Kinetics of Limonene Hydrogenation in High-Pressure CO<sub>2</sub> at Variation of Hydrogen Pressure

Anikeev, V. I.; Yermakova, A.; Bogel‐Łukasik, Ewa; Ponte, Manuel Nunes da

doi:10.1021/ie9010996

Cited by 8 publications

(3 citation statements)

References 8 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Within the current literature, it is common to find coupled rate equations involving a dozen or more species. ,− This begs the question as to whether ADM is applicable to such problems. The increase in the number of differential equations is primarily reflected in A ( i , n ) ( y ⃗( t )).…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Integration of the Chemical Rate Equations via a Discretized Adomian Decomposition

Younker

2011

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

Chemists are frequently interested in rate equations, which are first-order differential equations. Numerical integration of these equations allows the researcher to accurately predict the concentrations of chemical species at any time given the initial conditions. Explicit Runge-Kutta (RK) integration is widely used for solving the rate equations. In this article, Adomian decomposition methods (ADM) are used to obtain the solutions of chemical rate equations. The Adomian method outlined here outperforms high-order RK routines in the arenas of accuracy and truncation error. Additionally, four modifications are introduced that place the Adomian integration on par with RK in terms of speed (a primary reason for which Adomian decomposition methods are currently underemployed). The inclusion of up to the fifth term in the Adomian expansion gives a truncation error of order O(h 10 ). The method as presented yields solutions which are step-size independent in the nonstiff regime. The problem of rapid polynomial divergence is addressed through discretizing the time axis. Performance of the ADM method against an implicit algorithm is also given. ' INTRODUCTIONThe construction of a chemical mechanism is one of the first steps a chemist takes following the discovery of a novel reaction. Many tools are employed in order to determine the sequence of intermediates and the rates at which they change. The results of these studies can be succinctly expressed as coupled differential equations, the solutions of which yield the concentrations of the experimentally observed reactants at all times of interest. To uncover the desired rate constants, chemists and biochemists frequently analyze reactions under limiting conditions. These pseudo-first-order, steady-state, 1 and quasi-steady-state kinetics 2 simplify the differential equations through elimination of one or more degrees of freedom. When these conditions cannot be met, kinetic inversion or global analysis is employed to determine the rates. 3-14 These nonlinear regression techniques require solutions of the coupled chemical rate equations. Symbolic integration of the equations can be difficult and is, in most cases, impossible. 5-7 Thus, numerical integration is necessary. One popular numerical integration method was originally proposed in 1895 by Runge and later expanded by Kutta. 15,16 Fourth-order (RK4) and fourth-/fifth-order adaptive step size (RKF45) RungeKutta routines are frequently used to approximate ordinary differential equations as initial-value problems (IVP), 17,18 of which the rate equations are prime examples. 3,8,11 An alternative approach for solving differential equations was proposed by Adomian in the 1980s. His solution involves decomposing the nonlinear terms in the differential equation(s) into a series of polynomials. 19,20 The integration of this infinite series of polynomials, under known initial or boundary conditions, is called the Adomian Decomposition Method (ADM). 21 Truncation of the series yields an analytic approximation to the solution. Th...

show abstract

Section: Resultsmentioning

confidence: 99%

“…12,[43][44][45][46][47] This begs the question as to whether ADM is applicable to such problems. The increase in the number of differential equations is primarily reflected in A (i,n) (y B(t)).…”

Section: Articlementioning

confidence: 99%

Numerical Integration of the Chemical Rate Equations via a Discretized Adomian Decomposition

Younker

2011

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

show abstract

“…Concentration of limonene, which decreased due to the volumetric expansion of the liquid phase as CO 2 pressure increased, turned out to be the main factor in the kinetics of hydrogenation of limonene 3 in high-pressure CO 2 in the biphasic system catalyzed by Pd/C [59]. A mechanism of limonene 3 hydrogenation in high-pressure CO 2 was proposed based on the kinetics data [60].…”

Section: Environmentally Benign Transformations Of Monoterpenes and Mmentioning

confidence: 99%

Environmentally Benign Transformations of Monoterpenes and Monoterpenoids in Supercritical Fluids

Волчо

Anikeev

2014

Supercritical Fluid Technology for Energy and Environmental Applications

View full text Add to dashboard Cite

Terpenes: A Valuable Family of Compounds for the Production of Fine Chemicals

Rubulotta

Quadrelli

2019

Studies in Surface Science and Catalysis

View full text Add to dashboard Cite

Kinetics of Limonene Hydrogenation in High-Pressure CO₂ at Variation of Hydrogen Pressure

Cited by 8 publications

References 8 publications

Numerical Integration of the Chemical Rate Equations via a Discretized Adomian Decomposition

Numerical Integration of the Chemical Rate Equations via a Discretized Adomian Decomposition

Environmentally Benign Transformations of Monoterpenes and Monoterpenoids in Supercritical Fluids

Terpenes: A Valuable Family of Compounds for the Production of Fine Chemicals

Contact Info

Product

Resources

About

Kinetics of Limonene Hydrogenation in High-Pressure CO2 at Variation of Hydrogen Pressure

Cited by 8 publications

References 8 publications

Numerical Integration of the Chemical Rate Equations via a Discretized Adomian Decomposition

Numerical Integration of the Chemical Rate Equations via a Discretized Adomian Decomposition

Environmentally Benign Transformations of Monoterpenes and Monoterpenoids in Supercritical Fluids

Terpenes: A Valuable Family of Compounds for the Production of Fine Chemicals

Contact Info

Product

Resources

About

Kinetics of Limonene Hydrogenation in High-Pressure CO₂ at Variation of Hydrogen Pressure