Interval analysis for thermodynamic calculations in process design: a novel and completely reliable approach

Abstract

Recently, a robust new computational technique, based on interval analysis, has been developed for solving the difficult nonlinear problems arising in the modeling of phase behavior.This technique can be used, with mathematical and computational guarantees of certainty, to find the global optimum of a nonlinear function or to enclose any and all roots of a system of nonlinear equations. As shown in the applications here to phase stability analysis and to the location of homogeneous azeotropes, it provides a method that can guarantee that the correct result is found, thus eliminating computational problems that may potentially be encountered with currently available techniques. The method is initialization independent; it is also model independent, straightforward to use, and can be applied in connection with any equation of state or activity coefficient model.

A subdivision algorithm for phase equilibrium calculations at high pressures

“…It should be observed in this table that the results found with the SubDivNL algorithm are in agreement with the ones presented in the literature (Hua et al, 1999), where interval analysis was used (IN/GB algorithm). In this table the CPU time for all solutions of each calculation condition is also presented and it can be observed that, besides the algorithm's ability to find all roots, a very short CPU time is required for the calculations.…”

A new look at the topographical global optimization method and its application to the phase stability analysis of mixtures

“…This system was also analyzed by others. Hua et al (1999) employed the Newton-interval method, Nichita et al (2002a) used the Tunneling method, Balogh et al (2003) employed o GLOBAL algorithm, andBonilla-Petriciolet et al (2006) reported results using the Simulated Annealing (SA) algorithm. Table 14 shows the NFE of the TGO and of these others methods, at 3 different feed We consider the eight-component system methane(1)/ethane (2)/propane(3)/n-butane(4)/n-pentane(5)/n-hexane(6)/C 7-16 (7)/ C 17 þ (8) at near critical conditions (T ¼ 353 K, P ¼ 38; 500 kPa, z 1 ¼ 0:6883, z 2 ¼ 0:0914, z 3 ¼ 0:0460, z 4 ¼ 0:0333, z 5 ¼ 0:0139, z 6 ¼ 0:0152, z 7 ¼ 0:0896, z 8 ¼ 0:0222), which was analyzed initially by Nagarajan et al (1991).…”

“…To deal with such difficulties, in the last decades many deterministic or stochastic methods have been applied to obtain global minimizers of this objective function constructed from different models, which are decisive for the outcome of the phase stability analysis; see, for example, Trangenstein (1987), Stateva and Tsvetkov (1991), Nagarajan et al (1991), Sun and Seider (1995), McDonald and Floudas (1995), Wasylkiewicz et al (1996), Hua et al (1998Hua et al ( , 1999, Zhu and Xu (1999), Zhu and Inoue (2001), Zhu et al (2000 ), Tessier et al (2000), Henderson et al (2001Henderson et al ( , 2011Henderson et al ( , 2014, Rangaiah (2001) Nichita et al (2002a, 2002b, Xu et al (2002), Balogh et al (2003), Bonilla-Petriciolet et al (2006, Hoteit and Firoozabadi (2006), Srinivas and Rangaiah (2007), Saber and Shaw (2008), Nagatani et al (2008), Fateen et al (2012), Pereira et al (2012), Bhargava et al (2013), Staudt et al (2013), Ivanov et al (2013) and Castier (2014).…”

Computing Homogeneous Azeotropes Using Interval Analysis

“…In fact, application of this powerful equation solving technique is not limited to azeotrope problems. It can also be applied to the solution of Research News a wide variety of phase behavior problems [21], and to other difficult problems in process modeling [18].…”