An enhanced tanks-in-series model for interpretation of tracer tests

Imperfect hydraulic behaviour of water treatment units, expressed by stagnation space and bypassing, may substantially reduce treatment efficiency. Computational fluid dynamics (CFD) and residence-time distribution (RTD) based tracer test models may be used to identify such problems; the RTD models are more appropriate for operating treatment units. A three-parameter tank-in-series RTD model for interpretation of tracer tests is presented in this paper, where the parameters are the number of tanks, the portion of dead-space and the portion of bypassing. Expressions for the first three moments of the proposed RTD function are derived. An optimization procedure, implemented in MS Excel, is then used to obtain the number of tanks, and the fractions of dead-space and bypassing minimizing the difference between tracer test data and unit's residence-time distribution function. The uniqueness of the solution is discussed, and comparison with simpler one and two-parameter models is provided. Results were compared with experimental data obtained from real drinking water treatment plants located in the cities of Nuevo Laredo and Río Bravo, Tamaulipas; and Piedras Negras, Coahuila, Mexico.