Non-linear optimisation and energy integration of a particles separation–classification process

Figures & data

Figure 1. Particle size distributions for studied materials.

Figure 2. Particle size distributions accumulation for studied materials.

Table 1. Materials properties.

	Molecular weight	Density	Specific heat^a
Material	MW	Kg.m	J.gmol.K	Reference
Air	28.96	1.2
				Himmelblau (1997)
Dolomite	184.42	2770
		grain density
				Gupta (2011)
Limestone	100.09	2680
		grain density		Himmelblau (1997)
Sawdust	13.1	530
		with 12% moisture content		Jiménez, Baquero, and Diaz (2006)
Toner	100.1	568
		bulk density		XEROX (2002)

^aCp= a+bT+c.T+d.T; Cp= a+b.T+c.T+d.T+e.T+g.T+h.T; Cp= a+b.T+c.T.

Figure 3. Basic scheme for particles separation–classification process (BS). HE: heat exchanger; PF: powder feeder; CY: cyclone; FI: filter; BL: blower; F: process streams. and : control volumes for energy purpose.

Figure 4. Cyclone main dimensions. Tangential input. a: input height; b: input width; Dc: diameter; B: bottom outlet diameter, Ds: top outlet diameter; S: output height; h: cylindrical height; z: conical height, H: total height.

Figure 5. Energy integration scheme (EI). Mix: mixer; SP1: splitter 1; SP2: splitter 2; F: process streams. and : control volumes for energy purpose.

Table 2. Mass fractions x(i,j) for BS and EI process streams.

Stream	x(i,1)	x(i,2)	x(i,1)	x(i,2)
(i)	BS scheme	BS scheme	EI scheme	BS scheme
1	1	0	1	0
2	1	0	x(3,1)	x(3,2)
3	0	1	1-x(3,2)	Tol.
4	1-x(4,2)		0	1
5	0	1	1-x(5,2)
6	1-x(6,2)		0	1
7	0	1	1-x(7,2)
8	1-x(8,2)		0	1
9	x(8,1)	x(8,2)	1-x(9,2)
10	–	–	x(9,1)	x(9,2)
11	–	–	x(10,1)	x(10,2)
12	–	–	x(11,1)	x(11,2)
13	–	–	x(12,1)	x(12,2)
14	–	–	x(13,1)	x(13,2)

Tol.: maximum tolerance of fine particles at cyclone input.

Table 3. Geometric constraints for different cyclones models.

Dimensionless ratio	Stairmand (ST)	Swift (SW)
a/Dc	0.50	0.44
b/Dc	0.20	0.21
S/Dc	0.50	0.50
Ds/Dc	0.50	0.40
h/Dc	1.50	1.40
z/Dc	2.50	2.50
H/Dc	4.00	3.90
B/Dc	0.38	0.40

Table 4. Optimal process variables for BS scheme. C2:500 g/m.

	Limestone-1		Limestone-2		Dolomite		Sawdust		Toner
Variables	ST	SW	ST	SW	ST	SW	ST	SW	ST	SW
	90.66	90.45	92.97	92.66	85.89	85.68	99.90	99.87	81.50	78.27
Dc (m)	0.99	1.06	0.99	1.06	1.00	1.06	0.93	1.06	0.93	1.06
Ve (m/s)	24.79	23.30	24.79	23.30	24.36	23.28	28.00	23.30	28.00	23.30
	1,939.8	2,488.2	1,939.8	2,488.2	1,873.5	2,483.5	2,475.6	2,488.2	2,475.6	2,488.2
a (m)	0.49	0.46	0.49	0.46	0.50	0.46	0.46	0.46	0.46	0.46
b (m)	0.20	0.22	0.20	0.22	0.20	0.22	0.18	0.22	0.18	0.22
H (m)	3.95	4.12	3.95	4.12	3.98	4.12	3.72	4.12	3.72	4.12
x(6,1)	95.51	95.41	96.58	96.43	93.36	93.26	99.95	99.93	91.47	90.12
x(8,1)	99.77	99.76	99.82	99.82	99.65	99.64	99.998	99.997	99.54	99.46

Figure 6. Optimal process flows. BS scheme for sawdust particles. Flows [kg/s].

Figure 7. Optimal process flows. EI scheme for sawdust particles. Flows [kg/s].

Table 5. Energy consumptions for different process schemes and materials.

Variables	Dolomite		Limestone-1		Limestone-2		Sawdust		Toner
	BS	EI	BS	EI	BS	EI	BS	EI	BS	EI
Q (MWh)	865.85	375.02	865.85	375.05	878.11	387.41	18,450.62	7,815.22	990.13	499.74
Q (MWh)	130.91	130.87	130.28	131.13	133.20	133.15	1,134.24	557.53	142.01	142.29
Energy saving (MWh)	490.83		490.81		490.70		10,635.54		490.39
Energy saving (US$/h)	392.66		392.65		392.56		8,508.43		392.31

Himmelblau, D. M. 1997. “Principios básicos y cálculos en ingeniería química.” Pearson Educación. https://books.google.com.ar/books?id=JgysV9f1HmEC

 Google Scholar

Gupta, Harsh. 2011. “Encyclopedia of Solid Earth.” Geophysics 1: 1539.

 Google Scholar

Jiménez, L. F., M. C. Baquero, and J. J. Diaz. 2006. ““Carbonizados de Origen Vegetal (COV) Para la Generación de Antroposoles Obtención y Caracterización Fisicoquímica.” Revista Colombiana de Química 35 (2): 177–190. http://www.redalyc.org/articulo.oa?id=309026669001

 Google Scholar

XEROX. 2002. Ficha de Seguridad. Technical Report. España: XEROX.

 Google Scholar