@Article{icces.2023.09050,
AUTHOR = {Tao Zhang, Hua Bai, Shuyu Sun},
TITLE = {Thermodynamically-Consistent	NVT	Flash	Calculation	and	 Thermodynamics-Informed	Neural	Network (TINN)	Accelerating	Phase	 Equilibrium	Estimates},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {26},
YEAR = {2023},
NUMBER = {2},
PAGES = {1--2},
URL = {http://www.techscience.com/icces/v26n2/54033},
ISSN = {1933-2815},
ABSTRACT = {The	 current	 well-developed	 and	 widely-recognized	 models	 describing	 interfacial	 tension	 are	 explicit	
functions	of	volume,	temperature	and	moles	so	that	it	is	more	straightforward	to	compute	the	derivative	of	
interfacial	tension	with	respect	to	volume	than	pressure.	We	will	propose	a	novel	and	comprehensive	multicomponent	multi-phase	flow	simulation	algorithms	based	on	diffuse	interface	models.	In	order	to	improve	
the	robustness	and	reliability,	realistic	EoSs,	represented	by	Peng-Robinson	equation	of	states,	are	selected	
to	formulate	the	thermodynamic	correlations	and	an	NVT-based	flash	calculation	scheme	is	used	to	control	
the	 phase	 behaviors [1].	 Compared	 to	 the	 minimized	 Gibbs	 free	 energy	 often	 used	 in	 NPT-based	 flash	
schemes,	Helmholtz	free	energy	will	be	minimized	in	our	flash	framework	for	further	derivations.	The	ideal	
routine	will	start	from	the	first	law	of	thermodynamics	to	construct	the	entropy	balance	formulation,	and	
the	Helmholtz	free	energy	density	transport	equation	can	be	derived	based	on	that.	The	energy	dissipation	
in	the	whole	system	along	with	time	needs	to	be	proved	to	show	the	consistency	between	our	model	and	
general	thermodynamic	rules.	For	the	numerical	solutions	to	the	model,	we	plan	to	construct	an	efficient	
convex-concave	 splitting	 approach	 targeting	 the	 Helmholtz	 free	 energy	 density,	 which	 is	 believed	 to	
efficiently	handle	the	strong	nonlinearity	analyzed	above,	as	well	as	the	tight	coupling	between	fluid	velocity	
and	molar	densities.	Generally,	 for	a	NVT	 type	 framework,	 the	phase-wise	mole	compositions	as	well	as	
volume	 are	 chosen	 as	 the	 primary	 variables	 arbitrarily,	 and	 we	 need to	 involve	 other	 aforementioned	
constraints	resulted	from	thermodynamic	rules	and	mass	conservations	to	determine	the	counterparts	in	
the	other	phase. Recently	we	demonstrated	 that	 the	deep	neural	network	models,	while	preserving	high	
accuracy,	 are	 more	 than	 two	 hundred	 times	 faster	 than	 the	 conventional	 flash	 algorithms	 for	
multicomponent	mixtures [2].	Previous	machine	learning	methods	assume	a	fixed	number	of	components	
in	the	fluid	mixture,	which	makes	such	models	to	have	very	limited	practical	usefulness.	In	this	work,	we	
propose	 to	 develop	 self-adaptive	 deep	 learning	 methods	 for	 general	 flash	 calculations,	 which	 can	
automatically	 determine	 the	 total	 number	 of	 phases	 existing	 in	 the	 multicomponent	 fluid	 mixture	 and	
related	thermodynamic	properties at	equilibrium.	Our	preliminary	work	showed	that,	for	example,	the	deep	
learning	model	with	 the	8-component	Eagle	Ford	 oil	 flash	calculation	 results	as	 training	data	accurately	
predicts	the	phase	equilibrium	properties	of	a	14-component	Eagle	Ford	fluid	mixture.},
DOI = {10.32604/icces.2023.09050}
}