INVERSE PROBLEM OF TOXIC WASTE SPREADING
A. Dantsker (JWD Applied Algorithm, 15216 116 PL NE, Bothell WA 98011,
tel.: 206-526-6216, e-mail: dantsker@earthlink.net), B. Johnson (JWD Applied
Algorithm), V.Titov (University of Washington)
Fast location of the pollutant discharge is critical to prevent spreading of toxic
ingredients. Toxic discharge can occur due to technological failures (such as
damaged water pumps, filtration systems etc.) as well as a result of terrorist
activity (e.g. dumping large amount of toxic ingredient into sewage system
manhole).
We propose monitoring system including optimal sensor locating and algorithm of
inverse modeling of pollutant propagation in water systems that will determine the
origin of the toxic discharge propagating through water utility infrastructure.
A special algorithm is developed to determine best sensor location for a specific
pipe network. It calculates a boundary point on the pipe network scheme where
the unique location of pollutant source could be found at least with the nearest
sensor.
Proposed stochastic model to calculate the pollutant transport to build the
inversion calculation. With this model one can obtain a simple analytical solutions
to calculate contaminant distribution in water flow. The stochastic modeling for
pollutant migration has shown a good correlation with experiment for the
processes of chemical technology such as particle filtration, adsorption etc. [1,2].
One of the advantages of this approach is the possibility to use results for each
water pipe section consecutively. The results calculated from a previous element
of the pipe network can be used as input for the calculation in the next element.
That makes possible to apply the model to a pipe network with arbitrary
complexity. Another advantage is decrease of calculation time compared with
using convection-diffusion equations for inverse modeling. The equations can be
configured automatically for each new topology of water system.
References
1. Dantsker A.M. Filtration of Aerosol in Granular Bed, Abstract of 28th
Central Regional Meeting “Chemistry in 90’s and beyond”, June 1996,
Dayton Ohio
2. Derenyi I., Vicsek T. Cooperative Transport of Brownian Particles, Physical
Review Letters 1995, 75, pp.374-377