My adsorption journey: Ups and downs and other stories

A minha jornada em adsorção: altos e baixos e outras estórias

INTRODUCTION: FROM 1968 TO 1976

Undergraduate studies, training in industry, doctoral research, and teaching in Angola

When Mauricio Motta invited me to contribute to the special issue on Adsorption for "Engenharia Sanitária and Ambiental," I was in trouble: I couldn't say "no" to a friend, yet my task was not easy since I had recently presented my perspectives on the adsorption area (RODRIGUES, 2020, 2023a). Therefore, I decided to rephrase my ideas, linking them to my exchanges with Brazil, as illustrated in my "Life stories" (RODRIGUES, 2023b).

I graduated in Chemical Engineering (ChE) from the University of Porto in 1968. It was the era of hippies and the May 1968 revolution in France. At that time, ChE was a 6-year program, with the first 3 years at the Faculty of Sciences (now the Rectorate of University of Porto — Figure 1A) and the final 3 years at the Faculty of Engineering (FEUP) in the old school on Rua dos Bragas (now the Law School of University of Porto — Figure 1B). In 2000, FEUP relocated to a new campus (Figure 1C). From those times, classes of Analytical Chemistry in the lab shown in Figure 1D, now part of the Museum of University of Porto as "Laboratório de Química Ferreira da Silva," are particularly memorable; The task was to identify ions in a liquid mixture and present the results to the professor. I was finding nickel, but the professor repeatedly indicated that the result was incorrect. After obtaining the same (wrong?) result again, the professor, perhaps intrigued by the result, observed each step of the process. Although the initial mixture contained no Ni, an old lab claw was contaminating the initial mixture with it. This experience served as a valuable life lesson: watch closely what students do in the lab.

Figure 1
(A) Faculty of Sciences of University of Porto (now Rectorate of UP); (B) old School of Engineering; (C) new School of Engineering of University of Porto; and (D) Laboratory of Chemistry "Ferreira da Silva".

At that time, obtaining a Diploma in ChE (back then officially called Chemical-Industrial Engineering) required completing 3 training periods in industry/research labs: I spent 2 months at the nitric acid plant of Nitratos de Portugal in Alverca (Figure 2A), 1 month in the dyeing laboratory of Hoechst in Porto (Figure 2B), and the final month in the Electrochemistry and Corrosion laboratory in the Electrical Engineering department of FEUP.

Figure 2
(A) Nitric acid plant in Nitratos de Portugal (1966); (B) training in Hoechst lab (1967); and (C) Luanda and Bird, Stewart and Lighfoot (1968).

In 1968, Portugal was engaged in wars across its colonies, making it virtually impossible to secure employment before completing military service. This could consume 4 years of our lives — 2 years of training before being deployed to one of the colonies for an additional 2 years. An opportunity arose for paid training in Luanda, Angola (Figure 2C), offered by the Minister of Economy, which I applied for. Upon arriving there in October 1968, I started working at the CUCA brewery plant for several months, followed by a few months in the PETROFINA oil refinery laboratory (now SONANGOL).

Teaching at the University of Luanda marked a significant turning point for me. I found in the library the old book "Adsorption" (MANTELL, 1945), along with the Spanish version of "Transport phenomena" (BIRD; STEWART; LIGHTFOOT, 1961). During my studies at University of Porto, nobody mentioned that book, which represents the Second Paradigm of ChE: the Chemical Engineering Science Movement, reflecting a time lag of about 10 years in Portuguese academia.

Teaching at the University of Luanda allowed me to postpone the military service until the age of 30, leading to a move to Nancy in 1970 to pursue a doctoral thesis. My D.E.A. (Diplome d’Études Approfondies or the French MSc) supervisor was Pierre Le Goff and co-supervisor G. Gau in the first year of my research on "Étude de la carbonitruration du vanadium sur un support poreux à grande surface interne" (RODRIGUES, 1971). This period marked the beginning of involvement in adsorption and reaction studies. My focus then shifted to research on ion exchange with neutralization for my doctoral thesis, under the supervision of Le Goff and D. Tondeur (RODRIGUES, 1973), carried out at the Centre de Cinétique Physique et Chimique (CCPC) of CNRS (now LCPME) (Figure 3). The research lab was located near the Faculty of Sciences of the University of Nancy I in Villers-lès-Nancy. I attended lectures from P. Le Goff on Chemical Engineering, Villermaux on Chemical Reaction Engineering (CRE), and System Dynamics in the old town at ENSIC, rue Déglin (the building is now being repurposed), and the ENSIC library, which was located on rue Grandville (Figure 4).

Figure 3
P. Le Goff, D. Tondeur and Centre de Cinétique Physique et Chimique of CNRS (now LCPME).

Figure 4
ENSIC: building at rue Déglin in 1970, entrance to the library rue Grandville, Jacques Villermaux and old town of Nancy (Porte de la Craffe and Place Stanislas).

Le Goff's lectures were particularly memorable for his approach to modeling and simulating adsorption processes. He treated it as just another problem in chemical engineering; his recipe included writing of:

• Conservation equations (mass, energy, momentum, electric charge).

• Equilibrium laws at the interface(s).

• Constitutive laws (e.g. ideal gas law, Hooke's law).

• Kinetic laws of heat/mass transfer and reaction.

• Initial and boundary conditions.

• Optimization criterion.

From Villermaux, I learned CRE in detail and an appreciation for his System Dynamics course; system analogy is something I always keep in mind. Tondeur provided me with an equilibrium theory of adsorption, ion exchange, and chromatographic processes.

The basics for understanding the propagation of concentration waves in fixed-bed adsorption columns come from a "simplissime" model using Le Goff's language based on plug flow for the fluid phase, isothermal operation, negligible pressure drop, and infinitely fast kinetics of mass transfer. For dilute systems, model equations are simply the mass balance in a volume element of the column of thickness dz (Equation 1) and the adsorption equilibrium isotherm (Equation 2).

(1) $$u_0\frac{\partial c_i}{\partial z}+\epsilon \frac{\partial c_i}{\partial t}+\left(1-\epsilon \right)\frac{\partial q_i^{*}}{\partial t}=0$$

(2) $$q_i^{*}=f\left(c_i\right)$$

Where c_i is the fluid phase concentration, ε is the bed porosity, u₀ is the superficial velocity, t is time, and $q_i^{*}$ is the adsorbed phase concentration in equilibrium with c_i. By combining Equations 1 and 2, the velocity of propagation of a concentration c_i is obtained, which depends on the slope of the adsorption equilibrium isotherm, f ‘(c_i) (Equation 3).

(3) $$u_{c_i}=\frac{\partial z}{\partial t}{|}_{c_i}=\frac{u_0}{\epsilon +(1-\epsilon )f\text{'}(c_{i)}}$$

This is the De Vault equation (DE VAULT, 1943), derived in 1943, which contains the basic concepts of adsorption: unfavorable isotherms lead to dispersive fronts, while favorable isotherms (Langmuir type) lead to compressive fronts and shocks (Figure 5). It shows how the shape of adsorption isotherms is the primary factor to control the shape of a breakthrough curve. Secondary factors include axial/radial dispersion, kinetics of heat/mass transfer, etc.

Figure 5
Dispersive and compressive fronts linked to the shape of adsorption equilibrium isotherms (unfavorable and favorable).

Revisiting the unpublished results of the D.E.A. dissertation is intriguing. These results can be viewed as a process akin to chemical vapor deposition (CVD) of Vanadium from a challenging source, VCl₄, onto an activated carbon support in presence of H₂ to produce vanadium carbide (VC) (Materials Engineering). Alternatively, from a Process Engineering perspective, it can be seen as the production of hydrogen, syngas, or ammonia in two transport reactors, similar to Fluid Catalytic Cracking (FCC), where the solid alternates between CV and vanadium nitride (VN) depending on the feed stream: in one reactor, the solid is VN and the feed is CH₄, and the exit gas is H₂ +N₂, while the solid is transformed in VC; in the other reactor, solid VC is ideally converted back to VN when the feed is air, and the exit gas is CO.

The preparation of VC in a 100 mL reactor, operating at a temperature of 900°C in presence of hydrogen flowrate of 50 L/h for the entrainment of VCl₄ vapor (boiling point at 125°C), follows the reaction (Equation 4):

(4) $${\text{VCl}}_4+2{\text{H}}_2+\text{C}=\text{CV}+4\text{HCl}$$

The experimental setup is shown in Figure 5. The adsorption equilibrium isotherms of Kr at 77K on the activated carbon support alone, as well as on the support impregnated with VC, display similar hysteresis cycles and microporosity after the formation of VC, with a specific surface area of approximately 1,200 m²/g (Figures 6A and 6B).

Figure 6
(A) Experimental set-up for the preparation of vanadium carbide over activated carbon particles. (B) Adsorption equilibrium isotherms of Kr at 77K over activated carbon (1) and activated carbon with vanadium carbide (2). Sample 1 with 21 mg in the cell and sample 2 with 19 mg in the cell.

In the two transport reactors depicted in Figure 7, the reactions taking place are (Equations 5 and 6):

Figure 7
Transport reactors: one containing solid vanadium nitride fed by methane to produce H₂ + N₂; the other with circulating solid vanadium carbide fed by air to produce CO.

(5) $$\text{2}{\text{CH}}_4+2\text{NV}=2\text{CV}+{\text{N}}_2+4{\text{H}}_2$$

(6) $$\text{2 CV}+{\text{N}}_2+{\text{O}}_2=2\text{NV}+2\text{CO}$$

The concept had some connection with a patent from UOP (POHLENZ; SCOTT, 1966), titled "Method for hydrogen production by catalytic decomposition of a gaseous hydrocarbon stream." In this process, methane is decomposed into carbon and hydrogen in one reactor, while in the second reactor, the carbon deposited on the catalyst is oxidized with air, producing flue gas and regenerating the catalyst.

My doctoral thesis focused on the anionic step of water demineralization illustrated by the exchange between chloride ions and sulphate ions from water solution and a resin in OH^- form. The ion exchange equilibrium isotherm between Cl^- and OH^- is sketched by line 1 in Figure 8A, when the cation in the liquid solution is Na⁺ from sodium chloride (NaCl). However, if the cation in the solution is H⁺ from HCl, these H⁺ ions will neutralize the OH^- ions leaving the resin when exchanged with Cl^- ions. This scenario presents a challenge of ion exchange accompanied by neutralization, also known as Reaction-Enhanced Ion Exchange Separation, represented by Equations 7a and 7b:

Figure 8
(A) Ion exchange equilibrium isotherm Cl^-/OH- (line 1) and accompanied by neutralization (line 2); (B) Temporary residence card from my time in Nancy; (C) Ion exchange with neutralization in a batch system $\left(1-\frac{q_i{V}_R}{C_{io}{V}_L}\right)$ versus time t in semi-log scale.

(7a) $$RO{H}^{-}+C{l}^{-}⥂RC{l}^{-}+O{H}^{-}$$

(7b) $$H^{+}+O{H}^{-}\to H_{2}O$$

The neutralization reaction in Equation 7b displaces the equilibrium OH^-/Cl^- to the right side in Equation 7a. As a result, the isotherm becomes a rectangular or irreversible isotherm (line 2 in Figure 8A).

For film diffusion control in infinite bath systems, the electroneutrality equation dans le film implies that C_OH − ≤ C_H + and C_OH − ≤ 10^–7M, since the dissociation constant of water is K_w=10^-14 mole²/L². For solutions with H⁺ concentration well above 10^-7M, the OH^- ions are consumed at the particle surface. In this care, there is diffusion of H⁺ and Cl^- ions within a film of water and the flux of Cl^- ions is $\phi =D\frac{C_{Cl-}}{\delta }$ with $D=\frac{2D_{Cl-}{D}_{H+}}{D_{Cl-}+D_{H+}}$.

The concentration of chloride ions in the resin can be calculated using Equation 7c:

(7c) $$q_{Cl-}\left(t\right)=\frac{6D}{\delta d_p}{C}_{Cl-\left(t\right)}t$$

Where the concentration of chloride ions remains constant in infinite bath systems. Similar analysis can be made for finite volume systems with more chloride ions in solution than in the resin C_iV_L > q_iV_R, leading to Equation 7d:

(7d) $$\ln \left(1-\frac{q_i{V}_R}{C_{io}{V}_L}\right)=-\frac{6D{V}_R}{d_p\delta V_L}t$$

There is a time t_c when the concentration in the resin reaches its capacity Q; after that, the concentration in the solution stabilizes at a final value C_if. At that time, it resembled what is depicted in Figure 8B. Some experimental results are shown in Figure 8C.

Experiments were also carried out in a well-designed, perfectly mixed reactor (Figure 9A) and the results, shown in Figure 9B, were fitted with K = 500, approaching the rectangular ion-exchange isotherm when neutralization occurs.

Figure 9
The home-made continuous perfectly mixed reactor with volume 79 mL (A) and experimental results for Cl^-/OH^- ion exchange accompanied by neutralization: resin volume 21 mL, flowrate 13.44 mL/min; HCl concentration in the feed 0.01N, t_st=205.4 min (B).

The general ion-exchange reaction can be written as Equation 8:

(8) $${\left(C{l}^{-}{C}^{+}\right)}_L+RO{H}^{-}⥂RC{l}^{-}+O{H}^{-}+C^{+}$$

If the cation C is H⁺, neutralization occurs, shiftting the equilibrium in Equation 8 to the right. For an ion-exchange equilibrium described by the constant separation factor K (Equation 9):

(9) $$K=\frac{y\left(1-x\right)}{\left(1-y\right)x}\text{or}y=\frac{Kx}{1+\left(K-1\right)x}$$

Where the normalized concentrations of chloride ions (species i) in the resin with capacity Q and in the liquid solution are $y=\frac{q_i}{Q}$ and $x=\frac{C_i}{C_T}$, respectively, the mass balance for the open CSTR reactor with feed concentration of chloride ions C_io, assuming equilibrium theory, is given by Equation 10:

(10) $$\frac{dx}{d\theta }=\frac{1-x}{g\left(x\right)}$$

Where the dimensionless time $\theta =\frac{t}{t_{st}}$ and $g\left(x\right)=\frac{1+\xi y\prime \left(x\right)}{1+\xi }$; the stoichiometric time is t_st = 1 + ξ, and the slope of the normalized isotherm is $y\prime \left(x\right)=\frac{K}{{\left[1+\left(K-1\right)x\right]}^2}$.

After convenient linearization of g(x) the normalized response of the reactor to a step input in concentration C_io is (Equation 11):

(11) $$x=\left[1-e^{-\frac{\theta -{\theta }_o}{p}}\right]H\left(\theta -{\theta }_o\right)$$

With $p=\frac{\xi +K}{\left(1+\xi \right)K}$ and θ_o as the normalized time until which the outlet concentration is zero.

After completing my doctoral thesis, I returned to Angola. Following the April 25^th revolution in 1974, I was enrolled in the Army and returned to Portugal in October 1975, just before Angola gained independence.

I briefly taught at the University of Évora (then known as Instituto Universitário de Évora) for one semester, and completed my Habilitation (Agregação) at Instituto Superior Técnico (IST), now part of the University of Lisbon, presenting a lecture on "Fundamental concepts in Chemical reaction Engineering" (RODRIGUES, 1976) before joining the Department of Chemical Engineering of FEUP in September 1976. I was back home, on Rua dos Bragas.

Back to the University of Porto in 1976: The origin of the Laboratory of Separation and Reaction Engineering

Upon arriving at the University of Porto, I established a research line focused on "Separation and Reaction processes in porous and disperse media" with 3 PhD students working on "Adsorption of phenol in polymeric resins and parametric pumping" (Cyclic separations), "Wastewater denitrification in biological fluidized bed reactor" ((Bio)Reaction Engineering), and on the coupling of adsorption and reaction (Process Intensification). My connection with Brazil began in 1978, largely due to the late Giulio Massarani from COPPE (Figure 10). I first encountered his name in 1973 while working on my thesis and attending at NATO Advanced Study Institute on Filtration in Cambridge, UK. One of the lecturers was Frank Tiller from the University of Houston and mentioned Massarani, who had connections with COPPE and spoke some Portuguese. I was then invited to attend the VI ENEMP in Rio Claro, where I met two of his PhD students, José Freire and Satoshi Tobinaga. Time flies, and they have also retired. During this time, I also visited Universidade de Campinas (UNICAMP) (a turbulent start involving Saúl d’Ávila, João Pereira, César Santana…), UEM (Renato Sprung and Flávio Moraes returning from Cambridge), Aracaju (João d’Ávila), and COPPE, directed by Carlos Perlingeiro.

Figure 10
Giulio Massarani responsible for my "discovery" of Brazil in 1978 and Célio Cavalcante Jr., my second connection with Brazil in 1988.

Between 1978 to 1988, I organized four NATO Advanced Study Institutes in Portugal on Percolation Processes. Theory and applications (RODRIGUES; TONDEUR, 1980), Multiphase chemical reactors (RODRIGUES; CALO; SWEED, 1981), Ion Exchange Science and Technology (RODRIGUES, 1986), and Adsorption Science and Technology (RODRIGUES; LEVAN; TONDEUR, 1989). These events provided an opportunity to bring some of the world's leading researchers to Portugal and expose my people to global advancements. In 1988, while organizing the NATO ASI on Adsorption: Science and Technology, I was also on sabbatical at the University of Virginia in Charlotesville; this was after the sabbatical of Douglas LeVan in Porto in 1985 and a visit from Elmer Gaden, Head of ChE department at UVa, to the Biotechnology School of the Catholic University in Porto.

My second connection with Brazil stems from Célio Cavalcante Jr. I met Célio at the NATO ASI "Adsorption: Science and Technology" in Vimeiro (1988), where he was working at COPENE (now Braskem) in Camaçari, near Salvador. He later pursued a PhD under the supervision of Douglas Ruthven at New Brunswick, in the NATO ASI on Adsorption and eventually became a professor at UFC in his hometown of Fortaleza.

The need for modeling and simulation tools

In the late 1970s and 1980s, I felt the need to invest on modeling and simulation of adsorptive processes accounting for "second-order factors," which required learning numerical methods and finding the best available routines. The driving force was to generate more comprehensive models of cyclic adsorption processes including kinetic and thermal aspects. In the early PhD projects within my group, all computer programs were presented as annex in the theses (COSTA, 1984; LOUREIRO, 1986). It was the time to deal with Orthogonal Collocation in Finite Elements (OCFE), PDECOL (MADSEN; SINCOVEC, 1979), getting help from Hindmarsh from Lawrence Livermore Laboratory with GEAR (HINDMARSH, 1974), GEARIB (HINDMARSH, 1976), LSODE, LSODI packages (HINDMARSH, 1980), the method of lines (SCHIESSER, 1976), and hyperbolic systems (LOUREIRO; RODRIGUES, 1991), before embarking in the development of the Moving Finite Element Method (MFEM) in the PhD thesis of C.A. Sereno (SERENO, 1989; SERENO; RODRIGUES; VILLADSEN, 1991, 1992) with the help of John Villadsen. This approach was particularly suited for the movement of sharp fronts in adsorption processes, following the original work of Miller and Miller (1981). We continued to explore this research line in PhD theses of Maria do Carmo Coimbra (COIMBRA, 2000) and Jaime Rodrigues (RODRIGUES, 2010), culminating in a summary of our contributions in a book (COIMBRA et al., 2016).

A significant milestone was the paper by F.A. da Silva, "A general package for the simulation of cyclic adsorption processes" (DA SILVA; SILVA; RODRIGUES, 1999); it was applied by Davesac from UFSC in his MSc thesis, "A package for thermal parametric pumping adsorptive processes" (DAVESAC et al., 1999), following the PhD thesis of Licinio Ferreira, funded by a EU project (FERREIRA; RODRIGUES, 1995a, 1995b).

In the 1990s, I was involved at the request of the Rector of University of Porto in the UNESCO Unitwin Chair in Chemical Engineering at UFSC, Florianopolis, representing the Santander Group (University of Cantabria, TU Eindhoven, University of Leeds, University of Porto), with UFSC represented by Ariovaldo Bolzan. For about 5 years, I taught there for 2 weeks every August in the MSc program alongside Piet Kerkhoff (Adsorption), Colin Mc Greavy (CRE), Clovis Maliska, Evaristo Biscaia, and Feyo de Azevedo (System Dynamics and Control). I met various colleagues and friends for life there. Regina Moreira visited FEUP, where she prepared Carbon Molecular Sieves (CMS) for air separation and many of her students came to Porto for several projects. Selene Ulson de Souza was involved in a CYTED project, and I met Diana Azevedo from UFC in the System Dynamics and Control course (1995), who later pursued a full PhD with me in Porto (AZEVEDO, 2001).

I remember walking with Colin Mc Greavy in Florianopolis, where he predicted that in the future, with the advent of user-friendly software tools, the teaching load of numerical methods would decrease. He was talking against himself since he used those tools in the simulation of heterogeneous catalytic reactors; his prediction was accurate, as many packages emerged, including those from Imperial College (Sargent's Center for Process Systems Engineering) and spin-off as Speedup, PSE Ltd (now Siemens). In my group, I believe F.A. da Silva was the first student to test gPROMS (SIEMENS PROCESS SYSTEMS ENGINEERING, 2022) by the end of his PhD. Since then, all students have used gPROMS, both for the good and the bad.

Those years were filled with activity in the adsorption area, with many European projects covering novel topics as chiral separations with simulated moving bed and olefins/paraffins separation by pressure swing adsorption and reaction engineering. We hosted CHEMPOR’93 in Porto (Figure 11A), featuring plenary lectures by Horvath, Reklaitis, Le Goff, Mann, and Tondeur and our connections in Brazil organized the First Brazilian Adsorption meeting in Fortaleza in 1996 (Figure 11B), where Ruthven and Mazzotti gave talks, and I presented on "Understanding Adsorption: Wave propagation, permeable adsorbents, cycles and hybrid processes."

Figure 11
(A) Connection with UFSC since 1994 (Top): Regina Moreira, Selene Ulson de Souza, and Ariovaldo Bolzan; Bottom: CHEMPOR’93; (B) First Brazilian Meeting on Adsorption, Fortaleza 1996; (C) Diana in the old FEUP in the first project with COPENE and UFC, 1996 before coming to PhD.

From batch to continuous adsorption processes

What do we really need to understand adsorption processes? The answer is: get adsorption equilibrium isotherms first. This can be demonstrated with a liquid-solid adsorption example. The procedure involves conducting a series of N experiments at constant temperature in batch systems where a given volume of solution V_L with solute concentration C_i0 is contacted with various adsorbent masses m₁, m₂…m_N. After equilibrium is reached, the final concentrations in the liquid phase at equilibrium Cie are measured, namely: C_i1, C_i2,…,C_iN

The next step is to calculate the adsorbed phase concentration q_ie by mass balance assuming homogeneous particles (Equation 12):

(12) $$q_{ie}=\frac{V_L\left(C_{i0}-C_{ie}\right)}{m_{ads}}$$

From these N experimental points, the adsorption equilibrium isotherm can be determined as shown in Figure 11 (Equation 13).

(13) $$q_{ie}=f\left(C_{ie}\right)$$

Which can be fitted by various equations (Langmuir, Sips, Freundlich, Frumkin, etc.).

During one of these experiments, the evolution of the concentration in the liquid phase over time, Ci(t), can be analyzed. By applying a mass balance, the adsorbed phase concentration at each time point, q_i(t), can be calculated. Adsorption is a mass transfer operation between the liquid phase and the adsorbent (solid) phase; in this example, the solute is transferred from the liquid phase to the solid adsorbent particles, i.e., the mass of solute lost by the liquid phase in time dt is gained by the adsorbent phase in the same time interval (Equation 14):

(14) $$-V_L\frac{d{C}_i}{dt}=m_{ads}\frac{d{q}_i}{dt}$$

After integrating, the result it the operating line (integrated mass balance) relating q_i(t) and C_i(t), expressed as (Equation 15):

(15) $$q_i\left(t\right)=\frac{V_L}{m_{ads}}{C}_{i0}-\frac{V_L}{m_{ads}}{C}_i\left(t\right)$$

The essential information is summarized in the adsorption equilibrium isotherm (Equation 13) and the operating line, Equation 15. The time evolution of the batch isothermal process follows the operating line in Figure 12, and after sufficient time has passed to reach equilibrium, the solution of the problem is found at the intersection of the equilibrium and operating lines. For a linear adsorption equilibrium isotherm q_ie = KC_ie, the final equilibrium concentration in the liquid phase is (Equation 16):

Figure 12
Adsorption equilibrium isotherm and operating line for a batch isothermal adsorption process. Increasing the mass of adsorbent in the experiment decreases the slope of the operating line and the final C_ie decreases.

(16) $$C_{ie}=\frac{C_{i0}}{1+\xi }$$

Where $\xi =K\frac{m_{ads}}{V_L}$ is the mass capacity factor.

Now the question is: how long does it take to go from Ci₀ to the final equilibrium concentration C_ie? We enter the kinetics of adsorption area and the simplest model to describe this process is the Linear Driving Force (LDF) model by Glueckauf (1955), which says that the rate of adsorption is proportional to the driving force- difference q_is-q_i of the adsorbed phase concentration of species i at the particle surface q_is in equilibrium with the fluid concentration C_i and the average adsorbed phase concentration in the particle qi, i.e. (Equation 17):

(17) $$\frac{d{q}_i}{dt}=k_h\left(q_{is}-q\right)$$

Where the intraparticle mass transfer coefficient for spherical homogeneous particles of radius R_p is $k_h=\frac{15D_h}{R_p^2}$-, and D_h is the diffusivity in the "homogeneous" particle. The intraparticle diffusion time constant is just 1/k_h.

Now, moving on to fixed-bed processes, we start with the essential information obtained from adsorption equilibrium isotherms, i.e., information on the "first order factors" that govern the behavior of adsorption columns. If possible, we can also gather information on "second order factors:" adsorption kinetics (roughly estimated from batch experiments), axial dispersion from tracer experiments, etc. (Figure 13). However, it is important to remember that the art of chemical engineering lies in obtaining solutions with the minimum available information. Thus, we start by performing "accounting," which allows the calculation of the stoichiometric time (Equation 18):

Figure 13
(A) Langmuir, first order factor — equilibrium; (B) Factors governing the behavior of adsorption columns; (C) Glueckauf, second order factor — kinetics.

(18) $$t_{st}=\frac{\epsilon V}{Q_o}\left[1+\frac{1-\epsilon }{\epsilon }\frac{q_{io}}{C_{io}}\right]=\tau \left(1+\xi \right)$$

Ideally, the amount of solute introduced into the column until t_st remains in the interparticle fluid with feed concentration C_io and adsorbed in the particles with adsorbed concentration q_io, in equilibrium with C_io.

When the column reaches saturation, the useful capacity can be significantly lower than the total capacity befined by the stoichiometric time and is defined by the breakthrough time, t_Bp, i.e., the time at which the outlet concentration of the column starts to rise, or in practical terms, when the exit concentration reaches approximately 1% of the feed concentration. Remember: the shape of the breakthrough curve is primarily determined by the shape of the adsorption equilibrium isotherm.

The era of perfusion chromatography and enhanced diffusivity by convection: an example of cross-fertilization

In the 1980s, I was involved in data analysis from measurements of effective diffusivity in permeable catalysts via chromatography obtained by Ahn (1980), a PhD student of André Zoulalian at the Université Technologie Compiègne (UTC) (Figure 14).

Figure 14
(A) Diffusivity in a large pore catalyst measured by chromatography and analyzed with a conventional model with pore diffusion, lumped 14 as a function of Reynolds number, Re.; (B) André Zoulalian.

Ahn used a conventional model with pore diffusion and the result revealed that effective diffusivity changed with the flowrate used in experiments. However, the catalyst had large convective pores in addition to diffusive pores; progressive modelling was required, assuming mass transport not only by diffusion in pores D_e but also by convection (pore velocity v₀) (Table 1).

The equivalence with the conventional model, where both mechanisms were lumped into an apparent $\widetilde{D_e}$ dependent on flowrate (RODRIGUES; AHN; ZOULALIAN, 1982), is given by (Equation 19):

(19) $$\widetilde{D_e}=D_e\frac{1}{f\left(\lambda \right)}$$

Where the intraparticle Peclet number is $\lambda =\frac{v_0\ell }{D_e}$ for a slab catalyst with half thickness ℓ and (Equation 20):

(20) $$f\left(\lambda \right)=\frac{3}{\lambda }\left(\frac{1}{tanh\lambda }-\frac{1}{\lambda }\right)$$

The apparent diffusivity is augmented by convection, and the enhancement factor is 1 = f(λ) This result (Figure 15) explains how perfusion chromatography works (RODRIGUES; AHN; ZOULALIAN, 1982; AFEYAN et al., 1990a, 1990b; AFEYAN; REGNIER; DEAN JUNIOR, 1991). At low velocities, f(λ) = 1 (diffusion-controlled situation); at high velocities $f\left(\lambda \right)\approx \frac{3}{\lambda }$, and therefore $\widetilde{D_e}=D_e\frac{1}{f\left(\lambda \right)}=\frac{\ell v_0}{3}$ (convection-controlled regime).

Figure 15
Enhanced diffusivity by convection in large-pore catalysts or adsorbents.

This result emerged from a collaboration with Professor André Zoulalian from UTC. He was teaching me practical classes of CRE with Villermaux when I was a doctoral student in Nancy. In 1983, I spent a sabbatical year with him at UTC and met César Moraes Abreu from UFPE. This is a small world, and I have just found a declaration of César Abreu about my participation in the jury of the first MSc dissertation at UFPE in Chemical Engineering in 1995 (Figure 16).

Figure 16
(A) Declaration of my participation in the jury of the first MSc (Domingos Malta) in Chemical Engineering at UFPE. Professor Benachour was the supervisor and, fun fact: the student didn't acknowledge the supervision!; (B) celebrating 20 years of pos-graduation at UFPE with Profs César Abreu, and Benachour; (C) with Maurício Motta new generation of UFPE.

The effect of intraparticle convection in large-pore catalysts was addressed by Wheeler in 1951 (WHEELER, 1951).

I tell my students, "Intuition is not enough," and I use this case to illustrate the message (RODRIGUES, 2023b). In fact, Wheeler properly wrote the mass balance with diffusion, convection, and reaction terms but missed one important point recognized by Nir and Pismen (1977) many years later when solving equation 53 of Wheeler's paper: in the intermediate region of Thiele modulus (reaction rate and diffusion rate of the same order), the effectiveness factor is enhanced by pore convection (Figure 17).

Figure 17
(A) Wheeler addressed the problem of diffusion, convection, and reaction and drew conclusions (correctly) without solving the model equation 53 in his paper. (B) He overlooked one important point later recognized by Nir and Pismen: in the intermediate regime, the effectiveness factor increases.

A practical application of this concept is in the chromatographic separation of proteins. I entered the field during my sabbatical at the University of Virginia in 1988 and interacted with Giorgio Carta. I realized that I had all the tools to extend the classical Van Deemter equation (valid for conventional chromatographic particles) to the case of flow-through particles used in perfusion chromatography (Figure 18).

Figure 18
University of Virginia: collaboration with Douglas LeVan since 1985 (a); Giorgio Carta (b); Perfusion chromatography (c), and Extended Van Deemter equation (Rodrigues equation) (d).

The classic Van Deemter equation is (Equation 21):

(21) $$HETP=A+\frac{B}{u_o}+C{u}_o$$

Where HETP is the Height Equivalent to a Theoretical Plate (a measure of column efficiency), A is the eddy dispersion contribution, B is the molecular diffusion contribution, and C is the intraparticle mass transfer contribution, and u_o is the superficial velocity.

The intraparticle pore velocity v₀ can be estimated from the equality between the relative pressure drop at bed and particle scales, assuming that Darcy's law is valid; the result shows that the pore velocity is proportional to the superficial velocity, with the constant being the ratio of the permeabilities of the particle and the bed.

The Van Deemter equation for large-pore packings was proposed by Rodrigues (RODRIGUES; LU; LOUREIRO, 1991; RODRIGUES, 1993), where C is modified as Equation 22:

(22) $$HETP=A+\frac{B}{u_o}+Cf\left(\lambda \right)u_o$$

At high velocities, the C term becomes constant, which explains the effect of intraparticle convection; HETP reaches a plateau which depends only on the particle permeability and pressure gradient (convection-controlled limit). The C term of the Van Deemter equation is reduced, the column performance is improved, and the speed of separation is increased without decreasing efficiency (Figure 19).

Figure 19
HETP versus u_o for conventional and perfusive adsorbents.

Research work on protein adsorption continued later with PhDs of Ping Li (2006) and Ferreira Gomes (2018), who were involved in Expanded Bed Adsorption. This line of research is connected to work done later with monoliths (RODRIGUES et al., 2003; ZABKA, 2006).

Let me now make a remark: the literature is full of pseudo-order models, which I believe is excessive and one should move away from that line. I discussed the use of the Lagergreen model (or pseudo-first order model) elsewhere (RODRIGUES; SILVA, 2016). In the Lagergreen model, the rate of adsorption is proportional to the distance to equilibrium (Equation 23):

(23) $$\frac{d{q}_i}{dt}=k_{Lagergreen}\left(q_{ie}-q_i\right)$$

For linear adsorption equilibrium isotherms, the relation between k_Lagergreen and k_LDF is, for isothermal systems, given by Equation 24:

(24) $$k_{Lagergreen}=k_{LDF}\left(1+\xi \right)$$

These kinetic constants are only equal for non-adsorbing systems or for infinite bath systems where the initial concentration does not change significantly with time.

The era of cyclic adsorption/reaction processes

Adsorption processes are cyclic in nature. Regenerating the adsorbent is necessary for continuous processing of the feed rather than discharging it immediately. Regeneration can be achieved by lowering the pressure — as in Pressure Swing Adsorption (PSA) or Vacuum Swing Adsorption (VSA) —, by increasing temperature — as in Temperature Swing Adsorption (TSA) or Electric Swing Adsorption (ESA) —, or changing concentration — as in Concentration Swing Adsorption (CSA).

The first EU project I was involved in was "Purification of wastewaters by parametric pumping and ion exchange" in 1987, obtained in the Environmental area. Astarita once mentioned that naming straightforwardly might not secure funding. Parametric pumping (Figure 20) is a TSA combined with Flow Reversal between steps of a cycle.

Figure 20
Parametric pumping: TSA with Flow reversal. Experimental set-up and unit display (not yet a digital twin).

Later, PSA was introduced to the Laboratory of Separation and Reaction Engineering (LSRE), initially through a NATO Research Grant with Douglas LeVan titled "Dynamics of Pressure Swing Adsorption" 1989-1993 (LEVAN; RODRIGUES, 1989a) and various EU projects followed in the JOULE program starting with EEC JOUE-0052 C (TT) "The methodology of gas adsorption process design", 1989-1993 (RODRIGUES, 1989b). The first one-bed PSA was built by Da Silva (2000) and Silva (1998), working on propane/propylene separation and n/iso C₅-C₆ paraffins separation, respectively. Later, Carlos Grande (GRANDE, 2005) built a 2-bed PSA and Rui Ribeiro installed ESA (RIBEIRO, 2013) equipment for CO₂ capture (Figure 21). Layered PSA was addressed by Simone Cavenati for CH₄/CO₂/N₂ separation, and the upgrade of gasoline by separation of light naphtha was studied by Patrick Bárcia, now at SysAdvance. More recently, the laboratory has been involved in the use of MOFs for olefins/paraffins separation and xylenes separation under the EU project MACADEMIA "MOFs as catalysts and adsorbents. Discovery and engineering of materials for industrial applications", 2009-2013, coordinated by TOTAL.

Figure 21
1-bed PSA, 2-bed PSA, and ESA experimental equipment. "Each researcher has to put his/her fingerprint in the lab by making his own equipment".

It is interesting to note that my initial involvement with CO₂ adsorption was in coupling adsorption at high temperatures with hydrotalcites in steam methane reforming (Sorption Enhanced Reaction Processes – SERP) along the lines of pioneer research by Sircar at Air Products (HUFTON; MAYORGA; SIRCAR, 1999), now referred to as "blue hydrogen." Later, several Brazilian students supported by projects with Regina Moreira from UFSC and UFC. I had also a continuous stream of Chinese students coming for sandwich PhDs (most of them). Zhen Liu, for instance, returned to ECUST after one year and built a pilot plant to capture CO₂ from flue gases in a coal-fired power plant. I was impressed with how fast he worked (LIU, 2012; LIU et al., 2012; WANG et al., 2013); Figure 22 shows the pilot plant and his PhD defense.

Figure 22
Pilot plant built during Zhen Liu's PhD and his defense held in ECUST. In the jury: Dr. Lu Zuping, my first Chinese posdoc, and Prof. Yu Jianguo, who spent 2 months in my lab writing his thesis.

The Simulated Moving Bed (SMB) technology entered my lab with the EU project "Separation of optical isomers by chromatography in simulated moving beds," 1992-1995 (NICOUD, 1992). The project leader was R. M. Nicoud from SEPAREX, with Jean Blehaut as the operational person. By the end of the project, Nicoud founded NOVASEP and installed the first commercial unit for chiral separations at UCB Pharma late 1990s. The SMB I got was one of the first or second made by NOVASEP. As I recounted in my Life stories (RODRIGUES, 2023b), "I remember it was a Saturday in the old building of Rua dos Bragas and the equipment could not go in the elevator (there was no space!). We had to get help from a student passing by (J.A.C. Silva, who later got a PhD with me) and it was put in the lab with "human force" (I did not contribute much for that task…). By the end of the project a new company, NOVASEP, was started for the SMB business toward pharmaceutical industries and life sciences" (Figure 23). NOVASEP later became AXPLORA, and its history was recently described by Nicoud in Infochimie (LATIEULE, 2022). Our SMB LICOSEP 12-26 still exists and has hosted several PhDs, starting with Pais (1999) in chiral separations, followed by Diana Azevedo (AZEVEDO, 2001) in sugars separation and the first implementation of Simulated Moving Bed Reactor (SMBR) in the lab for sucrose coupling inversion and Glucose/Fructose separation.

Figure 23
SMB LICOSEP 12-26 (A) at LSRE and 80 cm SMB at AMPAC Fine Chemicals (B).

The SMB technology originated at UOP, combining the concept of SMB with Materials (adsorbent) and Technology (rotary valve) to develop a class of SORBEX processes, including PAREX for the separation of p-xylene from its isomers, and SAREX for the separation of glucose/fructose, etc. The names of Broughton, Gerhold, and Carlson are associated to this technology (SÁ GOMES; MINCEVA; RODRIGUES, 2006; RODRIGUES et al., 2015) (Figure 24).

Figure 24
(A) SMB development; (B) TMB; (C) and SMB schemes.

The idea is to "simulate" the movement of the solid adsorbent of a True Moving Bed (TMB) system using fixed-bed columns. This is achieved in SMB by periodically shifting the inlet/outlet ports one column in the direction of fluid flow. The switching time t* in SMB is the ratio between the column length L_c and the solid velocity u_S of TMB (Equation 25)

(25) $$t^{*}=\frac{L_c}{u_S}$$

and the fluid velocity in section j of the SMB is, due to the equality of relative velocities in both SMB and TMB, given by Equation 26:

(26) $$v_j^{*}=v_j+u_S$$

To successfully operate the SMB, constraints on the internal flowrates in the various sections of the TMB must be respected. The separation region based on equilibrium theory for linear isotherms (where K_A and K_B are the Henry constants for the more retained component A and the less retained species B) is represented in Figure 25 in terms of flowrate ratio of fluid and solid phases in separation sections 2 and 3 (Equation 27):

Figure 25
(A) Designing SMB based on internal flowrate constraints in TMB; (B) flowrate constraints; and (C) separation region.

(27) $${\gamma }_j=\frac{1-\epsilon }{\epsilon }\frac{Q_j}{Q_S}$$

It should be noted that constraints in regeneration sections 1 and 4 for cleaning adsorbent and recycle eluent must also be respected.

The methodology was extended to evaluate the effect of mass transfer resistances and flowrates in sections 1 and 4 on the "separation volume" (AZEVEDO, 2001). Significant contributions were made by Mirjana Minceva (now at TU Munich) and Pedro Sá Gomes. Mirjana also contributed to the experimental set-up for evaluating adsorbents (SILVA et al., 2012) for xylenes separation under industrial operating conditions, while Sá Gomes designed from scratch an SMB for gas phase separations (SÁ GOMES; LAMIA; RODRIGUES, 2009), which was built and eventually operated (not without difficulties) in an effort led by Alexandre Ferreira and Ana Mafalda Ribeiro (MARTINS et al., 2019; SEABRA et al., 2021). Both Mirjana and Sá Gomes were involved in the design and assembly of the FlexSMB equipment in our lab (SÁ GOMES et al., 2010). Figure 26A shows the FlexSMB and Figure 26B shows the Gas-phase SMB in LSRE.

Figure 26
(A) FlexSMB and Pedro Sá Gomes, AER, Mirjana Minceva at SPICA 2022 in Lisbon. (B) Gas phase SMB (b) with 8 columns in LSRE; Alexandre Ferreira and Ana Mafalda Ribeiro.

The PAREX process has been the subject of several PhD thesis in our lab, coupling the experimental measurement of adsorption equilibrium with modeling and simulation of PAREX units and hybrid systems (MINCEVA, 2004; SILVA, 2013; GONÇALVES, 2015; SHI, 2019) (Figure 27).

Figure 27
Contributions from LSRE to the understanding of PAREX and hybrid isomerization/separation processes: FEUP PhD thesis of Mirjana MInceva (now at TUM), Marta Silva, now at GALP, Jonathan Gonçalves now at BONDALTI, and Qian Shi (now at Sinopec Beijing Research Institute of the Chemical Industry).

I remember a phone call from a Japanese engineer who wanted to improve PAREX productivity by decreasing the switching time. Yes, you can…but be careful. Up to a point! — as illustrated in Figure 28.

Figure 28
Productivity and desorbent consumption of a PAREX process as a function of the switching time.

Time constant for pore diffusion needs to be considered…

The coupling of adsorption and reaction in SMBR has been an active research area in our lab. It started with the PhD thesis of Diana Azevedo and continued with Mirjana Minceva. Experimental work was demonstrated for reversible reactions in acetalizations (SILVA; RODRIGUES, 2005; PEREIRA et al., 2008; GRAÇA et al., 2011; FARIA et al., 2013) and esterifications (PEREIRA et al., 2009; CONSTANTINO et al., 2020). Process re-intensification was addressed by Carla Pereira and Viviana Silva (SILVA; PEREIRA; RODRIGUES, 2011), adding permeation through the wall of a catalytic module to remove product water from the media in the esterification of lactic acid to produce ethyl lactate. The PSE Model-Based Innovation Prize 2012 was awarded to the manuscript conveying that idea (Figure 29).

Figure 29
With Viviana Silva (Cargill Europe) and Carla Pereira (ExxonMobil, USA) winners of PSE Model-based Innovation Prize 2012.

In 2008, AIChE celebrated 100 years in Philadelphia, and I took a picture at the Chemical Heritage Foundation close to the Bakelite polymer reactor. In September 2021, Carla Pereira, now at ExxonMobil, received the 18^th Annual SCI Gordon E. Moore Medal in that building, which is now the Science History Institute (Figure 30), and took a picture close to the same polymer reactor.

Figure 30
From 2018 (100 years of AIChE) to 2021: Carla Pereira wins the SCI Gordon E. Moore Medal.

FUTURE

The research group still works on developing SMBR for the isomerization/separation of xylenes using new shaped Dual Function Materials, following the works by Gonçalves (SHI et al., 2020) and Shi Qian (SHI et al., 2021), as well as in other topics from petrochemical industry. As someone put it, "The Stone age came to an end not for a lack of stones and the oil age will end, but not for a lack of oil."

In the trending areas of CO₂ and H₂ (climate change and energy transition), the laboratory has been involved in CO₂ capture using adsorptive processes with carbons, zeolites, and MOFs (COELHO et al., 2017; MOREIRA et al., 2017; REGUFE et al., 2018). Significant efforts have been made in studying H₂ purification (RIBEIRO et al., 2009; LOPES; GRANDE; RODRIGUES, 2012), biogas upgrading (SANTOS; GRANDE; RODRIGUES, 2011; CAMPO et al., 2016), CO₂ utilization for DMC (SANTOS et al., 2014), biomethane (MARTINS et al., 2022), and cryogenic adsorption. However, it should be noted that the amount of CO₂ consumed in the existing industrial chemical processes is only a small fraction of the CO₂ to be captured, as stated by Manenti (MANENTI, 2019).

Shaping and 3D printing of adsorbents have become the focal point of research in composite monoliths for ESA. Difficult separations as light olefins/paraffins and CH₄/N₂ have been addressed with Gas-phase SMB.

I believe that multicolumn processes like SMB, pseudo-SMB, or the Japan Organo (JO) process (Figure 31) will have an impact not only in bioprocessing but also in the development of economic processes related to biorefineries and circular economy. This is particularly relevant for lignin valorization, aiming at separating acids (vanillic acid), aldehydes (vanillin, syringaldehyde), and ketones (acetovanillone) (MATA; RODRIGUES, 2001; BORGES DA SILVA; RODRIGUES, 2006; GOMES; RODRIGUES, 2019). This research line of oxidation of lignin toward vanillin stated in 1990 with the PhD of Alvaro Mathias (MATHIAS, 1993) from UFPR.

Figure 31
In the JO process, the cycle has steps. In the first, the system operates as a series of columns and the intermediate species is collected as QI; in the second step, the feed is stopped, the shifting of columns takes place as in the conventional SMB and the more retained and less retained components are collected at the extract X and raffinate ports, respectively

The idea of going from Molecules to Processes using Molecular Simulation tools is expected to grow in the future, potentially saving experimental efforts. This line of research was opened in the lab by Miguel Granato (GRANATO, 2008), now at UFSC, Blumenau, and Miguel Jorge (GRANATO et al., 2014), now at the University of Stratchlyde. In Brazil, the group of Mardónio in Fortaleza and the ATOMS group of Fred Tavares are deeply involved in this area (Figure 32).

Figure 32
Mardónio (or Sebastião Lucena) from UFC and with Fred Tavares in the ATOMS meeting in Hotel Regina, RJ.

A general problem is the recovery of solutes from dilute streams and their purification for process reuse; examples are Direct Air Capture (DAC) for CO₂ removal from the air (ERANS et al., 2022) and cleaning water in aniline production for reuse as process water (SANTOS; RODRIGUES, 2014).

In the lifetime I expect to have, I plan to focus on the effect of adsorption on skin in the evaporation and performance of perfumes (ALMEIDA et al., 2019).

However, the fundamentals will always be essential: the search for fast tools to acquire multicomponent adsorption equilibrium data as well as predictive models to describe those data remains a priority.

By training, I belong to the club of first principles or mechanistic models, but we should not ignore the developments in hybrid models and AI (GLASSEY; STOSCH, 2018; MORBIDELLI, 2022). My first attempt in 1998 with Y. Cheng to use neural networks was unsuccessful; the idea was to train ANN with our chromatographic models. Only a small advance in that direction was reported many years later (SANTOS et al., 2011). However, interest in AI has been renewed recently, as nicely reviewed by Venkatasubramanian (2019).

Certainly, the future will change, even if "the equations [of change] don't change" (SCHOWALTER, 2003). The implications for teaching tools as ChatGPT cannot be ignored (WHITE, 2023). For the moment, in technical aspects, it is not yet fully ready, as evidenced by my test on February 13, 2023. When I asked "How do I size a fixed-bed adsorption column?," the answer was:

Sizing a fixed-bed adsorption column involves determining the appropriate dimensions (diameter and length) for a given application. The following factors should be considered when sizing a fixed-bed adsorption column:

1. Adsorbent characteristics: The physical and chemical properties of the adsorbent, such as particle size, pore size distribution, and surface area, can impact the performance of the column and should be considered when determining its size.

2. Feed stream properties: The flow rate and composition of the feed stream can influence the performance of the adsorption column and should be considered when determining its size.

3. Operating conditions: The temperature and pressure of the system can impact the rate of adsorption and desorption and should be considered when determining the size of the column.

4. Bed depth: The depth of the bed can impact the rate of adsorption and desorption and should be considered when determining the size of the column. A deeper bed may provide a higher capacity for adsorption but may also result in a slower rate of adsorption.

5. Breakthrough behavior: The breakthrough behavior of the system, such as the breakthrough time and breakthrough curve, can be used to determine the size of the column needed to achieve a specific level of purification.

After considering the aforementioned factors, the size of the column can be estimated using various mathematical models and simulation tools. It is also important to consider practical considerations, such as the cost and availability of the adsorbent, when sizing a fixed-bed adsorption column."

For sure a design engineer did not get a given formula for calculations, offering instead quite nice sentences, though inaccurate statements.

The situation worsened when I asked another question: "How do I calculate the stoichiometric time?" The answer I got was entirely incorrect. Almost the entire response contained errors, as highlighted.

The calculation of stoichiometric time in adsorption depends on a number of factors, including adsorption kinetics and the system's adsorption capacity. As a result, there is no universal method for calculating stoichiometric time. However, a general approach that can be used in many cases is to model the adsorption process using a kinetic model and then solve for the time at which the adsorption capacity reaches its maximum value.

A commonly employed kinetic model for adsorption is the Langmuir adsorption model, which assumes that the adsorption process follows first-order reactions and that the adsorbate molecules are adsorbed onto the adsorbent's surface in a monolayer fashion. The Langmuir model can be expressed mathematically as:

$$\text{Q}=\text{Q}\_\text{m}\left(\text{K\_ads C\_0}\right)/\left(1+\text{K\_ads C\_0 t}\right)$$

where Q is the adsorption capacity at time t, Q_m is the maximum adsorption capacity, C_0 is the initial concentration of the adsorbate, and K_ads is the adsorption rate constant.

The stoichiometric time can be calculated by solving for the time at which the adsorption capacity reaches its maximum value, Q = Q_m. This can be done by rearranging the Langmuir equation to solve for t:

$$\text{t}=1/\left(\text{K}\_\text{ads C\_0}\right)*\left(\text{Q\_m/Q}-\text{1}\right)$$

Note that this approach assumes that the Langmuir model is appropriate for the adsorption process being studied, which may not always be the case. In some cases, other kinetic models, such as the Freundlich model, may provide a better fit to the adsorption data. In such cases, the stoichiometric time can be calculated using a similar approach, but with the appropriate model equations.

To conclude this story, I present (Figure 33) the Brazilian branches of my research tree (details provided in the Supporting Information) that contributed to the progress of the research laboratory and to the friendships fostered across the Atlantic.

Figure 33
Brazilian branches of my research tree.

• Funding:

  This work was financially supported by LA/P/0045/2020 (ALiCE), UIDB/50020/2020 and UIDP/50020/2020 (LSRE-LCM), funded by national funds through FCT/MCTES (PIDDAC).

ACKNOWLEDGEMENT

This work was financially supported by LA/P/0045/2020 (ALiCE), UIDB/50020/2020 and UIDP/50020/2020 (LSRE-LCM), funded by national funds through FCT/MCTES (PIDDAC).

The help of Isabella Corrêa with drawing of some figures is gratefully acknowledged.

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• GRANATO, M.; MARTINS, V.; SANTOS, J.C.; JORGE, M.; RODRIGUES, A.E. From Molecules to Processes: Molecular Simulation Applied to the design of SMB for ethane/ethylene separation. The Canadian Journal of Chemical Engineering, v. 92, n. 1, p. 148-155, 2014. https://doi.org/10.1002/cjce.21805
  » https://doi.org/10.1002/cjce.21805
• HINDMARSH, A.C. Gear-ordinary differential equation solver. rev. 3. Livermore: Lawrence Livermore Laboratory, 1974. Report UCID-30001.
• HINDMARSH, A.C. Preliminary documentation of GEARIB. Solution of Implicit Systems of ordinary differential equations with banded Jacobian. Livermore: Lawrence Livermore Laboratory, 1976. Report UCID-30130.
• HINDMARSH, A.C. LSODE and LSODI. Two new initial value ordinary differential equation solvers. ACM-SIGNUM Newsletter, v. 15, p. 10-11, 1980.
• HUFTON, J.R.; MAYORGA, S.; SIRCAR, S. Sorption-enhanced reaction process for hydrogen production. AIChE Journal, v. 45, n. 2, p. 248-256, 1999. https://doi.org/10.1002/aic.690450205
  » https://doi.org/10.1002/aic.690450205
• LATIEULE. S. The NOVASEP saga – by founder Roger-Marc Nicoud. InfoChimie Magazine, p. 1-51, 2022.
• LEVAN, M.D.; RODRIGUES, A.E. NATO Research Grant Dynamics of Pressure Swing Adsorption. Brussels: NATO, 1989-1993.
• LI, PING. Protein separation and purification by expanded bed chromatography and SMB technology. PhD Thesis – Faculdade de Engenharia, Universidade do Porto, Porto, 2006.
• LIU, Z. Adsorption process for CO2 capture from flue gas of coal-fired power plant, PhD thesis – ECUST, Shanghai, 2012.
• LIU, Z.; WANG, L.; KONG, X.; LI, P., YU, J.; RODRIGUES, A.E. On site CO2 capture from flue gas by adsorption process in coal-fired power plant. Industrial & Engineering Chemistry Research, v. 51, n. 21, p. 7355-7363, 2012. https://doi.org/10.1021/ie3005308
  » https://doi.org/10.1021/ie3005308
• LOPES, F.; GRANDE, C.; RODRIGUES, A.E. Fast-cycling VPSA for hydrogen purification. Fuel, v. 93, p. 510-523, 2012. https://doi.org/10.1016/j.fuel.2011.07.005
  » https://doi.org/10.1016/j.fuel.2011.07.005
• LOUREIRO, J.M. Adsorption and reaction in porous particles, Application to the removal of heavy metals and chelating resins. PhD Thesis – Faculdade de Engenharia, Universidade do Porto, Porto, 1986.
• LOUREIRO, J.M.; RODRIGUES, A.E. Two solution methods for hyperbolic systems of partial differential equations in chemical engineering. Chemical Engineering Science, v. 46, n. 12, p. 3259-3267, 1991. https://doi.org/10.1016/0009-2509(91)85027-U
  » https://doi.org/10.1016/0009-2509(91)85027-U
• MADSEN, N.K.; SINCOVEC, R.F. PDECOL: general collocation software for partial differential equations. ACM Transactions on Mathematical Software, v. 5, n. 3, p. 326-351, 1979.
• MANENTI, F. Perspectives for CO2 utilization Florence: ECCE-12, 2019.
• MANTELL, C.L. Adsorption New York: McGraw Hill, 1945.
• MARTINS, V.F.; RIBEIRO, A; KORTUNOV, P.; FERREIRA, A.; RODRIGUES, A.E. High purity ethane/ethylene separation by gas phase simulated moving bed using ZIF-8 adsorbent. AIChE Journal, v. 65, n. 8, p. e16619, 2019. https://doi.org/10.1002/aic.16619
  » https://doi.org/10.1002/aic.16619
• MARTINS, J.; MIGUEL, C.; RODRIGUES, A.E.; MADEIRA, L.M. Novel adsorption-reaction process for biomethane purification/ production and renewable energy storage. ACS Sustainable Chemistry & Engineering, v. 10, n. 24, p. 7833-7851, 2022. https://doi.org/10.1021/acssuschemeng.1c06844
  » https://doi.org/10.1021/acssuschemeng.1c06844
• MATA, V.; RODRIGUES, A.E. Separation of ternary mixtures by pseudo-simulated moving bed chromatography. Journal of Chromatography A, v. 939, n. 1/2, p. 23-40, 2001. https://doi.org/10.1016/S0021-9673(01)01335-8
  » https://doi.org/10.1016/S0021-9673(01)01335-8
• MATHIAS, A L. Production of vanillin from kraft lignin: kinetics and processes. Faculdade de Engenharia, Universidade do Porto, 1993.
• MILLER, K.; MILLER, R. Moving finite elements I. SIAM Journal on Numerical Analysis, v. 18, n. 6, p. 1019-1032, 1981.
• MORBIDELLI, M. Application of Machine-Learning methods to the production of therapeutic proteins. DataHow Workshop at SPICA, Lisbon, 2022.
• MOREIRA, M.; RIBEIRO, A.M.; FERREIRA, A.; RODRIGUES, A.E. Cryogenic pressure temperature swing for natural gas upgrade. Separation and Purification Technology, v. 173, p. 339-356, 2017. https://doi.org/10.1016/j.seppur.2016.09.044
  » https://doi.org/10.1016/j.seppur.2016.09.044
• NICOUD, R.M. EEC BRITE BRE2-CT92-0337 Separation of optical isomers by chromatography in simulated moving beds. 1992.
• NIR, A.; PISMEN, L. Simultaneous intraparticle forced convection, diffusion and reaction in a porous catalyst. Chemical Engineering Science, v. 32, n. 1, p. 35, 1977. https://doi.org/10.1016/0009-2509(77)80192-9
  » https://doi.org/10.1016/0009-2509(77)80192-9
• PAIS, L.S. Chiral separation by simulated moving bed chromatography. PhD Thesis – Faculdade de Engenharia, Universidade do Porto, Porto, 1999.
• PEREIRA, C.; SÁ GOMES, P.; SILVA, V.; GANDI, G.; RODRIGUES, A.E. Multifunctional reactor for the synthesis of dimethylacetal. Industrial & Engineering Chemistry Research, v. 47, n. 10, p. 3515-3524, 2008. https://doi.org/10.1021/ie070889t
  » https://doi.org/10.1021/ie070889t
• PEREIRA, C.S.M.; ZABKA, M.; SILVA, V.M.T.M.; RODRIGUES, A.E. A novel process for the Ethyl lactate synthesis in a Simulated Moving Bed reactor (SMBR). Chemical Engineering Science, v. 64, n. 14, p. 3301-3310, 2009. https://doi.org/10.1016/j.ces.2009.04.003
  » https://doi.org/10.1016/j.ces.2009.04.003
• POHLENZ, J.B.; SCOTT, N.H. Method for hydrogen production by catalytic decomposition of a gaseous hydrocarbon stream Assignee: Universal Oil Products, US Patent 3, 284,161, Nov. 8, 1966.
• REGUFE, M.J.; FERREIRA, A.; LOUREIRO, J.M.; SHI, Y.; RODRIGUES, A.E.; RIBEIRO, A.M. New hybrid composite monolith with 13X zeolite and activated carbon for CO2 capture. Adsorption, v. 24, n. 3, p. 249-265, 2018. https://doi.org/10.1007/s10450-018-9938-1
  » https://doi.org/10.1007/s10450-018-9938-1
• RIBEIRO, R. Electric swing adsorption PhD Thesis – Faculdade de Engenharia, Universidade do Porto, Porto, 2013.
• RIBEIRO, A.; GRANDE, C.; LOPES, F.; LOUREIRO, J.M.; RODRIGUES, A.E. Four beds pressure swing adsorption for hydrogen purification: case of humid feed and activated carbon beds. AIChE Journal, v. 55, n. 9, p. 2292-2302, 2009. https://doi.org/10.1002/aic.11886
  » https://doi.org/10.1002/aic.11886
• RODRIGUES, A.E. Étude de la carbonitruration du vanadium sur un support poreux a grande surface interne Nancy: D.E.A., Université de Nancy I, 1971.
• RODRIGUES, A.E. Apllication des méthodes du Génie Chimique appliquée à l’échange d'ions Example de l’étape anionique de la demineralisation de l'eau. Docteur-Ingenieur thesis, Université de Nancy I, Nancy, 1973.
• RODRIGUES, A.E. Conceitos fundamentais em engenharia da reação química Évora: Instituto Universitário de Évora, 1976.
• RODRIGUES, A.E. (Ed.). Ion exchange science and technology Dordrecht: M. Nijhoff, 1986. NATO ASI Series E 107.
• RODRIGUES, A.E. An extended Van Deemter equation (Rodrigues equation) for performing chromatographic processes using large-pore, permeable packings, LC-GC, v. 6, n. 1, p. 20-29, 1993.
• RODRIGUES, A.E., EEC JOUE-0052 C (TT) The methodology of gas adsorption process design, 1989-1993.
• RODRIGUES, A.E. Chemical engineering and environmental challenges. Cyclic adsorption/reaction technologies: materials and process together! Journal of Environmental Chemical Engineering, v. 8, n. 4, p. 103926, 2020. https://doi.org/10.1016/j.jece.2020.103926
  » https://doi.org/10.1016/j.jece.2020.103926
• RODRIGUES, A.E. Perspectives on adsorption. What else? A personal view. Fluid Phase Equilibria, v. 564, p. 113614, 2023a. https://doi.org/10.1016/j.fluid.2022.113614
  » https://doi.org/10.1016/j.fluid.2022.113614
• RODRIGUES, A.E. Life stories Porto: FEUP, 2023b.
• RODRIGUES, A.E.; AHN, B.; ZOULALIAN, A. Intraparticle forced convection effect in catalyst diffusivity measurements and reactor design. AIChE Journal, v. 28, n. 4, p. 925-930, 1982. https://doi.org/10.1002/aic.690280404
  » https://doi.org/10.1002/aic.690280404
• RODRIGUES, A.E.; CALO, J.; SWEED, N. (Eds.), Multiphase reactors. Alphen aan den Rijn: Sijthoff & Noordhoff, 1981. NATO ASI Series E 51and 52, Vol I-Fundamentals, Vol II-Design Methods.
• RODRIGUES, A.E.; LEVAN, M.D.; TONDEUR, D. (Eds.). Adsorption Science and Technology Dordrecht: Kluwer Academic Publishers, 1989.
• RODRIGUES, A.E.; LU, Z.P.; LOUREIRO, J.M. Residence time distribution of inert and linearly adsorbed species in fixed-bed containing large-pore supports: applications in separation engineering. Chemical Engineering Science, v. 46, p. 2765-2773, 1991. https://doi.org/10.1016/j.ces.2020.116188
  » https://doi.org/10.1016/j.ces.2020.116188
• RODRIGUES, A.E.; TONDEUR, D. (Eds.). Percolation processes Theory and Applications. NATO ASI Series E 33. Alphen aan den Rijn: Sijthoff & Noordhoff, 1980.
• RODRIGUES, A.E.; MATA, V.; ZABKA, M.; PAIS, L. Flow and mass transfer, in monoliths: preparation, materials and applications. In: SVEC, F. TENNIKOVA. T.; DEYL, Z. Series Journal of Chromatography Library 67. Amsterdam: Elsevier, 2003. p. 325-350.
• RODRIGUES, A.E.; PEREIRA, C.; PAIS, L.; RIBEIRO, A.M.; MINCEVA, M. Simulated bed technology. principles, design and process applications. Oxford: Butterworth-Heinemann Elsevier, 2015.
• RODRIGUES, J.D. Desenvolvimento do método de elementos finitos móveis para a simulação de processos. PhD Thesis – Faculdade de Engenharia, Universidade do Porto, Porto, 2010.
• RODRIGUES, A.E.; SILVA, C.M. What's wrong with Lagergreen pseudo first order model for adsorption kinetics? Chemical Engineering Journal, v. 306, p. 1138-1142, 2016. https://doi.org/10.1016/j.cej.2016.08.055
  » https://doi.org/10.1016/j.cej.2016.08.055
• SÁ GOMES, P.; MINCEVA, M.; RODRIGUES, A.E. Simulated moving bed: old and new. Adsorption, v. 12, p. 375-392, 2006. https://doi.org/10.1007/s10450-006-0566-9
  » https://doi.org/10.1007/s10450-006-0566-9
• SÁ GOMES, P.; LAMIA, N.; RODRIGUES, A.E. Design of a gas phase simulated moving bed for propane/propylene separation. Chemical Engineering Science, v. 64, p. 1336-1357, 2009. https://doi.org/10.1016/j.ces.2008.11.022
  » https://doi.org/10.1016/j.ces.2008.11.022
• SÁ GOMES, P.; ZABKOVA, M.; ZABKA, M.; MINCEVA, M.; RODRIGUES, A.E. Separation of chiral mixtures in real SMB units: the FLEXSMB-LSRE^® AIChEJ, v. 56, n. 1, p. 125-142, 2010. https://doi.org/10.1002/aic.11962
  » https://doi.org/10.1002/aic.11962
• SANTOS, J.C.; CHENG, Y.; DIAS, M.M.; RODRIGUES, A.E. Surface B-Splines fitting for Speeding Up the Simulation of Adsorption Processes with IAS Model. Computers and Chemical Engineering, v. 35, n. 7, p. 1186-1191, 2011. https://doi.org/10.1016/j.compchemeng.2010.08.003
  » https://doi.org/10.1016/j.compchemeng.2010.08.003
• SANTOS, M.S.; GRANDE, C.A.; RODRIGUES, A.E. Pressure Swing Adsorption for biogas upgrading. Effect of recycling streams in PSA design. Industrial & Engineering Chemistry Research, v. 50, n. 2, p. 974-985, 2011. https://doi.org/10.1021/ie100757u
  » https://doi.org/10.1021/ie100757u
• SANTOS, M.P.; RODRIGUES, A.E. Adsorption equilibrium and fixed bed adsorption of aniline onto polymeric resin and activated carbons. Separation Science and Technology, v. 49, n. 3, p. 335-344, 2014. https://doi.org/10.1080/01496395.2013.852226
  » https://doi.org/10.1080/01496395.2013.852226
• SANTOS, B.A.V.; SILVA, V.M.T.; LOUREIRO, J.M.; RODRIGUES, A.E. Review for the Direct Synthesis of Dimethyl Carbonate. ChemBioEng Review, v. 1, n. 5, p. 214-229, 2014. https://doi.org/10.1002/cben.201400020
  » https://doi.org/10.1002/cben.201400020
• SCHIESSER, W. DSS/2: an introduction to the numerical method of lines integration of partial differential equations. Bethlehem: Lehigh University, 1976.
• SCHOWALTER, W. The equations (of change) don't change but the profession of engineering does. Chemical Engineering Education, v. 37, n. 7, p. 242-247, 2003.
• SEABRA, R.A.; MARTINS, V.F.D.; RIBEIRO, A.M.; RODRIGUES, A.E.; FERREIRA, A.P. Ethylene/ethane separation by gas-phase smb in binderfree zeolite 13x monoliths. Chemical Engineering Science, v. 229, p. 116006, 2021. https://doi.org/10.1016/j.ces.2020.116006
  » https://doi.org/10.1016/j.ces.2020.116006
• SERENO, C.A. Método dos elementos finitos móveis. Aplicações em Engenharia Química. PhD Thesis – Faculdade de Engenharia, Universidade do Porto, Porto, 1989.
• SERENO, C.A.; RODRIGUES, A.E.; VILLADSEN, J. The moving finite element method with polynomial approximation of any degree. Computers & Chemical Engineering, v. 15, n. 1, p. 25-33, 1991. https://doi.org/10.1016/0098-1354(91)87003-R
  » https://doi.org/10.1016/0098-1354(91)87003-R
• SERENO, C.A.; RODRIGUES, A.E.; VILLADSEN, J. Solution of Partial Differential Equations Systems by the Moving Finite Element Method. Computers & Chemical Engineering, v. 6, n. 6, p. 583-592, 1992. https://doi.org/10.1016/0098-1354(92)80069-L
  » https://doi.org/10.1016/0098-1354(92)80069-L
• SHI, Q. New processes for isomerization/separation of xylenes. PhD Thesis – Faculdade de Engenharia, Universidade do Porto, Porto, 2019.
• SHI, Q.; GONÇALVES, J.C.; FERREIRA, A.P.; RODRIGUES, A.E. Simulated moving bed reactor for p-xylene production: modeling, simulation, and optimization. Chemical Engineering Science, v. 225, p. 115802, 2020. https://doi.org/10.1016/j.ces.2020.115802
  » https://doi.org/10.1016/j.ces.2020.115802
• SHI, Q.; GONÇALVES, J.C.; FERREIRA, A.F.P.; RODRIGUES, A.E. A review of advances in production and separation of xylene isomers. Chemical Engineering & Processing. Process Intensification, v. 169, n. 2, p. 108603, 2021. https://doi.org/10.1016/j.cep.2021.108603
  » https://doi.org/10.1016/j.cep.2021.108603
• SIEMENS PROCESS SYSTEMS ENGINEERING (SPSE). gPROMS General PROcess Modeling System London: [s.n.], 2023.
• SILVA, J.A.C. Separation of n/iso paraffins by adsorption processes. PhD Thesis – Faculdade de Engenharia, Universidade do Porto, Porto, 1998.
• SILVA, M. Optimization of the Parex unit of Matosinhos Refinery for the separation of p-xylene. PhD Thesis – Faculdade de Engenharia, Universidade do Porto, Porto, 2013.
• SILVA, M.; MOREIRA, M.; FERREIRA, A.; SILVA, V.; SÁ GOMES, P.; SANTOS, J.; MINCEVA, M.; MOTA, P.; RODRIGUES, A.E. Adsorbent evaluation based on experimental breakthrough curves: application to the separation of p-xylene from C8 isomers. Chemical Engineering and Processing, v. 35, n. 10, p. 1777-1785, 2012. https://doi.org/10.1016/j.cep.2021.108603
  » https://doi.org/10.1016/j.cep.2021.108603
• SILVA, V.M.T.M.; PEREIRA, C.; RODRIGUES, A.E. PermSMBR – a new hybrid technology: application on green solvent and biofuel production. AIChE Journal, v. 57, n. 7, p. 1841-1851, 2011. https://doi.org/10.1002/aic.12381
  » https://doi.org/10.1002/aic.12381
• SILVA, V.T.M.; RODRIGUES, A.E. A novel process for diethylacetal synthesis. AIChE Journal, v. 51, n. 10, p. 2752-2768, 2005. https://doi.org/10.1016/S0009-2509(00)00347-X
  » https://doi.org/10.1016/S0009-2509(00)00347-X
• VENKATASUBRAMANIAN, V. The promise of artificial intelligence in chemical engineering: is it here, finally? AIChE Journal, v. 65, n. 2, p. 466–478, 2019. https://doi.org/10.1002/aic.16489
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• ZABKA, M. Chiral separation in SMB and novel adsorbent structures PhD Thesis – Faculdade de Engenharia, Universidade do Porto, Porto, 2006.
• WANG, L.; YANG, Y.; SHEN, W.; KONG, X.; LI, P.; YU, J.; RODRIGUES, A.E. CO2 capture from flue gas in an existing coal-fired power plant by pilot-scale two successive VPSA units. Industrial & Engineering Chemistry Research, v. 52, n. 23, p. 7947-7955, 2013. https://doi.org/10.1021/ie4009716
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• WHEELER, A. Reaction rates and selectivity in catalyst pores. Advances in Catalysis, v. 3, p. 249-327, 1951. https://doi.org/10.1016/S0360-0564(08)60109-1
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• WHITE, J. The rise of ChatGPT and the age of artificial intelligence. Research Spotlight: News, School of Engineering, Vanderbilt University. Available from: https://engineering.vanderbilt.edu/2023/02/21/research-spotlight-the-rise-of-chatgpt-and-the-age-of-artificial-intelligence/ Accessed on: March 15, 2023.
  » https://engineering.vanderbilt.edu/2023/02/21/research-spotlight-the-rise-of-chatgpt-and-the-age-of-artificial-intelligence/

Appendix 1 Supporting Information.

Below is a list of the Brazilian researchers, including: names, institution of origin, year of dissertation defense for sandwich programs and at FEUP for full work and defense in Porto, title of research, and current affiliations.

Brazilian branches of my research tree

MSc

Rodrigo Rocha Davesac (UFSC); 1997,"Desenvolvimento de um pacote computacional para a simulacão de um processo de bombeamento paramétrico térmico", (co-direction with Leonel Pinto); FURG

Ana Clara Soares Carneiro (UFU), 2012, "Performance do perfume:modelagem e simulação da evaporação/difusão"; CARGILL

PhDs

Álvaro Luiz Mathias (UFPR), FEUP 1993, "Production of vanillin from kraft lignin: Kinetics and processes"; UFPR

Diana C.S. Azevedo (UFC), FEUP 2001, "Separation/Reaction in Simulated Moving Bed. Application to the production of industrial Sugars"; UFC

José Luciano Soares (UFSC), 2003, "Development of new adsorbents and hybrid processes in steam-reforming", sandwich PhD co-direction with Prof Regina Moreira; CASAN, Palhoça, SC

Eduardo A. Borges da Silva (UFSC), 2004 "Study of mass transfer in Simulated Moving Bed Reactor units",(sandwich PhD co-direction with Prof Selene Ulson de Souza; NOVOZYMES Araucária, PR

Rodrigo R. Davesac (UFSC) FEUP 2005, "Propane/propylene separation and Pressure Swing Adsorptive Reactors";FURG

Simone Cavenati (UFSC), FEUP 2005, "Separation of Methane/carbon dioxide/nitrogen mixtures by adsorptive processes "; CM Funchal

Miguel Granato (FAENQIL), FEUP 2008, "Molecular simulation of gas adsorption processes"; UFSC Blumenau

Tirzha Dantas (UFSC), 2009, "Separação de CO2 por adsorção a partir de misturas sintéticas do tipo gás de exaustao", (sandwich PhD co-supervision with Prof Regina Moreira); UFPR

Adriana Donelian (UFSC), 2010, "Fracionamento do óleo essencial de patchouli em meio supercrítico", (sandwich PhD co-supervision with Prof Ricardo Machado).; Mondelez International

Israel Pedruzzi (UCS), FEUP 2010, "Production of lactobionic acid", (co-supervision with E. Borges da Silva); Beifur Ltd, Garibaldi, RS

M. C. Rabelo (UFC) 2012, "Chromatographic separation of isomaltooligosaccharides on ion-exchange resins", sandwich PhD co-supervision with Diana Azevedo; posdoc UFC

Juliana Coelho (UFC),2016, " Adsorption of CO2 and CH4 in presence of water in MOF A520", 2014 (sandwich PhD co-supervision with Prof Diana Azevedo and Sebastião Mardónio; and Dr A.M. Ribeiro); UFRN- FELCS

Lucas Coelho (UFPE), 2017, "Purificação dos ácidos glicérico e tartrónico, derivados do glycerol, por leito móvel simulado (LMS) na resina Dowex 50WX-2",(sandwich PhD co-supervision with Prof Nelson Medeiros Filho); STEX

Daniel Gonçalves (FZEA, USP),2017, "Fracionamento de óleos essenciais cítricos utilizando etanol com diferentes níveis de hidratação como solventes: Equilíbrio de fases, propriedades físicas e extração em equipamento contínuo", sandwich PhD co-supervision with Prof Christianne Rodrigues, Cintia Gonçalves and Dr Patrícia Costa, UENF

Benjamim Henrique de Lima e Silva (UFPE), 2019, Cinética do processo heterogéneo de alcoólise alcalina de óleode soja em ésteres de biodiesel", PhD sandwich co-supervision with César Abreu, Alexandre Schuler and Rui Faria; Instituto Federal de Educação, Ciência e Tecnologia do Ceará - Campus Iguatu.

Rafael M. Siqueira (UFC),2020, "Carbon dioxide capture by pressure swing adsorption", sandwich PhD co-supervision with Moisés Bastos Neto and Diana Azevedo and Alexandre Ferreira; LSRE-LCM

Rafael Nolibos Almeida (PUCRS),2020, "Estudo Fenomenológico da Difusão de fragrâncias ", sandwich PhD co- supervision with Prof Eduardo Cassel and Dr Patrícia Costa; PUCRS

Ronney José Oliveira Santos (UNIT), 2021, "Sintese de sílicas aminofuncionalizadas com líquidos iónicos e polímero PEI para separação CO2/CH4 por adsorção", sandwich PhD co-supervision with Profs Elton Franceschi, Sílvia Doriva (UNIT) and Alexandre Ferreira; UFRJ

Caroline Maria Bezerra de Araújo (UFPE),2022, "Water and wastewater treatment using recyclable agar-graphene oxide biocomposite hydrogel in batch and fixed-bed adsorption column: bench experiments and modelling for the selective removal of organics" (sandwich PhD co-supervision with Profs Marcos Ghislandi, Mauricio Motta and Alexandre Ferreira); LSRE-ICM

Adriano Henrique (IPB-UTFPR,), FEUP 2022, "Upgrading of Total Isomerisation Processes with Metal-Organic Frameworks", co-supervision with J.A.C. Silva; IPB

Isabella Correa (U. Brasilia), "An innovative approach to the production of solketal: the Supercritical Simulated Moving Bed Reactor", co-supervision with Rui Faria, on-going, LSRE-LCM

Heloísa Helena Scorsato de Almeida (IPB-UFTPR), "Hydrosols as natural antimicrobials for food applications", co-supervision with Filomena Barreiro, on-going; IPB

Júlia Cristiê Kessler (UFSC), "Supercritical extraction and NETmix technology to produce green and stabilized M. oleifera functional ingredients having in view cosmeceutical formulations" (co-supervision with Madalena Dias and Filomena Barreiro, on-going); LSRE-LCM

Lucas Fernando Alves da Silva Zafanelli (IPB-UFTPR), "Green Hydrogen Recovery from Natural Gas Grids by Adsorption Processes", co-supervision with J.A.C. Silva, on-going; IPB

Giovana Colluci (IPB-UFTPR), "Lignin-based Pickering stabilizers for innovative cosmeceutical formulations" ", co-supervision with Filomena Barreiro, on-going; IPB

Ingrid Denardi Soares (FZEA/USP), "Avaliação de características sensoriais de cascas de amêndoa de cacao desengordurados com solvents etanólicos", PhD sandwich co-direction with Prof Christianne Rodrigues,; on-going LSRE-LCM

Post-docs

Regina Moreira (UFSC), 1999, "Carbon molecular sieves", UFSC

Eduardo Borges da Silva (UFSC), 2005-2007, "Simulated Moving Bed Processes"; Novozymes Latin America, Araucária, PR

Simone Cavenati (UFSC), 2005-2008, "Preparation of ETS adsorbents"; CM Funchal

Ticiane Sauer (UFSC), 2006-2007 " Separation CO2/CH4/H2"; UFTPR

Juan Carlos Pokrywiecki (UFSC),2006-2007, ""Processo de separação de CO2 com membranas seletivas em condições supercríticas e fracionamento de óleos essenciais"; UFTPR

Miguel Granato (FAENQUIL),2009-2014, "Molecular simulation of xylenes separation processes"; UFSC Blumenau

Lucas Coelho (UFPE), 2017-2019, "Purification of DHA and other organic acids resulting from glycerol by SMB" (co- supervision with Dr Rui Faria); STEX

Maria Carolina Capellini (FZEA/USP),2022, "Avaliação de características sensoriais de amostras de soja pré-tratada industrialmente e de farelo desengordurado de soja com hexano e etanol" FZEA/USP.

Caroline Maria Bezerra de Araújo (UFPE), 2023, " Adsorção de aminoácidos e proteínas em coluna de leito fixo utilizando hidrogéis biocompósitos à base de grafeno", co-supervision with Alexandre Ferreira; LSRE-LCM on going.

Publication Dates

• Publication in this collection
  16 Sept 2024
• Date of issue
  2024

History

• Received
  06 May 2024
• Accepted
  10 July 2024