Model a CSTR reactor with PHREEQC
A continuous-flow stirred tank reactor (CSTR) is widely applied in chemical- and bio-engineering for water treatment and making chemicals. In earth sciences, it can be useful for detecting system response on changes in water quality, temperature, pressure, residence time, etc.
The residence time in the reactor is:
Without reactions, an initial concentration in the tank changes as:
| 
|
Figure 1 shows PHREEQC results and the analytical solution of the tank concentration of Na+, with 1 mM Na+ initially in the tank, and 0.1 mM Na+ in the inflow (PHREEQC input file CSTR_example.phr). The standard deviation of the calculation is 1.05 μmol/L for the points in the graph; it can be reduced further with smaller time steps in the model.
|
Figure 1
| 
|
Kinetics, mineral- and gas-equilibria, and temperature- or pressure changes can be defined for the tank with the appropriate keywords.
For example, figure 2 shows modeled results of denitrification by denitrifying bacteria in the reactor (same input file CSTR_example.phr). The inflow stream contains 3 mM NO3-, which is reduced to about 1.1 mM in the outflow. The bacteria are supplied with H2 as reductant at a low concentration, and they use the energy gained from the reaction for growth.
|
Figure 2
| 
|
Bad mixing in the reactor can be simulated by adding more cells and mixing factors among the solutions.
Figure 3 show the results when 30% of the reactor volume is stagnant but mixes with the mobile part. The concentrations of Na+ and NO3- change quicker than before, because the reactor volume between in- and outlet is smaller. For the conservative (unreacting) Na+, the discrepancy with the analytical solution illustrates the physical non-equilibrium in the reactor. A stop-flow experiment (here of 8 hours) shows concentration changes of both the kinetic (NO3-) and conservative (Na+) solute. (In case of kinetic disequilibrium, a conservative tracer would not be affected.)
Mixing factors of mobile and stagnant water can be related to diffusion over the interface of the two, as explained in Multicomponent diffusion in clays
|
Figure 3
| 
|