(363f) Direct Parameter Optimization for Chemical Reaction Kinetics

A traditional method for calibration of parameters of chemical reaction rate laws from experimental concentration time-dependent data involves an ODE-solver in the loop. This is a laborious algorithm that relies on the solution of the ODE system at each optimization iteration step. Since ODE equations can be very sensitive to parameters and a solution can become unstable, this method is not without challenges. Alternatively, this work experiments with a direct method of parameter optimization using the time-derivative of the experimental data directly. This avoids the use of an ODE solver in the parameter optimization loop but requires differentiation of the experimental data. We use a smooth approximation of the concentration data that allows for differentiation, and solve the non-linear algebraic parameter optimization problem via a least-squares residual method. We apply this method to contrived reaction mechanisms analyzing its performance as compared to golden values. We investigate the role of rank-deficiency of the normal equations of the least-squares Gauss-Newton's method, and demonstrate the usage of the Hessian matrix for the general reaction rate power-law form. The eigenvalues of the Hessian matrix provide useful information about the stationary point of the objective function converged to. Last, computational experiment are made for the radiolysis of water reaction mechanism with and without borated water. In general, we find parameter optimization of reaction mechanisms for water radiolysis of interest to nuclear reactors and chemical reprocessing to be difficult to calibrate accurately. Also, the literature seems lacking on how reaction mechanism have been calibrated against experimental data which puts in question the applicability/trasferability of the reaction rate formulae.