Sizing the P removal structure: what is the required mass of P sorbing material (PSM) necessary for the job?

With the following information, we can now take the next step and estimate how much PSM is necessary for the job:

1. Annual P load at the site
2. Typical dissolved P concentration in runoff (or drainage) water to be treated
3. P removal goal i.e. the % of the annual P load that is desired to be removed
4. Characteristics of the locally available PSM

Annual P load and typical dissolved P concentrations

The annual P load was already determined as described in the previous post.  Turned out that at our site, we expect an annual P load of 22 kg.  This was calculated partly by knowing that our typical high-end dissolved P concentration is 2 mg/L.

P removal goal

Based on the large P load at this site, I am setting a range for removing the annual P load from 20 to 50%.
 

Characteristics of the locally available PSM

This is the part that requires a bit of work.  In order to properly design a P removal structure, one must develop a “design curve” for the PSM that they will be using in their structure.  A design curve is simply a quantitative description of the relationship between dissolved P loading of the PSM and the % discrete P removal.  This must be determined in a flow-through setting; a batch P sorption experiment will not suffice!  See Penn and McGrath (2011) and Stoner et al. (2012) for examples of this comparison.  We and other researchers have determined that in the context of a P removal structure, any assessment of P removal must be in a flow-through setting.  A batch sorption experiment in this context is only useful as an index to compare different PSMs, not to quantify how much P it will remove from a flowing solution.  There are several reasons why the batch sorption experiments fails in application to a flowing context such as a P removal structure:

1. Batch tests typically has a non-representative long contact time
2. Batch tests do not have constant removal of reaction products
3. Batch tests do not have constant addition of reactants (i.e. P) 

A design curve is specific with regard to the retention time (i.e. contact time) and the inflow P concentration that is moving through the PSM.  Below is an example of a design curve for an acid mine drainage residual (AMDR) that we collected from Eastern OK:

Note that this design curve is specific to an inflow P concentration of 1 mg P/L and a retention time of 30 seconds.  In other words, it takes 30 seconds for the inflowing solution to pass through the AMDR.  As you would expect, the P sorption is initially very high, but with further P loading the AMDR is not able to sorb as much P as it did previously.  The shape of this curve varies between PSMs, retention times, and inflow P concentrations.  This is discussed in detail in Stoner et al. (2012).

Knowledge of the equation of a design curve is necessary for choosing the necessary amount (mass) of PSM for your structure.  This curve can serve several purposes, depending on what you desire:

1. Estimate the lifetime of the structure if a given mass of a specific PSM is to be placed in the structure.  In this case, “lifetime” is defined as the amount of time until the P removal structure is no longer able to sorb P that flows into it.
2. Upon integration of the design curve, estimate how much P will be removed by the structure during that lifetime. 
3. Upon integration of the design curve, estimate how much of the PSM (i.e. mass) will be necessary to remove a desired amount of P under the condition of the design curve.     

For our purposes at this particular site, our use of the design curve will be for purpose number 3.  For example, at our site we have several PSMs locally available to us: steel slag from Fort Smith, drinking water treatment residuals (WTRs) from Tulsa, fly-ash from Muskogee, and an AMDR.  All of these are potential options for us.  Other PSMs may be available in different regions.  Some areas may have a greater abundance of steel slag or WTRs.  Perhaps you live in Western PA (God’s country) where AMDRs are highly available.  There may be some PSM that is unique to your region.

Considering our conditions previously determined: annual P load of 22 kg, typical inflow P concentration of 2 mg/L, and appropriate design curves for each material, it would require:

• 5.5 tons of the Tulsa WTR to remove 37% of the annual P load
• 3.1 tons of our AMDR to remove 49% of the annual P load
• 131 tons of sieved steel slag (1/4” and greater diameter) to remove 21% of the annual P load
• 41 tons of a treated sieved steel slag (1/4” and greater diameter) to remove 45% of the annual P load

Model for predicting the design curve instead of directly measuring it

We developed a model for predicting the equation of a design curve for a specific PSM, as a function of the retention time, inflow P concentration, and selected PSM characteristics (chemical and physical).  This model was developed for the following reasons:

1. Conducting a flow-through experiment for every single individual PSM sample and every possible flow condition (i.e. inflow P concentration and retention time) is extremely time consuming and expensive.
2. There is great variation in P sorption behavior between different PSMs.
3. There is great variation in P sorption behavior the same type of PSMs that come from different sources.
4. There can be variation in P sorption behavior among the same type of PSMs that come from the same source, but are produced at different times.   
5. It is much easier and less expensive to measure certain chemical and physical characteristics of PSMs to use in predicting a design curve, than it is to conduct many flow-through P sorption experiments. 

Through the tireless work of a former graduate student, Dustin Stoner (a living legend as far as I am concerned), we have developed a model to predict the equation for a design curve for a specific material under specific flow conditions.  One thing that we learned from conducting > 1000 flow through P sorption experiments, is that under the relatively short retention times that we are working with in the world of runoff and subsurface drainage P removal structures (seconds up to 20 minutes), retention time usually has little impact on P removal (see Stoner et al., 2012).  This is true for materials that dominantly remove P via fast kinetics by Al and Fe sorption (ligand exchange) and for Ca-rich materials that have a relatively high pH AND are buffered to a high pH.  For example, flue gas gypsum is an example of a Ca-rich material that is NOT highly buffered with regard to pH, and therefore the retention time does have a dramatic impact on P removal in a flow-through setting.  Gypsum is one of the few materials that I have observed this for.  For most PSMs, retention time does not have much impact at our scale of retention time that we are aiming for.  However, for materials such as gypsum, increased retention time will greatly increase P removal (see McGrath et al., 2012).  

While the details of this model for predicting the design curve will not be discussed here, the model is at the heart of the current software that we are developing, which essentially helps one to design a site-specific P removal structure in the same manner in which this blog describes.  If you are interested in a license to that software, please contact me.