Analysis and extension of the Furter equation, and its application in the simulation of saline extractive distillation columns

Timmermann, Ernesto O.; Muzzio, Cristian R.

doi:10.1590/0104-6632.20170342s20150102

Ernesto O. Timmermann

Instituto de Investigación y Desarrollo, Academia Nacional de Ciencias de Buenos Aires, Av. Alvear 1711, Buenos Aires, Argentina

+ passed away.

Cristian R. Muzzio ^**CTo whom correspondence should be addressed. E-mail: cmuzzio@fi.uba.ar. Tel.: +54 11 4343-0893

Departamento de Química, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, Buenos Aires, Argentina;

*CTo whom correspondence should be addressed. E-mail: cmuzzio@fi.uba.ar. Tel.: +54 11 4343-0893

+
passed away.

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Figure 1
Isobaric z'-y diagrams for acetone + methanol + lithium nitrate system ((: experimental data obtained from Vercher et al. ( 2006Vercher, E. , Orchillés, A. V., Miguel, P- J., González-Alfaro, V., Martínez-Andreu, A., Isobaric vapor-liquid equilibria for acetone + methanol + lithium nitrate at 100 kPa. Fluid Phase Equilibria, 249, p. 97-103 (2006).); ( ( ( (: calculated data using Furter equation; ( ( : calculated data using Wu equation; (: calculated data using FRS model; (: calculated data using FS model).

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Figure 2
Comparison between the SHA (left) and FEC-FRS (right) approach.

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Figure 3
Comparison of convergence time for the SHA approach (dark grey columns), and the FEC-FRS approach (light grey columns). Simulated system: 1-Prop-H₂O-LiNO₃.

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Figure 4
Comparison of the number of iterations required to achieve convergence, for the SHA approach (dark grey columns), and the FEC-FRS approach (light grey columns). Simulated system: 1-Prop-H₂O-LiNO₃.

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Figure 5
Comparison of convergence time for the SHA approach (dark grey columns), and the FEC-FRS approach (light grey columns). Simulated system: EtOH -H₂O-KAc.

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Figure 6
Comparison of the number of iterations required to achieve convergence, for the SHA addition approach (dark grey columns), and the FEC-FRS approach (light grey columns). Simulated system: EtOH -H₂O-KAc.

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Table 1
obtained from Furter, Wu, FRS and FS models.

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Table 2
Parameters of the Furter, Wu, FRS and FS models, used in the correlation of systems included in .

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Table 3
Properties and process conditions for the simulated systems.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15a)

(15b)

(16a)

(16b)

(17a)

(17b)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

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System	Condition	x₃ ^a	Δy_1,s
System	Condition	x₃ ^a	Furter^b	Wu^c	FRS^d	FS^e
Propanol-water-LiNO₃	100.0kPa	0.02-0.121	0.0151	0.0140	0.0081	0.0080
Acetic acid-water-CH₃COONa	100.0kPa	0.0038-0.1185	0.0116	0.0111	0.0094	0.0090
Propanol-water-LiCl	100.0kPa	0.021-0.126	0.0150	0.0150	0.0091	0.0094
Propanol-water-CuCl₂	100.0kPa	0.021-0.118	0.0120	0.0098	0.0113	0.0122
Propanol-water-Ca(NO₃)₂	100.0kPa	0.009-0.144	0.0188	0.0154	0.0164	0.0118
Ethanol-water-CH3COOK	101.33kPa	0.025-0.15	0.0260	0.0258	0.0217	0.0223
Acetone-methanol-LiNO₃	100.0kPa	0.021-0.16	0.1319	0.1250	0.0477	0.0273
Ethanol-water-[C6mim] -[Cl]	101.3kPa	0.002-0.325	0.0534	0.0406	0.0533	0.0342
Ethanol-water-KNO₃	100.0kPa	0.001-0.032	0.0123	0.0123	0.0104	0.0110
Ethanol-water-NaNO₃	100.0kPa	0.003-0.153	0.0202	0.0196	0.0188	0.0212
Ethanol-water-CuCl₂	100.0kPa	0.007-0.097	0.0167	0.0167	0.0166	0.0279
Ethanol-water-CoCl₂	100.0kPa	0.007-0.072	0.0146	0.0123	0.0142	0.0154
Ethanol-water-SrBr₂	100.6kPa	0.007-0.064	0.0197	0.0197	0.0162	0.0157
Ethanol-water-SrCl₂	100.0kPa	0.004-0.045	0.0196	0.0196	0.0194	0.0191
Ethanol-water-SrNO₃	100.0kPa	0.002-0.053	0.0192	0.0174	0.0160	0.0156
Acetic acid-water-CH₃COOK	100.0kPa	0.0099-0.1199	0.0162	0.0138	0.0114	0.0109
Acetic acid-water-CH₃COOLi	100.0kPa	0.021-0.127	0.0134	0.0087	0.0112	0.0108
Propanol-water--[emim] -[triflate]	100.0kPa	0.0533-0.3165	0.0823	0.0796	0.0343	0.0294
Propanol-water--[beim] -[triflate]	100.0kPa	0.0425-0.3239	0.0917	0.0904	0.0334	0.0294
Propanol-water--[bmpyr] -[triflate]	100.0kPa	0.0527-0.3274	0.0877	0.0867	0.0346	0.0307
Average			0.035	0.033	0.021	0.019

System	Furter^a	Wu^b		FRS^c				FS^d
System		k	k	k'	k	k'	A	ΔA	h₁₀	h₂₀
Propanol-water-LiNO₃	6.02	7.37	-13.67	4.23	4.33	6.40	2.17	-10.62	2.80
Acetic acid-water-CH₃COONa	0.39	-0.03	4.59	-1.41	4.47	0.83	2.24	-2.72	-1.34
Propanol-water-LiCl	7.81	7.74	0.63	6.33	4.22	8.44	2.11	-13.86	4.03
Propanol-water-CuCl₂	4.55	6.28	-19.69	4.04	1.32	4.70	0.66	-6.14	2.92
Propanol-water-Ca(NO₃)₂	10.17	13.09	-36.03	6.85	6.19	9.95	3.10	-18.61	4.16
Ethanol-water-CH₃COOK	6.03	7.64	-20.82	2.77	7.62	6.58	3.81	-11.77	1.97
Acetone-methanol-LiNO₃	7.03	17.29	-89.46	-7.45	43.10	14.10	21.55	-130.62	-31.84
Ethanol-water-[C6mim] [Cl]	-1.68	-4.42	16.10	-2.65	2.42	-1.44	1.21	0.24	-0.41
Ethanol-water-KNO₃	9.35	9.34	0.17	13.25	-48.87	-11.19	-24.44	10.08	9.32
Ethanol-water-NaNO₃	7.12	5.70	13.55	7.98	-11.93	2.01	-5.96	-5.31	4.38
Ethanol-water-CuCl₂	5.45	5.44	0.16	5.12	1.52	5.88	0.76	5.10	4.82
Ethanol-water-CoCl₂	10.85	14.53	-81.85	12.71	-4.69	10.36	-2.35	-8.83	9.52
Ethanol-water-SrBr₂	16.79	16.77	0.60	13.91	11.38	19.60	5.69	-33.78	9.63
Ethanol-water-SrCl₂	17.28	17.28	-0.02	16.04	7.20	19.64	3.60	-29.44	12.01
Ethanol-water-SrNO₃	10.03	3.39	177.80	13.11	-31.36	-2.57	-15.68	6.77	9.27
Acetic acid-water-CH₃COOK	2.01	-1.93	48.79	-1.46	7.56	2.32	3.78	-6.00	-1.51
Acetic acid-water-CH₃COOLi	-1.69	-4.60	31.41	-3.15	3.19	-1.55	1.59	-0.04	-3.33
Propanol-water-[emim] [triflate]	1.45	3.32	-8.02	-2.30	10.39	2.89	5.20	-8.99	-3.37
Propanol-water-[beim] [triflate]	0.03	1.44	-5.03	-3.69	10.33	1.47	5.16	-7.34	-6.57
Propanol-water-[bmpyr] [triflate]	0.48	1.49	-4.01	-3.10	9.79	1.80	4.90	-7.32	-5.15

System	1-Propanol-Water-LiNO₃		EtOH-Water-KAc
Algorithm	SHA^a	FEC-FRS^b	SHA^a	FEC-FRS^b
Rigorous model	E-NRTL	E-NRTL	E-NRTL	E-NRTL
Main feed - flow rate ("F")	100 kmol/h	100 kmol/h	100 kmol/h	100 kmol/h
Main feed - mole fraction ("Fx1")	0.3	0.3	0.3	0.3
Main feed - water mole fraction ("Fx2")	0.7	0.7	0.7	0.7
Main feed - temperature ("TF")	362 K	362 K	357 K	357 K
Main feed - stage	4	4	5-14	5-14
Salt feed - flow rate ("Q")	1 kmol/h	1 kmol/h	3 kmol/h	3 kmol/h
Salt feed - mole fraction ("Qx1")	0.8-0.95	0.8-0.95	0.95	0.95
Salt feed - salt mole fraction ("Fx2")	0.05-0.2	0.05-0.2	0.05	0.05
Salt feed - stage	1	1	1	1
Salt feed - temperature ("TQ")	360 K	360 K	360 K	360 K
Operating pressure ("P")	1 atm	1 atm	1 atm	1 atm
Number of equilibrium stages ("N")	7	7	7-16	7-16
Condenser duty ("Qc")	-100000 kJ/h	-100000 kJ/h	-500000 kJ/h	-500000 kJ/h
Reboiler duty ("Qr")	100000 kJ/h	100000 kJ/h	100000 kJ/h	100000 kJ/h

\frac{α_{s}}{α_{0}} = (\frac{y_{1, s}}{z_{1, s}} \frac{z_{2, s}}{y_{2, s}}) / (\frac{y_{1,0}}{x_{1,0}} \frac{x_{2,0}}{y_{2,0}}) = \frac{y_{1, s}}{y_{1,0}} \frac{y_{2,0}}{y_{2, s}}

\frac{α_{s}}{α_{0}} = \frac{γ_{1, s} γ_{2,0} x_{1, s} x_{2,0}}{γ_{1,0} γ_{2, s} x_{2, s} x_{1,0}} \frac{P_{1}^{o} (T_{s}) P_{2}^{o} (T)}{P_{2}^{o} (T_{s}) P_{1}^{o} (T)} = \frac{γ_{1, s} γ_{2,0}}{γ_{1,0} γ_{2, s}} \frac{P_{1}^{o} (T_{s}) P_{2}^{o} (T)}{P_{2}^{o} (T_{s}) P_{1}^{o} (T)}

l n (\frac{γ_{1, s}}{γ_{2, s}}) = β^{2} \{[z_{2}^{2} . A + z_{3}^{2} . A_{13} + z_{2} . z_{3} . (A + Δ A)] - [z_{1}^{2} . A + z_{3}^{2} . A_{23} + z_{1} . z_{3} . (A - Δ A)]\} {= β}^{2} [(1 - 2 . z_{1}) . A + (1 - 2 . z_{1}) . z_{3} A + z_{3}^{2} . Δ A + z_{3} Δ A] = β [A . (1 - 2 . z_{1}) + z_{3} Δ A] (19)

l n (\frac{α_{s}}{α_{0}}) = l n (\frac{γ_{1, s} γ_{2,0}}{γ_{1,0} γ_{2, s}}) = β [A . (1 - 2 . z_{1}) + z_{3} Δ A] - (1 - 2 . z_{1}) . A

l n (\frac{α_{s}}{α_{0}}) = l n (\frac{γ_{1, s} γ_{2,0}}{γ_{1,0} γ_{2, s}}) = l n (\frac{γ_{1, s}^{L R} γ_{1, s}^{S R} γ_{2,0}^{S R}}{γ_{2, s}^{L R} γ_{2, s}^{S R} γ_{1,0}^{S R}})

l n (γ_{i}^{L R}) = (2 A M_{i} d / b^{3} d_{i}) [1 + b I^{1 / 2} - {(1 + b I^{1 / 2})}^{- 1} - 2 l n (1 + b I^{1 / 2})]

l n (\frac{α_{s}}{α_{0}}) = l n (\frac{γ_{1, s} γ_{2,0}}{γ_{1,0} γ_{2, s}}) = l n (\frac{γ_{1, s}^{S R} γ_{2,0}^{S R}}{γ_{2, s}^{S R} γ_{1,0}^{S R}})

x_{i, F} = \frac{n_{i} - \sum_{i} h_{i} n_{3}}{\sum_{j} n_{j} + (ν_{3} - \sum_{j} h_{j}) n_{3}} = \frac{z_{i} - \sum_{i} h_{i} z_{3}}{1 + (ν_{3} - \sum_{j} h_{j}) z_{3}}; j =1,2

l n (γ_{1}) = l n [\frac{(1 - \frac{{h_{1} z}_{3}}{z_{1}}) (1 + {ν_{3} z}_{3})}{1 + (ν_{3} - h_{1} - h_{2}) z_{3}}] + l n (γ_{1,0}^{S R}) + l n (γ_{1}^{D H})

l n (γ_{2}) = l n [\frac{(1 - \frac{{h_{2} z}_{3}}{z_{2}}) (1 + {ν_{3} z}_{3})}{1 + (ν_{3} - h_{1} - h_{2}) z_{3}}] + l n (γ_{2,0}^{S R}) + l n (γ_{2}^{D H})

l n (\frac{α_{s}}{α_{0}}) = l n (\frac{γ_{1, s}^{S R} γ_{2,0}^{S R}}{γ_{2, s}^{S R} γ_{1,0}^{S R}}) = l n (\frac{x_{1, F} x_{2}}{x_{2, F} x_{1}})

l n (\frac{α_{s}}{α_{0}}) = l n [(1 - h_{1}^{\infty} z_{1} z_{3}) / (1 - h_{2}^{\infty} z_{2} z_{3})]

[1] *CTo whom correspondence should be addressed. E-mail: cmuzzio@fi.uba.ar. Tel.: +54 11 4343-0893

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Analysis and extension of the Furter equation, and its application in the simulation of saline extractive distillation columns

ABSTRACT