Nonequilibrium Stage Based Modeling of a Falling Film Distillation Unit

Abstract

A novel nonequilibrium stage based model was developed for a falling film distillation unit. The model combines mass and energy balances in the liquid and vapor phases, without the need of separation efficiency factors. The modeled pilot scale falling film distillation unit is differentiated because the heat supply is carried out axially by means of a thermosyphon. In terms of the algorithm proposed, the central contribution is in reducing the number of variables to be determined by the method, which brings benefits such as reduction of computational time and increase of robustness in the convergence. The results obtained were compared with experimental data from the pilot scale plant, and showed good predictability, with deviations in the top temperature below 2.60%, 6.59% in the distillated ethanol fraction, 12.32% in the resistance power and only one case above 10% for distillate flow rate.

APPENDIX A

The physical parameters used in the modelling were obtained from the references described in Tables A1 and A2. Table A1 refers to the data of the pure components, and several of the properties described therein are temperature dependent functions. In terms of modelling, the values of any desired property were obtained by interpolating the data provided in the references.

Table A1.   Physical properties of the pure components in the liquid and vapor phases

In Table A1, the parameters of the collision integral, as well as the critical parameters of the pure components were used for the calculation of the binary diffusion coefficient, using the modified Wilke and Lee correlation [40]. Table A2 describes the methods used to obtain properties of the ethanol-water solution, from pure data. In the case of the properties present in Table A1 and not listed in Table A2, a linear mixing rule was assumed, given by the weighted average (in terms of molar fraction) of the information of the pure components.

Table A2.   Methods of calculating properties of the ethanol-water mixture

Finally, the parameters of the activity coefficient model (Wilson) were obtained from the model described by Faúndez and Valderrama [44].

NOTATION

A	interfacial area (m2)
D	difusivity (m2/s)
d	diameter (m)
E	energy balance function (J/s)
E	quadratic approximation error
e	point energy flux (J/m2 s)
ε	energy transfer rate (J/s)
F	flow rate
g	gravity acceleration (9.81 m/s2)
H	enthalpy (J/kg)
h	heat transfer coefficient (J/m2 K)
h*	dimensionless heat transfer coefficient
K	equilibrium ratio
k	mass transfer coefficient (kg/m2 s)
k	thermal conductivity (W/m K)
k Boltz	Boltzmann constant (1.3806 × 10–23 m2 kg/s2 K)
L	liquid flow rate (kg/s)
M	mass balance function
N	number of elements
N	transfer flux (kg/m2 s)
$\mathbb{N}_{{i,j}}^{{\text{V}}},\,\,\mathbb{N}_{{i,j}}^{{\text{L}}}$	transfer rates (kg/s)
P	pressure (kPa)
p	adjustable parameter
Pc	critical pressure (bar)
Pr	Prandtl number
Q	energy added or removed (kW)
R	rate relation functions
Re	Reynolds number
Rec	critical Reynolds number
S	summation functions
Sc	Schmidt number
Sh	Sherwood number
T	temperature (K)
T c	critical temperature (K)
u	velocity (m2/s)
V	vapor flow rate (kg/s)
W	internal perimeter (m)
w	mass flow (kg/s)
x	mass fraction in the liquid phase
x	spatial coordinate in the radial direction (m)
y	mass fraction in the vapor phase
Zc	critical compressibility factor
ϕ	fugacity coefficient
∆	variation difference
α	weighting coefficient
γ	activity coefficient
δ	film thickness (m)
δpi	Kronecker delta
ε	maximum attraction energy
μ	fuid viscosity (Pa s)
ρ	fuid density (kg/m3)
σ	collision diameter (angstroms)
ω	acentric factor

SUBSCRIPTS AND SUPERSCRIPTS

C	composition
c	total number of components
D	top flow rate
et	ethanol
i	component i
I	interface
j	staje
k	component k
L	liquid phase
mod	modified
P	thermosyphon power
T	top temperature
t	total
transf	transference
V	vapor phase
vap	vaporization
w	wall