Feature Article: Further Studies on Protein Skimmer Performance — Advanced Aquarist. We published a paper on skimmer performance in the January 2. Advanced Aquarist magazine that detailed, for the first time, an experimental methodology to provide meaningful metrics for both the rate at which skimmers removed organics and the extent of the removal of these organics from aquarium water (Feldman, 2. Highlights of these earlier studies included: Development of a mathematical representation of the skimming process based upon a . Key experimental parameters extracted from this mathematical modeling included the rate constant, k, for organic (BSA or TOC) removal, which is a singular metric reflecting the intrinsic capacity of a given skimmer to remove the organics in question, and the total % of the available organics (BSA or TOC) that were removed before the skimmer . In this article, we report the results of these efforts. Specifically, we have: Modified our mathematical model to take into account the observation that there is a (significant) component of TOC that is not skimmable.
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We have applied this new model to the old skimmer data as well as to new data with new skimmers. Examined the performance of three new skimmers, all of which have bubble plates; the Bubble King Mini 1. Royal Exclusiv 1. Cone needlewheel skimmer, and the Reef Octopus 1. The Modified Mathematical Model.
The mathematical model derived in the January 2. Advanced Aquarist article was based upon four assumptions: The water reservoir can be treated as a continuously stirred reactor. The skimmer mixing volume can be treated as a continuously stirred reactor. The reservoir volume is much larger than the skimmer mixing volume. The rate of TOC removal in the skimmer is proportion to the amount of TOC present in the water. There is no reason to doubt the validity of assumptions 1 - 3. However, assumption #4 does not take into account the experimental observation that only some of the TOC in reef tank water is susceptible to removal by skimming.
Thus, a more appropriate and general starting point would involve explicitly breaking down TOC into two functionally distinct components. The recirculating reservoir/skimmer system (Fig. A component of the water is depleted in the skimmer by bubble- mediated removal.
Figure 1. A generic skimmer with all mathematical quantities defined. Where. To account for this observation, we have divided the TOC into a labile, or skimmer- removable component . Therefore, the total TOC that we measure experimentally is the sum of these two types of TOC: .
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However, only the labile TOC's concentration . Thus, we can confine our mathematical derivation to this labile TOC, TOCl, and at the end take into account the fact that experimentally, we can only measure the total TOC, TOCT.
Since both . In our experimental setup, a liquid volume Vr (reef tank water in a Rubbermaid tub) has an input stream and an output stream, and TOC in the water becomes depleted over time via bubble- mediated removal in a skimmer with mixing water volume Vs (see Fig. Inspection of the skimmers in action permits measurement of this . For the purposes of this analysis, we will assume that all of the active volume is water; that is, we will ignore the void volume of the bubbles, as we cannot independently assess the relative contributions of bubbles and water. This assumption will introduce an error into the calculations, but that error. Knowledge of the precise mechanism by which the skimmer's bubbles removes the water component(s) is not required; all that we need to know is that the concentration of the measured water component (TOCT in this case) is diminishing with time in the reservoir. It is essential for solving this problem that both the reservoir and the skimmer water volumes are well mixed to avoid concentration gradients. The reservoir water mixing in the experiments described below is provided by the skimmer return flow and by two powerheads in the reservoir.
We independently tested the . We observed that the site- to- site variation in TOC levels at different locations was no greater than the sample- to- sample variation at one location (both ~ 1. The mixing in the skimmer reaction chamber is provided by both rapid water movement and the agitation caused by the motion of the bubble stream. We have no independent experimental measurement/confirmation of mixing behavior in the skimmer. The application of this mathematical approach to the protein skimmer problem leads ultimately to two important equations, labeled 2.
The complete mathematical derivation (i. Eqs. This derivation that is largely taken from the 2. Advanced Aquarist article. This new version of the derivation takes into account the presence of refractory TOC, TOCr.(2. Experimentally, the quantities . In addition to this expression which determines the amount of TOC present at a given time t, we can also manipulate the mathematical formula to arrive at an equation that defines the rate of TOC removal, a metric that takes into account the rate constant k as well as the flow Q, and the skimmer and reservoir volumes, Vs and Vr, respectively.(2.
For the Precision Marine ES1. Precision Marine AP6. Euro. Reef CS8. 0, Q/k. The fundamental mass balance equation is given in Eq. Details can be found in the Wikipedia entry for . In addition, since there is no TOC generation, there will be no TOC accumulation; rather, TOC is depleted in the system over time, so we will replace the . So, the new mass balance expression applicable to both the reservoir, and independently, the skimmer is: (2) input + removal = output + depletion.
We will focus on the labile TOC in the reservoir first. There is no explicit TOC removal in the reservoir, so . The input is equivalent to the mass of TOC added over time, say milligrams- per- minute (mg/min). In fact, since one term of Eq. The mass (amount) of TOC added in the input stream is the concentration of TOC, . That is,(3) mass of TOC added over time in input stream = Q.
The output stream of the reservoir can be treated in a similar manner: (4) mass of TOC removed over time in output stream = Q. The amount of TOC in the reservoir volume Vr is simply the product of the TOC concentration, .
Note that once again, the units of this term are in mass/time (. Note that this expression includes information about TOC concentrations in both the reservoir and the skimmer. A similar expression can be developed for the fate of the TOC concentration just in the skimmer.
However, in this case, . This TOC removal term must take into account the function of the bubbles. The fundamental chemical equation for TOC removal by the bubbles is: (1.
TOC + bubbles . This assumption permits us to connect the . Since the bubbles are continually being introduced in large excess compared to the TOC concentration in solution, the . This model (and its underlying assumptions) greatly simplifies the mathematical analysis.
In terms of the discipline of chemical kinetics, this approach is called the . So, the amount of labile TOC in the active skimmer reaction chamber volume Vs is. TOC in the active water volume of the skimmer = Vs.
We can introduce a proportionality constant, k, to convert Eq. As such, k is often referred to as a rate constant; it expresses how something changes over time (. This proportionality constant is not just a mathematical convenience. It will report on a fundamentally important property of a skimmer. The constant k can be viewed as a measure of how efficiently the skimmer/bubbles remove TOC.
The efficiency of TOC removal is a complex function of many factors (skimmer geometry, bubble size/density, bubble residence time, solution diffusion, mass transfer to the bubble, foam coalescence, binding to the bubble surface, etc.). In fact, it is just this value k that we are after; k is actually a singular measure of skimmer efficiency in removing TOC.
The. larger that k is, the faster that a given skimmer will remove TOC. Thus, k is an intrinsic measure for TOC removal, and it reflects, in the aggregate, all of the parameters that contribute to the efficiency of TOC removal for a given skimmer. However, k does not offer any insight into which parameters, in particular, are more or less important in determining skimmer performance. We can measure experimentally k for different skimmers, and compare these values.
Skimmers with larger k values will be more efficient (i. TOC from aquarium water. So, by including the information in Eq. We define a dimensionless time t = Q. Applying this definition to Eq. The use of t allows us to isolate the dimensionless quantity Vs/Vr, which is the ratio of the active skimmer volume to the reservoir volume. We can inject a dose of physical reality into the mathematics at this point.
The reservoir volume (3. Vs/Vr hovers in the 0. If the second term in the left- hand part of Eq. We have obtained experimental justification for the claim that d.
However, we cannot measure just the labile component of TOC; we can only measure the total TOC, . Thus, we have to substitute . Experimentally, the quantities . Plotting the experimentally measured . Remember that the rate constant k for TOC removal has the units min- 1; that is, k is expressed as .
Our interest in comparing different skimmers focuses our attention on the rate constant k. As discussed above, this single value is an aggregate measure of the efficiency of a given skimmer in removing TOC; it reflects all of the intimate structural and molecular details that impact on organics removal (see above).
However, the overall rate of TOC removal (different than the rate constant!) is expressed by Eq. That is, the rate is defined as the depletion of TOC over time, or d. Thus, increasing k, or increasing Q, or decreasing. Vr will all increase the overall rate of TOCl removal. There is nothing in the mathematical derivation to indicate whether k itself is a function of Q or not.
This point was tested through experiment with the Reef Octopus 1. It is possible to algebraically manipulate the complex .