Conservative tracer dispersion

Rivers are generally considered as a plug flow reactor with dispersion. Determination of the dispersion coefficient for rivers was covered in Chapter 6, and determination of the gas transfer coefficient is a slight addition to that process. We will be measuring the concentration of two tracers a volatile tracer that is generally a gas (termed a gas tracer, C) and a conservative tracer of concentration (Cc). The transported quantity... 

R was determined from the area under the breakthrough curves using a planimeter. Mass eluted compared well with mass injected, indicating that mass balance was achieved. Dispersion (D) for a conservative tracer was determined by fitting the KCl breakthrough curve to the equilibrium model the fitted parameters were R and P. A nonlinear least squares method was used for parameter estimation 7. The sum of the squares of the deviation between model and data (ssq) was used as a measure of total error in the model fit. 

The effects of velocity, column size, and packing on dispersion of a conservative tracer were investigated in order to separate the effects of slow sorption and desorption from hydrodynamic dispersion. D values were obtained by fitting an equilibrium model to the breakthrough curves (Table III). There was no correlation between dispersion and column length or diameter, as expected. Dispersion and velocity are related, however. 

It is worth a short detour into fluid mechanics to explore some details of this approach and how it fits into the reactor conservation equations. For moderate flow velocities the dispersion of a tracer in laminar flow will occur by axial and radial diffusion from the flow front of the tracer and, in the absence of eddy motion, this will be via a molecular diffusion mechanism. However, the net contribution of diffusion in the axial direction can be taken as small in comparison to the contribution of the flow velocity profile. This leaves us with a two-dimensional problem with diffusion in the radial direction and convection in the longitudinal direction the situation is considered in illustrated in Figure 5.7. 

Let us go back to Equation 1.1, but now imagine that the Brownian particle diffuses in a colloidal dispersion formed by other N particles in the volume V with which it interacts by means of pairwise direct (i.e., conservative) interactions but in the absence of hydrodynamic interactions. The pairwise force that this tracer particle (T) exerts on particle / is given by Fj- = -V M( r - rj. ), so that Equation... 

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