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phosphorus and phosphorus control (4)


Tests with a simple model of phosphorus states in aquariums show that
reducing feeding rates is the most effective means of reducing phosphate
concentrations.  The second most effective ploy is to encourage higher
rates of phosphate precipitation or sorption and the third most effective
ploy is to increase water changes.

Here it is the familiar diagram again, this time for the last installment:

                    Water                 Water
                    changes               changes
                      ^^                    ^^
                      ^^                    ^^
                      ^^                    ^^
                      ^^                    ^^
                      ^^                    ^^
                    ----------           ----------
Water change        Dissolved <<<<<<<<<< Dissolved     
Fish waste >>>>>>>> Inorganic <<<<<<<<<< Organic   <<<<<<<< Fish waste
Additives           Phosphorus           Phosphorus
                    ---------- __        ----------
                      vv       |\
                      vv         \
                      vv          \
                      vv           \
                      vv            \
                      vv             \
                      vv              \
                      vv               \
                      vv                \
                    -----------          -----------
 Fish Food          Particulate          Particulate        Fish Food
 Fish Waste >>>>>>> Inorganic            Organic    <<<<<<< Fish Waste
                    Phosphorus           Phosphorus
                    -----------          -----------
                      vv                   vv
                      vv                   vv
                      vv                   vv
                      vv                   vv 
                    Removal              Removal

In my three previous letters I described the major elements in this
diagram, discussed the terms that add and remove phosphorus from the
system, and most recently described the interactions between the forms of
phosphorus within the aquarium.  In this last letter I hope to present a
simple model of the system and describe the model's results pertinent to
controlling dissolved phosphorus levels in aquariums.

Very briefly, the model consists of four equations, each representing the
mass balance for each of the four forms of phosphorus in the system.  The
arrowed lines in the diagram above are represented in the model by a term
in one or two of the equations.  The resulting system of equations can be
solved for the concentration of each of the four phosphorus forms as a
function of the input of fish food and fish wastes, with the terms in the
equation representing the rates of water changes, sediment removal,
phosphatase activity and precipitation or sorption.

Many of the coefficients in the model depend on details of an aquarium
setup; maintenance, food composition, species selection and so on.  Some
of the details are fairly insignificant, and others have duplicative
effects.  The model has 10 coefficients. I varied two of the coefficients
to create three different test cases that cover a range of possible
aquarium conditions, Here are all 10 of the model coefficients, and the
values used for each of the three test cases.

                                    case 1     case 2      case 3

Feeding rate
   grams phosphorus/week             0.02       same         same

Phosphorus digestibility
   percent                           50%        same         same

proportion of inorganic phosphorus
   in undigestible fraction          80%        same         same

proportion of inorganic phosphorus
   in digestible fraction            20%        same         same

precipitation rate for
   dissolved inorganic phosphorus
   percent per week                  67%        100%          25%

mineralization rate for
   dissolved organic phosphorus
   percent per week                 100%        same         same

phosphatase activity for
   particulate organic phosphorus
   percent per week                  50%        10%          67%

water change rate
   percent per week                  15%        same         same

cleaning efficiency
   percent per week                  67%        same         same

resulting phosphate
   concentration in a
   55 gallon tank                  0.21 ppm     0.12 ppm     0.42 ppm

I used the cases to test 5 coefficients to see which ones could be used to
most effectively control phosphate concentrations.  I measured the
effectiveness by calculating the ratio between the percent change in the
phosphate concentration and the percent change in the coefficient.  Here
are the results for each model and each tested coefficient:

                                    case 1     case 2     case 3

feeding rate                          1.0        1.0        1.0

precipitation rate                   -.8073    -.8622     -.6098      

water change rate                    -.2713    -.2261     -.4540

cleaning efficiency                  -.0496    -.0243     -.0499

phosphatase activity
  for particulate organic phosphorus  .0494     .0242      .0497 

There aren't very many suprises here.  In all cases, reducing the feeding
rate is the most effective way to decrease phosphate concentrations.  The
second most effective alternative is to increase the rate of precipitation
or sorption of dissolved phosphate.  It's interesting that among the three
cases, precipitation is less effective for case 3, where the phosphate
concentration is highest.  Increasing water changes was the third most
effective ploy.  Again, case 3 is interesting because in the case with the
highest phosphate concentration water changes are relatively more

The effectiveness of changing cleaning efficiency and phosphatase activity
were substantially lower than for the first three tactics.  Oddly, in
every case improvements in the cleaning efficiency and decreases in the
phosphatase activity had nearly identical effects.

I hope that those of you who managed to plow through all this found
it useful and thought-provoking.

Roger Miller