Solute Dispersion and Transport in Pipes under Transient Hydraulic Conditions

Solving or approximating the advection-diffusion/dispersion equation (ADE) is a challenging and important problem and has thus motivated a great deal of intense research. A specific complication arises from the nature of the governing partial differential equation: it is characterized by a hyperbolic non-dissipative advective transport term, a parabolic diffusive (dispersive) term and, possibly, an additional reaction/decay mechanism. In most pipeline applications, the numerical transport scheme is coupled to a steady or nearly steady hydraulic model. By contrast, this paper presents an implicit finite difference scheme for the solution of the advection-dispersion-reaction (ADR) superimposed on a full transient, method of characteristics (MOC) based, hydraulic solution. This contribution represents one of the first serious attempts to analyze the impact of water hammer conditions, and in particular fluid inertia and compressibility, on the evolution of water quality in pipe networks. The results reflect the potential of the method especially as a foundation for a more comprehensive water quality analysis in water distribution systems. The combined effect of advection, dispersion and reaction are evident at distinct stages in the modelling results.