Numerical Parameters Estimation in Models of Pollutant Transport with Chemical Reaction

Abstract

Part 7: Applications and Control of Lumped Parameter SystemsInternational audienceIn this work we present an iterative algorithm for solving a parameter identification problem relative to a system of diffusion, convection and reaction equations. The parameters to estimate are the retardation factors, diffusivity, reaction and transport coefficients relative to a model of pollutant transport with chemical reaction. The proposed method solves the nonlinear least squares problem by means of a sequence of constrained optimization problems. The algorithm does not depend on the type of discretization method used to solve the state equation. The results reported in the numerical tests show the efficiency of the algorithm in terms of performance and solution quality

Continuous flow adsorption of phenolic compounds from olive mill wastewater with resin XAD16N: life cycle assessment, cost–benefit analysis and process optimization

“…Estimates of ϵ sand and α L , sand obtained in preliminary tests and the ϵ resin estimated as described above were used as input values. The best‐fit value and 95% confidence interval of α L , resin were determined by applying the Gauss–Newton method, following a procedure specifically adapted to convection–dispersion problems . In short, the integration of Eqn (1) was repeated for different values of α L , resin in order to minimize the sum of squared residuals between calculated and experimental NaCl concentrations at the column outlet.…”

“…The PC‐normalized concentrations were thus simulated by means of the following mass balance equations, relative to the liquid [Eqn (2)] and sorbent [Eqn (3)] phases: where C L , PC represents the PC liquid phase concentration, C S , PC the solid‐phase concentration (g PC /g dry resin ), k L a the mass‐transfer coefficient referred to liquid volume (h −1 ), ρ b the sand or resin bulk density (calculated as mass of dry sand or resin divided by the volume of the corresponding column portion; kg m –3 ), ϵ the resin or sand porosity (−), K eq , PC the equilibrium adsorption constant (L kg dry resin –1 ) and D eq the equivalent diffusion coefficient, calculated as α L , resin · v int , resin or α L,sand · v int , sand . K eq , PC and k L a were estimated by best‐fit on the experimental PC concentrations following the Gauss–Newton method, according to the procedure for its application to convection–dispersion problems described previously . The quality of each best‐fit was evaluated by means of the correlation coefficient R 2 as defined previously …”

“…The best-fit value and 95% confidence interval of L,resin were determined by applying the Gauss-Newton method, following a procedure specifically adapted to convection-dispersion problems. [55][56][57] In short, the integration of Eqn (1) was repeated for different values of L,resin in order to minimize the sum of squared residuals between calculated and experimental NaCl concentrations at the column outlet. The Gauss-Newton iterative algorithm was stopped when the wileyonlinelibrary.com/jctb relative variation in L,resin resulted <10 −3 .…”

Chloroform aerobic cometabolic biodegradation in a continuous‐flow reactor: Model calibration by means of the gauss‐newton method

“…The main advantages of the Gauss‐Newton method are the need to compute only first order derivatives and the rapid local convergence . However, if the Gauss‐Newton convergence is poor, quasi‐Newton methods such as Levemberg Marquardt can be suitably applied …”

“…[41] However, if the Gauss-Newton convergence is poor, quasi-Newton methods such as Levemberg Marquardt can be suitably applied. [44][45][46] The third step for the modelling of a CAH AC process consists in the application of a model adequacy test to the calibrated model. Such tests, often neglected in the modelling studies, provide a statistical criterion to evaluate whether the quality of the fit attained with a certain model is acceptable, in relation to the quality of the experimental data.…”