The important considerations in the design of high-rate trickling filters are the organic loading rate and the recirculation ratio. The efficiency of a high-rate trickling filter depends on both organic loading rate and recirculation ratio. A number of equations are available for the determination of plant efficiency based on organic loading rate and recirculation ratio.
The sizing of the trickling filters is based on those values of organic loading rates and recirculation ratios which will provide maximum plant efficiency. Once the organic loading rate is selected the required filter volume can be calculated. The depth and surface area of the filter are then suitably chosen to secure hydraulic loading rates within the prescribed range.
Out of the various equations available for the determination of plant efficiency based on organic loading rate and recirculation ratio those developed by Rankin and National Research Council (NRC) of Canada are commonly used for the design of trickling filters. Other equations used for the design are Velz equation, Eckenfelder equation, and Galler and Gotaas equation.
All these equations are indicated below:
1. Rankin’s Equations:
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Rankin developed a set of equations for the performance of high-rate trickling filters of various flow diagrams based on the requirements of the Ten State Standards of U.S.A. Rankin’s equations for single- stage and two-stage filters are as indicated below.
(a) For Single Stage Filters:
For single stage filters, the Ten State Standards state that the BOD of the influent to the filter including circulation shall not exceed three times of BOD of the required settled effluent. Thus Rankin’s equation for single stage high-rate filter of flow diagrams of Fig. 14.8 a (i) and (ii) express the above relation as under.
The above equations are applicable only when the organic loading rate on the filter, including recirculation, is less than 1.8 kg BOD5 /m3/d, and hydraulic loading rate, including recirculation, is maintained between 10 to 30 m3/d/m2.
When the organic loading ranges between 1.8 to 2.8 kg BOD5/m3/d, the following equation is used-
For all loadings in excess of 2.8 kg BOD5/m3/d, the BOD removal is assumed to be 1.8 kg BOD5/m3/d only.
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The above equations are also applicable to single stage filter of flow diagram of Fig. 14.8 a (iii).
(b) For First Stage of Two Stage Filters:
For the first stage filter of flow diagram of Fig. 14.8b (i) the above indicated equations are applicable.
In the flow diagrams of Fig. 14.8 b (ii) and (iv) the effluent from first stage filter is applied to second stage filter without settling and in these cases for the first stage plant effluent the following equations are applied.
(c) For Second Stage of Two Stage Filters:
The efficiency of removal of BOD for the second stage of two stage filter is less than that of the first stage because the amenability to treatment of the applied BOD is affected by previous treatment. Hence for the second stage filters the Ten State Standards stipulate that the BOD of the sewage applied to the second stage filter, including recirculation, shall not exceed two times the BOD expected in the settled effluent.
For the flow diagrams of Fig. 14.8 b (i), (ii) and (iv), Rankin’s equations are as under:
2. NRC Equations:
The NRC equations for trickling filter performance are empirical expressions developed from a study of the operation results of trickling filters serving military installations in USA. These equations are applicable to both low-rate as well as high-rate filters. The efficiency of single stage filter or first stage of two stage filters is given by-
3. Velz Equation:
In contrast to previous equations, which are based on the data analysis, Velz equation is based on a fundamental law relating to BOD remaining at depth D as follows:
The Velz equation then takes the following form:
The experimental constant K ranges from 0.49 for high-rate filters to 0.57 for low-rate filters. The corresponding values of k ranges from 0.213 for high-rate filters to 0.248 for low-rate filters.
4. Eckenfelder Equation:
Eckenfelder assumed that trickling filter can be represented as a plug flow reactor and that substrate utilization follows the first order kinetics. He considered the effect of time of contact between sewage and micro-organism through the measurable variables of depth of filter media and surface hydraulic loading as well as of micro-organism concentration which is related to the specific surface area of the filter media and other factors.
Eckenfelder’s equation can be written as:
For design of trickling filter, treatability studies to evaluate the constant involved in the above equation should be conducted especially with industrial sewage treatment.
A brief procedure to conduct treatability studies and to evaluate constant in the Eckenfelder’s equation is described below-
A bench scale cylindrical column (typical dimensions being 200 mm diameter, 2 m or more in height), preferably of plexiglass, having adequate number (minimum three) of sampling ports, is filled with filter medium. Suitable arrangements for feeding the sewage at 3 to 4 hydraulic surface loadings are made.
The filter is fed with sewage to be treated to generate slime layer on the filter medium which may take from a few days to several weeks depending on the nature of the sewage. The filter is operated at several hydraulic surface loadings by changing the flow rate and steady state effluent substrate concentration (BOD or COD) remaining at different depths is determined.
Percent BOD (or COD) remaining versus sampling depths is plotted on semilog paper for each of the hydraulic loadings and the slope of each straight line is determined. A log-log plot of slope versus surface loading is drawn. The slope of the line gives the value of constant n.
A table of [D/(QIA)] versus (Le/La) x 100 for various values of D and (Q/A) is constructed and on a semilog graph paper (Le/La) x 100 versus [D/(Q/A)] is plotted. The slope of the straight line gives the value of the treatability factor Ko.
The values of treatability factor Ko range from 0.01 to 0.1. Average values for municipal sewage for filters using plastic media have been reported to be around 0.06 at 20°C. The constant n for plastic media modular construction can be assumed as 0.5 without significant error.
Eckenfelder has also suggested the following empirical equation:
5. Galler and Gotaas Equation:
Galler and Gotaas, based on a multiple regression analysis of data from existing plants and providing for the effect of recirculation, hydraulic loading, filter depth and temperature of sewage, developed the following equation-
Galler and Gotaas suggested that recirculation improves the performance of the filter but established that a ratio of 4:1 was the practical upper limit of recirculation.
Applicability of the Different Equations:
In general Rankin’s equations have been found to give fairly satisfactory results in Indian conditions. The NRC equations would seem to apply when recirculation is not considered, when seasonal variations in temperature are not large and when sewage load is highly variable and of high strength.
The Eckenfelder equation is based on rational approach as it considers the effect of specific surface area of filter medium and time of contact between sewage and micro-organisms. This approach is versatile and applicable to low-rate, high-rate and super-rate filters using plastic media.
The application of this equation requires that bench or pilot scale treatability studies should be conducted or the values of treatability factor Ko and constant n should be suitably assumed. If it is not possible to conduct treatability studies or values of Ko and n cannot be assumed, empirical equations may be used. However, considerably different filter volumes are obtained by using different empirical equations for any given situation.