Estimation of micromixing parameters from tracer concentration fluctuations.

Abstract

The tracer concentration fluctuation response (TCFR) matching method for estimating micromixing parameters was developed and the characteristics of this method were evaluated. In this method, micromixing parameters were estimated from measurements of small-scale fluctuations in the concentration of an inert tracer in the exit stream during a dynamic tracer test of a chemical reactor. Computational experiments demonstrated that this method was a viable alternative to existing parameter estimation methods. Predicted fluctuation responses were determined for 21 mixing models, including the IEM (interaction by exchange with the mean), coalescence-redispersion, and 2-, 3-, and 4-environment models. The responses for these models could be efficiently calculated in terms of definite integrals. A computer program was written to perform not only parameter estimation using the TCFR matching method, but also reactor simulation and parameter estimation by steady-state performance matching. The reliability and efficiency of the TCFR matching method was evaluated through computational experiments using simulated response measurements. Systematic measurement errors expected for typical experimental apparatus (one to two percent) resulted in one to two percent error in the estimated parameters. Expected r and om measurement errors (five to ten percent) resulted in one to two percent error in the estimated parameters. Approximate bounds for the parameter estimation error in terms of the measurement error were also determined. Results showed that parameters estimated from the TCFR and steady-state performance (SSP) matching methods for the same conditions were correlated with a coefficient of 0.9916. The equivalence of the corresponding parameter estimate was supported, in that the hypothesis of equivalence could not be rejected even at the ten percent significance level. Computational experiments demonstrated that the TCFR method was about 500 times more computationally efficient than the SSP matching method. Computational experiments confirmed that it was possible to discriminate between competing mixing models based on statistical analysis of residual errors. It was found that model inadequacy was always detected when the relative error in the measurements was less than one percent, but was detected in only eight percent of the cases where the error exceeded ten percent.