State function‐based flash specifications for open systems in the absence or presence of chemical reactions

Abstract

Diverse engineering fields require flash calculations like isothermal flash, isenthalpic flash, and isentropic flash. They can be cast as minimization of a thermodynamic state function and solved by Michelsen's Q‐function approach. Flash calculations for open systems, that is, systems where chemical potentials are specified instead of the mole numbers for some components, also belong to this scope. By analyzing the construction of Q‐functions through Legendre transforms, we extend this approach to the flash for open systems in the absence or presence of chemical reactions, resulting in general formulations for various specifications. For systems without reactions, the classical framework using mole numbers as independent variables is employed; for those with reactions, the modified‐RAND framework is employed. We present examples for open systems at constant temperature and pressure. Using the Q‐function minimization, we can solve multicomponent nonreactive or reactive systems at a specified chemical potential with quadratic convergence over a wide range of conditions.

A unified presentation of phase stability analysis including all major specifications

“…In Michelsen's [1] general formulation for flash calculations, in that of Smejkal and Mikyška [55], as well as in unified treatments of using RAND-type methods [46][47][48], a common Jacobian matrix is assembled, capable of handling all specifications. This is also possible for phase stability testing, but it would be rather a mathematical exercise, with no practical use, since minimization of TPD functions in their hyperspaces is not recommended for most specifications, as discussed throughout this paper; as shown earlier, phase stability testing for any major specifications can be reduced to either PT or VTN stability testing.…”

“…Another topic related to VTN stability is phase envelope construction in the VT (or molar density-temperature) plane [26,27,30,35]. PHN (isobaric isenthalpic) phase equilibrium (consisting of the maximization of entropy at given pressure, enthalpy and moles) [1][2][3][36][37][38][39][40][41][42][43][44][45][46][47][48] has many practical applications, such as adiabatic expansions, throttling processes, compositional reservoir simulation of thermal recovery processes, etc. Phase stability testing at PHN conditions can be assessed using a classical PT stability testing, as correctly mentioned by Michelsen [36], Zhu and Okuno [39], Sun et al [40]; however, no detailed analysis of phase stability testing was given for these very important specifications.…”

“…For the SVN (isochoric-isentropic) phase equilibrium (consisting of the minimization of internal energy at given entropy, volume and moles) [46][47][48][49][50], there are no known applications to date, but the problem has a similar structure and fits the general pattern [46]. Phase stability is addressed here for the first time.…”

“…Michelsen's Q-functions are listed in Table 1. Several recent papers [46][47][48], originating from the same research group at DTU, presented unified approaches including all major specifications, for various phase and chemical equilibrium problems using modified RAND methods.…”