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Using Breakthrough Curves for Parameter Estimation in the Convection-Dispersion Model of Solute Transport

Dep. of Environmental Science and Engineering, Faculty of Engineering, Hiroshima Univ., Higashi-Hiroshima, 724, Japan

P. Moldrup

Environmental Engineering Lab., Dep. of Civil Engineering, Univ. of Aalborg, Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark

*Corresponding author.

ABSTRACT

We present two easily applicable models for simultaneous estimation of the convective velocity (u₀) and the hydrodynamic dispersion coefficient (D₀) from breakthrough curve (BTC) data. The two models can be used for both saturated and unsaturated flow. Both models are derived from an analytical solution to the convection-dispersion equation (CDE). The first model, labeled the "slope method," is exact. It uses the slope of the BTC to estimate u₀ and D₀. The second method is approximate because it is only based on the first term of the analytical solution to the CDE. This model is labeled the "first-term method" and is not valid for very small values of Brenner number. A simple version of both models is developed. A discussion of numerical stability and choice of increments in the model calculations is given. The simple version of the slope method is found to be too numerically unstable when applied to actual BTC data. The remaining methods are tested against two sets of actual measured BTC data by applying each method several times for different parts of each BTC. The values of coefficient of variation between the results are low for all methods (0.1–1.3% for u₀ and 2.7–32% for D₀). The agreement between the mean values of the parameters u₀ and D₀ obtained by using the methods presented in this paper and the parameter values for the same BTC data sets reported by other authors is excellent.

Contribution from Hiroshima Univ., Univ. of Aalborg, and the Danish Technical Res. Council.

Received for publication July 8, 1988.

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