Lumped Kinetic Model Research Articles

Pyrolysis of the mixture of biomass and plastics in countercurrent flow reactor Part I: Experimental analysis and modeling of kinetics

A shaft kiln is considered to be a promising pyrolysis device for the efficient decomposition of municipal wastes. In this device, the temperature distributions of the gas and solid phases can be separately controlled, thereby leading to considerably different profiles for both the phases. The temperature controllability in a shaft kiln helps us to obtain a suitable profile of the gas-phase temperature for the decomposition of tar that evolves from the solid phase. By leveraging this advantage of the shaft kiln, we performed further pyrolysis and steam reforming of the volatiles formed from the pyrolysis of biomass and several polymers using a two-stage reactor that was maintained at different temperatures. The amount of tar decreased with an increase in the temperature in the upper reactor in the absence of a catalyst. By using the experimental results, we developed a lumped kinetic model for secondary gas-phase reactions and performed a kinetic analysis of the reactions that proceeded in the upper reactor. It is confirmed that the simulation model is successful in reproducing the product distribution of the gas-phase reactions of volatiles from biomass and polymers.

Removal of tar component over cracking catalysts from high temperature fuel gas

Five catalysts were evaluated for removal of tar components in high temperature fuel gas cleaning. 1-Methylnaphthalene was chosen as a model of the tar components. The NiMo catalyst having the highest surface area exhibited the highest activity of tar removal among the five catalysts. The effects of reaction temperature and space velocity on tar removal were studied in the range of 250–650 °C and 3000–9000 h −1, respectively. A lumped kinetic model was developed to describe the removal process. A sequential method to estimate the rate constants in the lumped kinetic model was adopted, which greatly simplifies the data treatments. Kinetic constants and activation energies were determined by a nonlinear regression program. The results showed that the predicted yields were very close to the experimental ones.

Oxidative coupling of methane in a fixed bed reactor over perovskite catalyst: A simulation study using experimental kinetic model

The oxidative coupling of methane (OCM) to ethylene over a perovskite titanate catalyst in a fixed bed reactor was studied experimentally and numerically. The two-dimensional steady state model accounted for separate energy equations for the gas and solid phases coupled with an experimental kinetic model. A lumped kinetic model containing four main species CH 4, O 2, CO x (CO 2, CO),and C 2 (C 2H 4 and C 2H 6) was used with a plug flow reactor model as well. The results from the model agreed with the experimental data. The model was used to analyze the influence of temperature and feed gas composition on the conversion and selectivity of the reactor performance. The analytical results indicate that the conversion decreases, whereas, C 2 selectivity increases by increasing gas hourly space velocity (GHSV) and the methane conversion also decreases by increasing the methane to oxygen ratio.

Aromatic alkylation catalyst

For the methanol-to-propylene process, a lumped kinetic model was developed on the basis of dual-cycle reaction mechanism, which attempted to reflect the main reaction paths with a combination to show the evolution of mole fraction of individual light olefins (C2, C3 and C4) with space time. The experiments were performed in a continuous flow fixed-bed reactor at 0.1 MPa as well as varied reaction temperature from 400 to 480 °C and space time from 0.3 to 32.0 gcatalyst h mol−1, and the experimental data obtained on the structured [email protected] and powdered HZSM-5 catalysts were fitted by MATLAB software based on the established model. The fitted results show that the lumped kinetic model well describes the product distribution and is identified to be suitable by model identification. Compared to the powdered HZSM-5, the [email protected] shows higher diffusion efficiency and narrower residence time distribution, not only promoting the propylene formation but also improving the utilization efficiency of the structured HZSM-5.

Concentration control for protein crystallization via a continuously-fed crystallization chamber

A continuously-fed crystallization chamber that allows for kinetic path control through the crystallization phase diagram (from labile/nucleation to metastable/growth) was fabricated and used to crystallize lysozyme. A lumped kinetic model was developed, and parameters for heterogeneous nucleation kinetics were determined. Heterogeneous nucleation was found to have faster nucleation kinetics and slower growth kinetics than homogeneous nucleation, as expected. The major contributions of the new device are (1) to allow better control of the chemical environment for studies of crystal nucleation and growth, and (2) to allow lumped-model analysis of those studies to extract kinetic parameters.

Model discrimination in hydrocracking of vacuum gas oil using discrete lumped kinetics

In this work, a discrete lump kinetic model for hydrocracking is developed from continuous kinetics using carbon number and true boiling point as the basis. The typical global reactions that occur in hydrocracking are isomerization and cracking. The latter reaction is assumed to model the hydrocracking process. The C–C bond cleavage in hydrocracking is a binary process in which only two products are formed in each scission. The product yield distribution is assumed to be defined by the stoichiometric kernels. This describes the frequency distribution of the reactions, which each lump undergoes. The preexponential factor and activation energy of the lumped rate coefficients are estimated by regression. The applicability of the proposed method is validated using data cited in the literature.

MODELING AND SIMULATION OF INDUSTRIAL FCC RISERS

Risers are considered vital parts in Fluidized Catalytic Cracking (FCC) conversion units. It is inside the riser reactor that the heavy hydrocarbon molecules are cracked into lighter petroleum fractions such as liquified Petroleum gas (LPG) and gasoline. The FCC process is considered a key process in the world petroleum industry, since it is the main responsible for the profitable conversion of heavy gasoil into commercial valuable products. This work presents a simplified transient model to predict the response of a FCC riser reactor, i.e., the fluid flow, temperature and concentrations of the mixture components throughout the riser and at the exit. A bi-dimensional fluid flow field combined with a 6 lumps kinetic model and two energy equations are used to model the gasoil mixture flow and the cracking process inside the riser reactor. The numerical results are in good agreement with experimental data, as a result, the model can be utilized for design, and optimization of FCC units. The simulation herein presented shows the applicability of the proposed method for the numerical simulation and control of industrial riser’s units.

Adsorption of monoclonal antibody variants on analytical cation-exchange resin

Monoclonal antibody (MAb) variants differing by one or two C-terminal lysine residues can be separated by cation-exchange chromatography due to the difference in their charge distribution. The adsorption of the three MAb variants on a weak cation-exchange resin was characterized using directly the raw mixture in spite of the presence of some impurities. The effects of both, pH and eluent salt concentration, on the adsorption isotherm were investigated. Under certain experimental conditions distorted peak shapes and even peak doubling for single variant injections were obtained, in addition to unexpectedly long retention times. These observations were explained based on equilibrium theory. The separation of the MAb variants was designed for an isocratic and a linear salt gradient operation. The corresponding optimal values of pH and salt concentration were determined. The use of salt gradients not only allows reducing the process time and increasing enrichment of the variants, but also leads to some loss in purity. A baseline separation could be obtained under isocratic and strongly adsorbing conditions at pH 6.3. A lumped kinetic model and a procedure for estimating the corresponding parameters were developed and validated by comparison with experimental elution chromatograms in a wide range of operating conditions.

Modeling of the kinetic for the acidolysis of different triacylglycerols and caprylic acid catalyzed by Lipozyme IM immobilized in packed bed reactor

This work proposes a lumped kinetic model for the acidolysis of a triacylglycerol (TAG) and an odd free fatty acid (FFA) in a non-aqueous medium, catalyzed by a 1,3 specific lipase immobilized on a solid support. This model is based on the mechanism of the acidolysis reaction by considering the following hypothesis: (1) only the fatty acids in positions 1 and 3 of TAG are exchanged and these two positions in the glycerol backbone are equivalent and (2) the only intermediate of appreciable lifespan in which the enzyme participates is the acyl-enzyme complex. The kinetic equation obtained for the rate of incorporation of an odd fatty acid to TAG has been applied to the results obtained in the acidolysis of three oils (commercial triolein, cod liver oil (CLO) and a commercial oil enriched in eicosapentaenoic acid (EPA), EPAX 4510TG) with caprylic acid (CA), catalyzed by the immobilized lipase Lipozyme IM contained in a packed bed reactor (PBR). The acidolysis has been carried out by recirculating the reaction mixture through the PBR until the reaction equilibrium was reached. In these conditions it has been proved that the PBR behaves as a perfect mixed dispersion reactor and the experimental results obtained at low TAG concentrations ( < 100 mol / m 3 ) have been acceptably fitted to the kinetic expression obtained from the proposed model, with only two fitting parameters. However, for TAG concentrations higher than 100 mol / m 3 , an appreciable reduction of the reaction rate was observed. This result was due to the decrease of the effective diffusivity of reactants within the pores of the support where the lipase is immobilized, since the viscosity of the reaction mixture increases appreciably when the reactant concentration also does. When this phenomenon is included in the developed kinetic model, the experimental results obtained at high TAG concentrations could also be explained, even in absence of the organic solvent ( n -hexane). It is observed that the influence of diffusion into the pores increases with the degree of CA incorporation to TAG, which was due to the increase of TAG and native fatty acid concentrations in the particle pores, which determines a continuous decrease in the effective diffusivity of CA.

Five lumped kinetic models of liquefied petroleum gas under aromatization reaction conditions

The aromatization reaction of liquefied petroleum gas has been studied by using three liquefied petroleum gases as raw material and LBO-A as catalyst, and a five lumped kinetics model network has been put forward on the basis of lumped theory and the aromatization reaction mechanism. In the network the aromatization reaction species were firstly lumped into C4=, C40, propylene, low molecule hydrocarbon, liquid and coke. A mathematical method is first introduced to study the product distribution of liquefied petroleum gas aromatization reaction. The results from experimental data are in accordance with the quantitatively analytical conclusions drawn from the calculated data.

Kinetics of gas oil catalytic cracking

In the present work catalytic cracking of gas oils has been studied in a standard MAT reactor. The cracking product distribution was measured at four different temperatures. Based on the experimental results, a 4-lump kinetic model was applied. Kinetic constants were estimated using the sequential step optimization method. Simulation results have shown to be in a good agreement with experimental data. An isothermal pseudo steady-state model for fixed bed MAT reactor is proposed.

Mass transfer kinetics and breakthrough and elution curves for bovine serum albumin using cibacron blue cellulose membranes

The mass transfer of bovine serum albumin onto a stack of cibacron blue cellulose membranes in the loading and elution stages were studied. The breakthrough curves obtained in the loading stage were fitted to the pore and the lumped kinetic (LK) models, respectively. Then experimental data obtained in the elution stage were described by using the LK model in which the kinetic equation, the initial and the boundary conditions were rewritten according to the operation. For the breakthrough curves it was found that the contribution of the sorption kinetics to band broadening was significant whereas that of axial dispersion was negligible. In contrast, both of these contributions were significant to the profile of the elution curve. By studying the mass transfer kinetics in the elution stage, information about the influence of the module geometry on the performance of affinity membrane separations may be obtained.

Nine lumped kinetic models of FCC gasoline under the aromatization reaction conditions

The aromatization reaction of FCC gasolines has been studied by using three FCC gasoline (Shenghua, Lanlian and Fushun) and LBO-A as catalyst, and the nine lumped kinetics models network has been put forward on the basis of lumped theory and the aromatization reaction mechanism. In the network, the aromatization reaction species were firstly lumped into n-paraffins, i-paraffins, olefins, aromatics, coke, C 4 = , C 4 0 , C 2 – 3 = and H 2 + C 1 – 3 0 . The results from the experimental data are in accordance with the quantitative analytical conclusions drawn from the calculated data.

Computational model of excitable cell indicates ATP free energy dynamics in response to calcium oscillations are undampened by cytosolic ATP buffers

Mitochondria in excitable cells are recurrently exposed to pulsatile calcium gradients that activate cell function. Rapid calcium uptake by the mitochondria has previously been shown to cause uncoupling of oxidative phosphorylation. To test (i) if periodic nerve firing may cause oscillation of the cytosolic thermodynamic potential of ATP hydrolysis and (ii) if cytosolic adenylate (AK) and creatine kinase (CK) ATP buffering reactions dampen such oscillations, a lumped kinetic model of an excitable cell capturing major aspects of the physiology has been developed. Activation of ATP metabolism by low-frequency calcium pulses caused large oscillation of the cytosolic, but not mitochondrial ATP/ADP, ratio. This outcome was independent of net ATP synthesis or hydrolysis during mitochondrial calcium uptake. The AK/CK ATP buffering reactions dampened the amplitude and rate of cytosolic ATP/ADP changes on a timescale of seconds, but not milliseconds. These model predictions suggest that alternative sources of capacitance in neurons and striated muscles should be considered to protect ATP-free energy-driven cell functions.

Modeling and Simulation of an Industrial Fluid Catalytic Cracking Riser Reactor Using a Lump-Kinetic Model for a Distinct Feedstock

A process model for an industrial fluid catalytic cracking reactor is an important tool for predicting the flexibility to operate with different feedstocks within the expected range of conversion, yield of gasoline, and coke production. In this work, a steady-state process model has been developed to describe a two-phase transported-bed riser reactor that incorporates the stripping section and uses a lump-kinetic scheme to account for the cracking of different feedstocks characterized by the paraffin, aromatic, and naphthene contents. The dependency of the kinetic parameters on the type of feedstock is accounted for by expressing frequency factors as a function of the aromatic/naphthenic ratio in the feedstock. The stripping section, where the recovery of adsorbed hydrocarbons takes place, is modeled as a continuous stirred tank reactor where mainly the thermal cracking of the adsorbed species takes place. The process model is used to predict product yields from the catalytic cracking of three different g...

A Four Lump Kinetic Model for the Simulation of the Hydrocracking Process

: Hydrocracking is a very important secondary refining process used to convert low value vacuum gas oils into high value fuels. The chemistry of the hydrocracking process is very complex due to the involvement of high molecular weight complex hydrocarbons in the reactions. Process modeling and simulation of the hydrocracking unit is very challenging due to the complexities of chemistry and the process. In the present work, a mathematical model is described to analyze the performance of the hydrocracking process in terms of product yields. A four lump discrete lumping approach is employed with a hydrocracking reaction scheme involving six reactions. The kinetic constants for the reactions were estimated by minimizing the error between the experimental and predicted yields of kinetic lumps. Experimental data reported by Ali et al. (2002) were used to validate the proposed model. The model predictions were found to agree well with the experimental data. The proposed model can be used to simulate the performance of commercial hydrocrackers using kinetic parameters estimated from pilot plant experiments.

A lumped kinetic model for gold ore cyanidation

The effect of particle size on the kinetics of gold cyanidation was investigated for a gold ore from the Abitibi region (Canada). Six size fractions representative of the plant operation were used to carry out the gold leaching and cyanide consumption kinetic tests. A two-level factorial experimental design was used for the gold leaching tests of the six size fractions. The free cyanide concentrations were selected as 260 and 650 mg/L, the dissolved oxygen concentrations as 8 and 40 mg/L, and the pH was maintained constant at 12. The gold concentration as a function of time was fitted to a lumped pseudo-homogeneous kinetic model, using a least-squares method. The results show that the gold dissolution kinetic reaction orders are approximately two for gold, one for free cyanide and a quarter for dissolved oxygen, and that the kinetic rate constant is a decreasing cubic function of the ore particle average diameter. In the cyanide consumption tests, conducted also for the six different size fractions, the pH was maintained at 12, the dissolved oxygen concentration was chosen as 8 mg/L, and the initial free cyanide concentration as 260 mg/L. The cyanide consumption lumped kinetic model shows that the reaction order is approximately three for free cyanide, and that the rate constant is a decreasing reciprocal square-root function of the ore particle size. Although finer grind of the ore enhances gold release, it considerably increases the cyanide consumption due to the liberation of the copper and iron bearing minerals, thus leading to a possible optimization of the ore size fraction that can simultaneously promote high gold recovery and acceptable cyanide consumption.

Kinetic Model for Moderate Hydrocracking of Heavy Oils

In this work, a kinetic model for hydrocracking of heavy oils is proposed. The model includes five lumps: unconverted resid (538 °C+), vacuum gas oil (VGO; 343−538 °C), distillates (204−343 °C), naphtha (IBP-204 °C), and gases. Kinetic parameters were estimated from the experimental results obtained in a fixed-bed downflow reactor. The proposed lump kinetic model fitted the data for hydrocracking of Maya heavy crude with a Ni/Mo catalyst at 380−420 °C reaction temperature, 0.33−1.5 h-1 liquid hourly space velocity, 5000 scf/bbl, and 70 kg/cm2. Only resid cracked to naphtha at 380 °C, but all heavier fractions produced some naphtha at higher temperature. The predicted product composition is in good agreement with experimental values with an average absolute error of less than 5%.

A kinetic modeling study of the thermal degradation of halogenated polymers

This paper presents a semi-detailed and lumped kinetic model of poly(chloroprene) thermal degradation. This is the extension of a previous paper in which a polyvinylchloride (PVC) pyrolysis mechanism was presented. The mechanism of 38 species and pseudo-components (molecules and radicals) involved in about 190 reactions reproduces the main characteristics of poly(chloroprene) degradation and volatilization quite well. The presence of the two-step mechanism – the first step of which corresponds to dehydrochlorination/condensation and the second to TAR release and residue CHAR formation – are correctly predicted both in quantitative terms and in the temperature ranges. The model was validated by comparison with some thermogravimetric analyses. Similarities and differences with PVC are discussed both in terms of degradation behavior and chemical mechanisms. A further extension of the proposed approach refers to a brominated plastic (polyvinylbromide). In fact, a few modifications to the rate constants of the kinetic model also predict the pyrolysis of this plastic quite well. When compared with the typical one-step global apparent degradation models, the approach proposed here is much more flexible: in fact it spans quite large operating ranges, especially when it comes to predicting product distributions. The initial results of these product predictions, even though still limited, are encouraging and confirm the validity of the proposed model.

Equivalence of the microscopic and macroscopic models of chromatography: stochastic–dispersive versus lumped kinetic model

The microscopic model of chromatography is a stochastic model that consists of two fundamental processes: (i) the random migration of the molecules in the mobile phase, and (ii) the random adsorption–desorption of molecules on the stationary phase contained in a chromatographic column. The diffusion and drift of the molecules in the mobile phase is described with a simple one-dimensional random walk. The adsorption–desorption process is modeled by a Poisson process that assumes exponential sojourn times of the molecules in both the mobile and the stationary phases. The microscopic, or molecular model of chromatography studied here turns out to be identical to the macroscopic lumped kinetic model of chromatography, whose solution is well known in chromatography. A complete equivalence of the two models is established via the identical expressions they provide for the band profiles.