MODELLING AND PARAMETER ESTIMATION IN REACTIVE CONTINUOUS MIXTURES: THE CATALYTIC CRACKING OF ALKANES. PART I

Fragmentation kinetics is employed to model a continuous reactive mixture. An explicit solution is found and experimental data on the catalytic cracking of a mixture of alkanes are used for deactivation and kinetic parameter estimation.

modelling; catalytic cracking; mixture

Authorship

F. C. PEIXOTO

Instituto de Pesquisa e Desenvolvimento, Rio de Janeiro, RJ, BrasilInstituto de Pesquisa e DesenvolvimentoBrasilRio de Janeiro, RJ, BrasilInstituto de Pesquisa e Desenvolvimento, Rio de Janeiro, RJ, Brasil

J.L. de MEDEIROS

Universidade Federal do Rio de Janeiro, Depto. de Eng. Química , Escola de Química, Rio de Janeiro, RJ, BrasilUniversidade Federal do Rio de JaneiroBrasilRio de Janeiro, RJ, BrasilUniversidade Federal do Rio de Janeiro, Depto. de Eng. Química , Escola de Química, Rio de Janeiro, RJ, Brasil

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (13)
Tables (7)

Thumbnail

Figure 1:
Graphic representation of R(x)^tR(x) with m = k = 3.

Thumbnail

Figure 2:
Graphic representation of R(x)^tR(x) with m = k = 7.

Thumbnail

Figure 3:
Experimental compositional histogram versus estimated distribution (Z0(x)).

Thumbnail

Table 1:
1: Decay of the residue of Equation 36 with the size of matrix

Thumbnail

N° of carbonsMass fractions (% w/w)60.750072.930086.6400910.04001011.62001112.19001211.20001310.0300148.5500157.4000166.1100174.9900183.7300192.5000201.2700

Thumbnail

- lumped mass fraction around index x with D x=0.5) }Parameters (b )e , h Independent Variable (molecule size)xEstimated Dependent Variable ( - lumped mass fraction around index x with D x=0.5) Replications (pi) 1 Scale Factor (ri) 10% of Z0(xi) (experimental) Weight Matrix (W) Diag (p1/r1 ... pn/rn) Fundamental Variance Estimator (S2y) (n: number of experiments)Confidence Region (p: number of parameters)Objective Function (F ) Min{}

Thumbnail

Table 4: Statistical results in the fresh oil DCDF tuning.

Thumbnail

tf (min)2.042.053.354.969.5617.9530.90N° of carbonsMass fractions (% w/w)60.87000.89000.95000.94001.18001.18001.320073.29003.27003.50003.82003.82003.66004.150087.01007.12007.85007.70007.81008.03008.6300910.730010.230010.800010.280010.650010.500010.62001012.120011.720012.110011.830012.170011.990012.01001111.950011.950012.050011.930012.070011.950011.92001211.060011.190011.050011.160011.230010.980010.9600139.77009.99009.71009.88009.88009.70009.5800148.29008.53008.26008.39008.37008.28008.1700157.12007.25006.97007.04007.03006.96006.9300165.92005.91005.85005.90005.77005.79005.6600174.90004.90004.79004.76004.64004.79004.6300183.56003.61003.40003.46003.27003.40003.2400192.35002.38002.15002.21001.99002.17001.9900201.13001.15000.90000.97000.70000.93000.7400

Thumbnail

Table 6: Statistical entities for model tuning.

Thumbnail

Table 7: Statistical results for model tuning.

Figure 1: Graphic representation of R(x)^tR(x) with m = k = 3.

Figure 2: Graphic representation of R(x)^tR(x) with m = k = 7.

Figure 3: Experimental compositional histogram versus estimated distribution (Z0(x)).

Table 1: 1: Decay of the residue of Equation 36 with the size of matrix

N° of carbons	Mass fractions (% w/w)
6	0.7500
7	2.9300
8	6.6400
9	10.0400
10	11.6200
11	12.1900
12	11.2000
13	10.0300
14	8.5500
15	7.4000
16	6.1100
17	4.9900
18	3.7300
19	2.5000
20	1.2700

Parameters (b )	e , h
Independent Variable (molecule size)	x
Estimated Dependent Variable ( - lumped mass fraction around index x with D x=0.5)
Replications (p_i)	1
Scale Factor (r_i)	10% of Z0(x_i) (experimental)
Weight Matrix (W)	Diag (p₁/r₁ ... p_n/r_n)
Fundamental Variance Estimator (S²_y) (n: number of experiments)
Confidence Region (p: number of parameters)
Objective Function (F )	Min {}

Table 4: Statistical results in the fresh oil DCDF tuning.

1.0744

11.5212

S²_y = 0.0132

tf (min)	2.04	2.05	3.35	4.96	9.56	17.95	30.90
N° of carbons	Mass fractions (% w/w)
6	0.8700	0.8900	0.9500	0.9400	1.1800	1.1800	1.3200
7	3.2900	3.2700	3.5000	3.8200	3.8200	3.6600	4.1500
8	7.0100	7.1200	7.8500	7.7000	7.8100	8.0300	8.6300
9	10.7300	10.2300	10.8000	10.2800	10.6500	10.5000	10.6200
10	12.1200	11.7200	12.1100	11.8300	12.1700	11.9900	12.0100
11	11.9500	11.9500	12.0500	11.9300	12.0700	11.9500	11.9200
12	11.0600	11.1900	11.0500	11.1600	11.2300	10.9800	10.9600
13	9.7700	9.9900	9.7100	9.8800	9.8800	9.7000	9.5800
14	8.2900	8.5300	8.2600	8.3900	8.3700	8.2800	8.1700
15	7.1200	7.2500	6.9700	7.0400	7.0300	6.9600	6.9300
16	5.9200	5.9100	5.8500	5.9000	5.7700	5.7900	5.6600
17	4.9000	4.9000	4.7900	4.7600	4.6400	4.7900	4.6300
18	3.5600	3.6100	3.4000	3.4600	3.2700	3.4000	3.2400
19	2.3500	2.3800	2.1500	2.2100	1.9900	2.1700	1.9900
20	1.1300	1.1500	0.9000	0.9700	0.7000	0.9300	0.7400

Table 6: Statistical entities for model tuning.

Parameters (b )	kcin, Gd, Nd
Independent Variable	tf, g , x
Estimated Dependent Variable ( - lumped mass fraction around index x with D x=0.5, after reaction time tf)
Replications (p_i)	1
Scale Factor (r_i)	10% of (experimental)
Weight Matrix (W)	Diag (p₁/r₁ ... p_n/r_n)
Fundamental Variance Estimator (S²_y) (n: number of experiments)
Confidence Region (p: number of parameters)
Objective Function (F )	Min {}

Table 7: Statistical results for model tuning.

= 0.0051 kg cat/(kg oil-sec)					= 4.4140.10^-4 seg^-1
= 2.1742					S²_y = 0.0153

H =	2.7355	-5.2357	3.3899	-0.7014		-0.3687	0.1160	0.0875	0.0071
	23.4661	-19.5005	-5.1492	1.6845		0.4420	-0.3896	-0.2228	-0.0832
	1.8761	32.3961	-10.2372	-11.9353		-4.5583	-1.2111	-0.6328	-0.3220
	-23.8678	-26.6629	34.1358	22.0223		4.6287	-0.9839	-0.7475	-0.4170
	57.8383	5.2951	-59.0711	-30.7419		-0.0740	7.3352	3.6625	1.5871
	-118.5952	53.7782	75.1490	43.7424		-8.0628	-17.5540	-8.6564	-2.5965
	242.3835	-228.9712	-27.8408	-79.9112		24.5924	28.4299	19.3452	3.3452

How to cite

copy

Brazilian Society of Chemical Engineering Rua Líbero Badaró, 152 , 11. and., 01008-903 São Paulo SP Brazil, Tel.: +55 11 3107-8747, Fax.: +55 11 3104-4649, Fax: +55 11 3104-4649 - São Paulo - SP - Brazil
E-mail: rgiudici@usp.br

Acompanhe os números deste periódico no seu leitor de RSS

Versão para download de PDF

O periódico não forneceu este documento em formato PDF.

Versões e tradução automática

Versão original do texto

English

Tradução automática

Google Translator
Microsoft Translator

Como citar

RIS

BIBTEX

Outros formatos de citação e exportação:

SciELO - Scientific Electronic Library Online
Rua Dr. Diogo de Faria, 1087 – 9º andar – Vila Clementino 04037-003 São Paulo/SP - Brasil
E-mail: scielo@scielo.org

Leia a Declaração de Acesso Aberto

Métricas

MODELLING AND PARAMETER ESTIMATION IN REACTIVE CONTINUOUS MIXTURES: THE CATALYTIC CRACKING OF ALKANES. PART I

PlumX