Estimating dispersivity and injected mass from breakthrough curve due to instantaneous source

A simple method and an optimization method for explicit estimation of specific dispersivity and injected mass from an ideal breakthrough curve (BTC) due to an instantaneous injection of a solute are proposed. The specific dispersivity is defined as dispersivity divided by the distance between the injection and sampling points. An estimate of the injected mass is the pollution load from a point source. The proposed simple method yields successive estimates of the specific dispersivity and injected mass as additional data become available, which identifies the time after which the test may be terminated as the collection of data beyond this time would not improve the estimates. Using this method, the data for different flow rates and injected masses can be analyzed simultaneously. The proposed simple method does not require the full BTC to be observed. The proposed optimization method uses a derivative based technique in which the analytical derivatives are derived. The optimization method is applicable for any value of specific dispersivity.