Markov hydrocracking and Markov cathalitic hydrocracking revisited
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The document discusses advancements in Markov lumping hydrocracking and catalytic hydrocracking models, presented at the 18th international conference on catalysis, chemical engineering, and technology. New analytical expressions for continuous-time Markov chains and state evolution in hydrocracking processes are introduced, alongside methods for evaluating mean first passage times and application to industrial hydrocarbon production. It highlights contributions to understanding kinetics and process dynamics in hydrocracking from various research references.
![Abstract
The Markov lumping hydrocracking and Markov catalytic hydrocracking
analytical investigation are here extended.
The analytical expressions of the originating continuos-time Markov
chains are formulated in [I.L. MacDonald, E.A.D. Pienaar,
Continuous-time Markov-chain models for reaction systems: fast and
slow processes, Reac. Kinet. Mech. Cat. 136, 1757 (2023) ].
In the preset work, further analytcal expressions of continuous-time
Markov chains of lumping
hydrocracking, of fast lumping hydrocracking, of catalytical
hydrocracking and of detailed- balance catalytic hydrocracking are newly
analytically provided with; the time evolution of the
generic states are newly analytically written.
18th Edition of International Conference on Catalysis, Chemical Engineering a
Markov lumping hydrocracking and M](https://image.slidesharecdn.com/catalysis2024franceslideomlecian-240618141553-4e849de6/85/Markov-hydrocracking-and-Markov-cathalitic-hydrocracking-revisited-2-320.jpg)
![MacDonald four-lumps hydrocracking
The four-lumps hydrocracking is schematised after the
Markov-chain-related process, whose fundamental matrix Q̂4l is spelled as
Q̂4l ≡ {qij }
Q̂4l =
−k1 − k2 − k3 k1 k2 k3
0 −k4 − k5 k4 k5
0 0 −k6 k6
0 0 0 0
The values of the rates are considered from [?] and [?] as
k1 = 0.2323, k2 = 0.0487, k3 = 0.0336, k4 = 0, k5 = 0, k6 = 0.1244), i.e.
kj << 1∀j = 1, 2, ..., 6.
18th Edition of International Conference on Catalysis, Chemical Engineering a
Markov lumping hydrocracking and M](https://image.slidesharecdn.com/catalysis2024franceslideomlecian-240618141553-4e849de6/85/Markov-hydrocracking-and-Markov-cathalitic-hydrocracking-revisited-16-320.jpg)
![Outlook:
Lumps hydrocracking and catalysis processes
Bouzouita hydrocraking
- catalyst assumed is metallic Nikel on alumina
S. Alkhaldi, M.M. Husein, Hydrocracking of Heavy Oil by Means of In Situ Prepared Ultradispersed Nickel
Nanocatalyst, Energy Fuels 28, 643 (2014).
because of its hydrogenation function;
- experimental validation theoretically enquired about after the study of
the compositions on Thermo Scientific FLASH 2000 Organic Elemental
Analyzer and the study of the products from NMR data from Bruker
Avance (Quad Nucleus Probe).
Statistical analysis of the processes
- stochastic simulation in catalytic reactions.
A. Sengar, Multiscale reaction kinetics in different flow regimes. [Phd Thesis 1 (Research TU/e / Graduation
TU/e), Chemical Engineering and Chemistry]. Technische Universiteit Eindhoven (2019).
18th Edition of International Conference on Catalysis, Chemical Engineering a
Markov lumping hydrocracking and M](https://image.slidesharecdn.com/catalysis2024franceslideomlecian-240618141553-4e849de6/85/Markov-hydrocracking-and-Markov-cathalitic-hydrocracking-revisited-28-320.jpg)
Markov hydrocracking and Markov cathalitic hydrocracking revisited
- 1. Markov lumping hydrocracking and Markov catalytic hydrocracking revisited. 18th Edition of International Conference on Catalysis, Chemical Engineering and Technology From Discovery to Application: Catalytic Innovations for Industrial Progress Orchidea Maria Lecian Sapienza University of Rome, Rome, Italy. 17-19 June 2024 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 2. Abstract The Markov lumping hydrocracking and Markov catalytic hydrocracking analytical investigation are here extended. The analytical expressions of the originating continuos-time Markov chains are formulated in [I.L. MacDonald, E.A.D. Pienaar, Continuous-time Markov-chain models for reaction systems: fast and slow processes, Reac. Kinet. Mech. Cat. 136, 1757 (2023) ]. In the preset work, further analytcal expressions of continuous-time Markov chains of lumping hydrocracking, of fast lumping hydrocracking, of catalytical hydrocracking and of detailed- balance catalytic hydrocracking are newly analytically provided with; the time evolution of the generic states are newly analytically written. 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 3. Introduction Some hydrocracking models are considered. The analytical expressions of the Markov chains are analytically constructed. The analytical expressions of the probability matrix are newly provided with, whose opportune representation is indicated after the experimental data (available). The methods to evaluate the MFPT’s (Mean first Passage Times) of the states is recalled. The time evolution of the state (vector) is newly written. The method allows one to control the time evolution of the processes. The industrial applications in hydrocarbons production have to be projected accordingly. O.M. Lecian, Analytical expressions of Markov chain of metallic-Nikel-catalysts hydrocracking; O.M. Lecian, Analytical expressions of continuous-time Markov chains models of lumping hydrocracking; O.M. Lecian, Analytical expressions of continuous-time Markov chains models of catalytic hydrocracking. 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 4. Summary Introduction. Methodologies. Processes: - MacDonald three-lumps hydrocracking, - MacDonald three-lumps fast process, - MacDonald four-lumps hydrocracking, - MacDonald four-lumps ’fast’ process, - MacDonald catalysis, - MacDonald ’fast’ catalysis, - MacDonald detailed-balance catalysis. Industrial applications. Outlook. 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 5. Lump Bouzoita hydrocraking -from D. Bouzouita, A. Lelevic, C. Lorentz, R. Venderbosch, T.H. Pedersen, C. Geantet, Y. Schuurman, Co-processing bio-liquids with vacuum gasoil through hydrocracking, Applied catalysis B: Environmental 304, 120911 (2022). MacDonald catalysis - experimental data from L.A. Soto-Azuara, R. Ramı́rez-López, M.-B. del Carmen, I. Elizalde, Mathematical modeling of the hydrocracking kinetics of a heavy oil fraction using the discrete lumping approach: the effect of the variation of the lump number, Reac. Kinet. Mech. Cat. 135, 655 (2022). Further hydrocracking models - Six-lumps hydrocracking S. Sadighi, A. Ahmad, R. Seif Mohaddecy, 6Lump Kinetic Model for a Commercial Vacuum Gas Oil Hydrocracker, International Journal of Chemical Reactor Engineering 8 (2010); F.J. Vela, R. Palos, D. Trueba, T. Cordero-Lanzac, J. Bilbao, J.M. Arandes, A. Gutiérrez, A six-lump kinetic model for HDPE/VGO blend hydrocracking, Fuel 333, 126211 (2023). 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 6. Normalisation of the rates and error propagations Transition rates Ki of reactions are obtained form the experimental data. We will work with normalised rates ki as ki ≡ Ki P j Kj . In the absence of report of experimental errors from the cosidered items of bibliography, the best experimental conditions are assumed for the calculations of the error propagations. 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 7. MFPT’s- Populations of the states The time evolution of a particular vector (state) ⃗ u(t) is investigated in the presented bibliography, with initial conditions ⃗ u0 ≡ (1, 0, 0). As an example, in the MacDonald four-lumps hydrocracking, the Markovian time evolution is ⃗ u(t) = ⃗ u0P̂4l (t) = (e−µ1t , p12, p13, p14) with pij << 1. The time-evolutions of the eigenvalue µ1 at which the state 2 begins being populated is calculated in the Galerkin description after the corresponding MFPT t∗ ≡ t1 ± ∆t1 as λ̃τ = R ∞ t∗ e−θΛ(t+τ) e−θδ̃Λ dθ = 1 Λ(t+τ)+δ̃Λ e−(t∗ )(Λ(t+τ)+δ̃Λ) OML, Analytical Expressions of the Markov Chain of K-Ras4B Protein within the Catalytic Environment and a New Markov-State Model, IgMin Res., 2023; 1(2): 170-174. 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 8. Markov Catalytic processes The represenations of the matrices of the chains are chosen such that they obey the Kolmogorov forward and backward equations. OML, Analytical expressions of Markov chains of Michaelis-Menten enzymatic catalysis of rapid turnover of substrates with low enzyme sequestration and MSM’s implementation, Journal of Biomedical Sciences and Biotechnology Research, in press. 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 9. The four-Lump exact Bouzouita hydrocracking It takes place within - the ’vacuum gasoil’ (VGO) as feed, - the MD as middle distillates, - the N as naphta, and - the G as products. The states are here numbered as i = 1, 2, ..., 4 with normalised rates of the process as ki VGO q12 − − − → MD, q12 ≡ k1, VGO q13 − − − → N, q13 ≡ k2, VGO q14 − − − → G, q14 ≡ k3, MD q23 − − − → N, q23 ≡ k4, MD q24 − − − → G, q24 ≡ k5, N q34 − − − → G, q34 ≡ k6, The numerical values of the rates are written k1 = (1.0 ± 0.1%) min −1 , k2 = (0 ± 0.1%) min −1 , k3 = (0 ± 0.1%) min −1 , k4 = (0.4 ± 0.1%) min −1 , k5 = (0.2 ± 0.1%) min −1 , k6 = (0.6 ± 0.1%) min −1 . 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 10. The four-Lump exact Bouzouita hydrocracking revisited Markov chain The fundamental matrix Q̂ is here newly written as Q̂ ≡ {qij } Q̂ = −k1 − k2 − k3 k1 k2 k3 0 −k4 − k5 k4 k5 0 0 −k6 k6 0 0 0 0 0 The probability matrix P̂ is defined as P̂ = eQ̂t = {pij } P̂ = e−λ1t p12 p13 p14 0 e−λ2t p23 p24 0 0 e−λ3t p34 0 0 0 1 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 11. with p12 = o(k1), p13 = o(k2), p14 = o(k3), p23 = o(k4), p24 = o(k5), p34 = o(k6) For a generic vector ⃗ V (t) such that ⃗ v(t = 0) = ⃗ v0 ≡ (v1, v2, v3, v4), the time evolution is calculated as ⃗ v(t) = ⃗ v0P̂(t) as ⃗ v(t) = (v1e−λ1t +v2p12+v3p13+v4p14, v2e−λ2t +v3p23+v4p24, v3e−λ3t +v4p34, v4). 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 12. MacDonald Three-lumps hydrocracking revisited According to the quantitative (numerical) values of the rates, the following new analytical expressions hold. The corresponding probability P̂3l (t) matrix is written as P̂3l (t) ≡ eQ̂3l t P̂3l (t) = e−λ1t p12 p13 0 e−λ2t p23 0 0 1 with pij≡pij (t), i ̸= j as p12(t) = o(k1), p13(t) = o(k2), p23(t) = o(k3). 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 13. The generic vector (state) ⃗ v(t) with initial conditions ⃗ v0 ≡ (v1, v2, v3) i.e. ⃗ v(t) ≡ (v1(t), v2(t), v3(t)) is evolved under the Markov dynamics as ⃗ v(t) ≡ ⃗ v0P̂3l (t), i.e. ⃗ v(t) = (v1e−λ1t , p12v1 + v2e−λ2t , p13v1 + p23v2). 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 14. MacDonald three-lumps fast process The fast-process is described after the position of the rate k3 as k3 ≡ 0. The Markov chain is written an Q̂3l ≡ {qij } Q̂3l = −k1 − k2 k1 k2 0 −k2 0 0 0 0 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 15. MacDonald three-lumps fast process revisited The generic vector (state) is evolved under the Markovian dynamics as ⃗ vk3=0(t) as ⃗ vk3=0(t) ≡ (v1e−λ1t , p12v1 + v2, p13v1) 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 16. MacDonald four-lumps hydrocracking The four-lumps hydrocracking is schematised after the Markov-chain-related process, whose fundamental matrix Q̂4l is spelled as Q̂4l ≡ {qij } Q̂4l = −k1 − k2 − k3 k1 k2 k3 0 −k4 − k5 k4 k5 0 0 −k6 k6 0 0 0 0 The values of the rates are considered from [?] and [?] as k1 = 0.2323, k2 = 0.0487, k3 = 0.0336, k4 = 0, k5 = 0, k6 = 0.1244), i.e. kj << 1∀j = 1, 2, ..., 6. 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 17. MacDonald four-lumps hydrocracking revisited The probability matrix P̂4l (t) is calculated as P̂4l (t) ≡ e−Q̂6k t P̂4l (t) = e−µ1t p12 p13 p14 0 e−µ2t p23 p24 0 0 e−µ3t p34 0 0 0 1 with µ1 = −k1 − k2 − k3, µ2 = −k4 − k5, µ3 = −k6, 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 18. pij ≡ pij (t), i ̸= j as p12(t) = o(k1), p13(t) = o(k2), p14(t) = o(k3), p23(t) = o(k4), p24(t) = o(k5), p34(t) = o(k6). The time evolution of the vector (state) ⃗ v′ (t) from the generic initial condition ⃗ v′ 0 = (v1, v2, v − 3, v4) is calculated as ⃗ v′ (t) = (v1e−µ1t , p12v1 +e−µ2t v2, p13v1 +p23v2 +e−µ3t v3, p14v1 +p24v2 +p34v3 +v4). 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 19. MacDonald four-lumps ’fast’ process The four-lumps ’fast’ process is defined after the request k4 = k5 ≡ 0 as Q̂4lfp ≡ {qij } Q̂4lfp = −k1 − k2 − k3 k1 k2 k3 0 0 0 0 0 0 −k6 k6 0 0 0 0 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 20. MacDonald four-lumps ’fast’ process revisited The Markovian time evolution in the ’fast’ version of the four-lumps hydrocracking of the vector (state) ⃗ v′ (t) is written as ⃗ v′ (t) = (v1e−µ1t , p12v1 + e−µ2t v2, p13v1 + e−µ3t v3, p14v1 + p34v3 + v4). 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 21. MacDonald catalysis The process is a Markovian one described after the fundamental matrix Q̂ = {qij } Q̂ = −k1 k1 0 k2 −k2 − k3 k3 0 0 0 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 22. MacDonald catalysis revisited The probability matrix P̂ is written as P̂ = eQ̂t ≡ {pij (t)} P̂ = e−λ1t p12 0 p21 e−λ2t p23 0 0 1 with p12 = o(k1), p21 = o(k2), p23 = o(k3). The generic vector ⃗ v(t) = ⃗ v(t) = (v1(t), v2(t), v3(t)) is considered; after the initial conditions ⃗ v0 ≡ (v1, v2, v3), the Markovian time evolution of the generic vector ⃗ v(t) is studied, whose expression is written as ⃗ v(t) = ⃗ v0P̂ = (v1eλ1t + p21v2, p12v1 + e−λ2t v2, p23v2 + v3). 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 23. MacDonald ’fast’ catalysis The process is a Markovian one described after the MacDonald catalysis with k3 ≡ 0 as Q̂ = {qij } Q̂ = −k1 k1 0 k2 −k2 0 0 0 0 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 24. MacDonald ’fast’ catalysis revisited The ’fast’ MacDonald dynamics is here newly investigated from k3 ≡ 0. The transition matrix P̂f of the MacDonald ’fast’ catalysis is written as P̂f = eQ̂f t ≡ {pij (t)} P̂ = e−λ1t p12 0 p21 e−λ2t 0 0 0 1 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 25. MacDonald detailed-balance catalysis The detailed-balance catalysis A1 + A2 ⇌ A2 + A3 ← 2A2 is studied according to the fundamental matrix Q̂db as Q̂db = {qij } Q̂db = −k1 k1 0 k2 −k2 0 0 k3 −k3 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 26. MacDonald detailed-balance catalysis revisited The probability matrix P̂db is here newly calculated as P̂db = eQ̂dbt P̂db = {pij } = e−λ1t p12 0 p21 e−λ2t 0 0 p32 e−λ3t with p12 = o(k1), p21 = o(k2), p32 = o(k3). The time evolution of the generic vector ⃗ v is ⃗ v(t) = ⃗ v0P̂db = (e−λ2t v1 + p21v2, p12v1 + e−λ−2t v2 + p32v3, e−λ3t ve). 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 27. Industrial applications Theoretical features - steps of hydorckacking J.W. Ward, Hydrocracking processes and catalysts, Fuel Processing Technology 35, 55 (1993). - kynetics of hydrocracking L.A. Soto-Azuara, R. Ramı́rez-López, M.-B. del Carmen, I. Elizalde Mathematical modeling of the hydrocracking kinetics of a heavy oil fraction using the discrete lumping approach: the effect of the variation of the lump number, Reac. Kinet. Mech. Cat. 135, 655 (2022). Data analyses S. S. Hosseini Boosari, N. Makouei, P. Stewart, Application of Bayesian Approach in the Parameter Estimation of Continuous Lumping Kinetic Model of Hydrocracking Process, Advances in Chemical Engineering and Science 7, 257 (2017); L. Iapteff, J. Jacques, M. Rolland, B. Celse, Modeling the hydrocracking process with kriging through Bayesian Transfer Learning, 2021 AIChE Virtual Spring Meeting and 17th Global Congress on Process Safety, Apr 2021, virtual, United States. ffhal-03561361f. Industrial plants - relevance of hydrocracking in the design of experiments about carbonaceous material for the production of hydrocarubres; D.A. Duncan, Process for hydrocracking carbonaceous material to provide fuels or chemical feed stock, United States. https://www.osti.gov/servlets/purl/863721 (1980). - features of the carbonaceous-material plants. M.S. Sarli, S.J. McGovern, D.W. Lewis, Improved hydrocracker temperature control: Mobil quench zone technology, United States. https://www.osti.gov/biblio/7286052 (1993). 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 28. Outlook: Lumps hydrocracking and catalysis processes Bouzouita hydrocraking - catalyst assumed is metallic Nikel on alumina S. Alkhaldi, M.M. Husein, Hydrocracking of Heavy Oil by Means of In Situ Prepared Ultradispersed Nickel Nanocatalyst, Energy Fuels 28, 643 (2014). because of its hydrogenation function; - experimental validation theoretically enquired about after the study of the compositions on Thermo Scientific FLASH 2000 Organic Elemental Analyzer and the study of the products from NMR data from Bruker Avance (Quad Nucleus Probe). Statistical analysis of the processes - stochastic simulation in catalytic reactions. A. Sengar, Multiscale reaction kinetics in different flow regimes. [Phd Thesis 1 (Research TU/e / Graduation TU/e), Chemical Engineering and Chemistry]. Technische Universiteit Eindhoven (2019). 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M
- 29. Thank You for Your attention. 18th Edition of International Conference on Catalysis, Chemical Engineering a Markov lumping hydrocracking and M