but a 5 g sample deflagrates during the initial decomposition. 

Basically, there are two different ways to decompose a 2S-MILP (see Figure 9.10). The scenario decomposition separates the 2S-MILP by the constraints associated to a scenario, whereas the stage decomposition separates the variables into first-stage and second-stage decisions. For both approaches, the resulting subproblems are MILPs which can be solved by standard optimization software. 

Before a new stage decomposition based hybrid evolutionary algorithm is proposed in Section 9.4, we briefly review the algorithm for general 2S-MILPs of Caroe and Schultz [11] which is regarded as the state-of-the-art exact algorithm for 2S-MILPs... 

Fig. 9.10 Decomposition scenario decomposition and stage decomposition of a 2S-MILP.

The main idea of stage decomposition (see Figure 9.10) is to remove the ties between the scenario subproblems of the 2S-MILP by fixing the first-stage variables. The 2S-MILP is written in its intensive form [9], where the resulting master problem is... 

The mathematical model of two-stage stochastic mixed-integer linear optimization problems was discussed as well as state-of-the-art solution algorithms. A new hybrid evolutionary algorithm for solving this class of optimization problems was presented. The new algorithm exploits the specific problem structure by stage decomposition. 

Simultaneous elimination of unmeasured variables a two-stage decomposition procedure is not advantageous because measurements are involved in Category 3 flowrates... 

The mass loss of the first-stage decomposition of the AP particles with 10% LiF is 56.7 %, and that of the second-stage decomposition is 28.5 %. The residue remaining above 790 K is 14.8%. As shown in Fig. 7.26, the two-stage decomposition process can be summarized as follows [i5]... 

Fig. 7.32 Two-stage decomposition process of AP + SrCOj as measured by thermogravimetry.

The urea-product solution, leaving the first decomposition stage and still containing some unreacted carbamate and excess NH3, is let down in pressure and steam heated in the second-staged decomposition section, which operates at about 2 atm and 120°C. Practically all of the residual carbamate is decomposed and stripped from the urea-product solution together with the residual excess ammonia. The 74—75 wt % urea solution thus obtained is further processed to solid urea... 

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