About Harlan Bengtson

Dr. Bengtson has B.S. and M.S. degrees from Iowa State University and a PhD from the University of Colorado, all in Chemical Engineering. He is now retired after 30 years in engineering education, in teaching and administrative positions. His areas of expertise are environmental engineering, hydrology, engineering science and renewable energy. He is a licensed Professional Engineer in Missouri. He did consulting work while in academia and had prior industrial experience. Dr. Bengtson has authored numerous publications, presentations and technical reports. He is currently active as a technical writer.

Horizontal Flow Grit Chamber Spreadsheet

Where to Find a Horizontal Flow Grit Chamber Spreadsheet

To obtain a spreadsheet for Horizontal Flow Grit Chamber Design, click here to visit our spreadsheet store.  This Excel spreadsheet has worksheets for calculating the peaking factor and for calculating the required dimensions for the horizontal flow grit chamber based on user input values for several parameters . There is also a worksheet for design of the exit sutro weir to control the horizontal velocity in the grit chamber. You can buy a convenient horizontal flow grit chamber spreadsheet for a very reasonable price.  It is available in either U.S. units or S.I. units.  Read on for background information about a Horizontal Flow Grit Chamber Design spreadsheet.

Background for a Horizontal Flow Grit Chamber Design Spreadsheet

The size and dimensions of a horizontal flow grit chamber are typically based on the detention time and horizontal velocity. Table 1, shown below, gives typical values for the design parameters, detention time and horizontal velocity, as well as typical added length for .the inlet and outlet.

Table 1. Typical Values for Design Parameters for Horizontal flow Grit Chamber

Exit Sutro Weir Design

A sutro weir is typically used as the exit from a horizontal flow grit chamber, because it maintains a constant horizontal velocity through the grit chamber. The diagram below shows the shape of a sutro weir, as plotted for an example horizontal flow grit chamber.

Sutro Weir pattern from spreadsheet

Example Horizontal Flow Grit Chamber Spreadsheet

An example Horizontal Flow Grit Chamber Design spreadsheet is partially shown in the image below.  .  This Excel spreadsheet can be used to calculate the required tank volume, tank length and tank depth, .based on user input values for wastewater flow rate, design horizontal velocity, detention time, and tank width..  This Excel spreadsheet, as well as others for water and wastewater treatment calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.n

Horizontal Flow Grit Chamber Spreadsheet Screenshot

References:

1. Metcalf & Eddy, Inc, (Revised by Tchobanoglous, G, Burton, F.L, Stensel, H.D.), Wastewater Engineering, Treatment and Resource Recovery, 5th Ed., New York, NY, 2014.

2. Bengtson, Harlan H.,  “Horizontal Flow Grit Chamber Design Calculations,” an online blog article.

Wastewater Metal Precipitation Spreadsheet

Where to Find a Wastewater Metal Precipitation Spreadsheet

To obtain a Wastewater Metal Preciptitation Spreadsheetclick here to visit our spreadsheet store.  This Excel spreadsheet has worksheets for calculating equilibrium values and design values for precipitation of seven metals from wastewater, based on user input values for several parameters . You can buy a convenient metal hydroxide preciptiation spreadsheet for a very reasonable price.  It is available in either U.S. units or S.I. units.  Read on for background information about a Wastewater Metal Precipitation Spreadsheet.

Background for a Wastewater Metal Precipitation Spreadsheet

To make calculation for metal hydroxide precipitation from wastewater, data for the solubility of that metal vs pH can be used to obtain an equation for the metal hydroxide solubility as a function of pH.  An example graph for zinc solubility vs pH is shown below.

Wastewater Metal Precipitation Spreadsheet Zn vs pH graphUsing an equation like that shown on the graph, equilibrium values can be calculated for effluent metal concentration, chemical usage and solids production.  Application of a safety factor will give design values for effluent metal concentration, chemical usage and solids production.

Example Wastewater Metal Precipitation Spreadsheet

An example wastewater metal precipitation spreadsheet is partially shown in the image below.  .  This Excel spreadsheet can be used to calculate equilibrium and design values for effluent metal concentration, chemical usage and solids production.based on user input values for wastewater flow rate, metal concentrations, design safety factor, and chemical used and its purity, .  This Excel spreadsheet, as well as others for water and wastewater treatment calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

References:

1. Metcalf & Eddy, Inc, (Revised by Tchobanoglous, G, Burton, F.L, Stensel, H.D.), Wastewater Engineering, Treatment and Reuse, 4th Ed., New York, NY, 2003.

2. Metcalf & Eddy, Inc, (Revised by Tchobanoglous, G, Burton, F.L, Stensel, H.D.), Wastewater Engineering, Treatment and Resource Recovery, 5th Ed., New York, NY, 2014.

3. Bengtson, Harlan H.,  “Wastewater Metal Precipitation Calculations,” an online blog article.

Wastewater Screening Calculations Spreadsheet

Where to Find a Wastewater Screening Calculations Spreadsheet

To obtain a Wastewater Screening Calculations Spreadsheetclick here to visit our spreadsheet store.  This Excel spreadsheet has worksheets for calculating the head loss through a bar screen, head loss through a fine screen, estimated daily volume of screenings collected for a fine screen and for a bar screen, based on user input values for several parameters . You can buy a convenient wastewater screening calculations spreadsheet for a very reasonable price.  It is available in either U.S. units or S.I. units.  Read on for background information about a Wastewater Screening Calculations Spreadsheet.

Background for a Wastewater Screening Calculations Spreadsheet

For information about making calculations for wastewater screening, including bar screens and perforated screens (also known as fine screens).  The equation used to calculate the head loss across a bar screen is:

Wastewater Screening Calculations Spreadsheet equationWhere:

Wastewater Screening Calculations Spreadsheet variablesThe liquid velocity in the approach channel can be calculated using the Manning Equation and the liquid velocity going through the screen can be calculated if information about the number of bars, space between bars, channel width, and flow depth are known.

An equation for calculating the head loss across a fine screen is also available as a function of the flow rate through the screen, the discharge coefficient for the screen (typically 0.6 for a clean screen, and the effective open area of the submerged screen.

Example Wastewater Screening Calculations Spreadsheet

An example wastewater screening calculations spreadsheet is partially shown in the image below.  .  This Excel spreadsheet can be used to calculate the head loss across either a bar screen or a perforated screen and an estimate of the daily screenings volume for either a bar screen or a perforated screen.based on several user input values.  This Excel spreadsheet, as well as others for water and wastewater treatment calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

Wastewater Screening Calculations Spreadsheet ScreenshotReferences:

1. Metcalf & Eddy, Inc, (Revised by Tchobanoglous, G, Burton, F.L, Stensel, H.D.), Wastewater Engineering, Treatment and Reuse, 4th Ed., New York, NY, 2003.

2. Metcalf & Eddy, Inc, (Revised by Tchobanoglous, G, Burton, F.L, Stensel, H.D.), Wastewater Engineering, Treatment and Resource Recovery, 5th Ed., New York, NY, 2014.

3. Bengtson, Harlan H.,  “Fine Screen and Bar Screen Calculations,” an online blog article.

EBPR A2O Design Calculations Spreadsheet

Where to Find an EBPR A2O Design Calculations Spreadsheet

To obtain an EBPR A2O Design Calculations Spreadsheetclick here to visit our spreadsheet store.  This Excel spreadsheet is intended for making design calculations for pre-anoxic denitrification and enhanced biological phosphorus removal in a CMAS (completely mixed activated sludge) system. You can buy a convenient EBPR A2O Design Calculations Spreadsheet for a very reasonable price.  It is available in either U.S. units or S.I. units.  Read on for background information about EBPR A2O Design Calculations.

Background for an EBPR A2O Design Calculations Spreadsheet

Enhanced Biological Phosphorus Removal  can be carried out with the A2O (Anaerobic, Anoxic process, as shown in the diagram below.

EBPR A2O Design Calculations Spreadsheet process flow diagramThe primary effluent goes first to an anaerobic tank, then to an anoxic tank and then to the aerated activated sludge tank.  The recycle flows include an internal reycle (IR) flow from the aeration tank effluent to the anoxic tank, and recycle activated sludge from the secondary clarifier underflow to the anaerobic tank.

 Example EBPR A2O Design Calculations Spreadsheet

An example EBPR design calculations spreadsheet is partially shown in the image below.  This Excel spreadsheet can be used to calculate the required anaerobic tank size, and calculate the phosphorus removal rate and sludge production rate.  This Excel spreadsheet, as well as others for wastewater treatment process design calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

EBPR A2O Design Calculations Spreadsheet ScreenshotReferences:

1. Metcalf & Eddy, Inc, (Revised by Tchobanoglous, G, Burton, F.L, Stensel, H.D.), Wastewater Engineering, Treatment and Resource Recovery, 5th Ed., New York, NY, 2014.

2. Bengtson, Harlan H.,  “EPBR Design Calculations Spreadsheet” an online blog article.

Lamella Inclined Plate Clarifier Design Spreadsheet

Where to Find a Lamella Inclined Plate Clarifer Design Spreadsheet

To obtain a Lamella Inclined Plate Clarifier Design Spreadsheetclick here to visit our spreadsheet store.  This Excel spreadsheet is intended for calculating design parameters such as total plate area, plate width, module width, length, and height, and HRT for flow between plates for a lamella inclined plate clarifier, based on user input values for several parameters . You can buy a convenient lamella inclned plate clarifier design spreadsheet for a very reasonable price.  It is available in either U.S. units or S.I. units.  Read on for background information about an Lamella Inclined Plate Clarifier Design Spreadsheet.

Background for a Lamella Inclined Plate Clarifier Design Spreadsheet

For information about making calculations for an activated sludge secondary clarifier, see the post  Activated Sludge Secondary Clarifier Design Spreadsheet, Instead of an activated sludge secondary clarifier, this post is about a lamella inclined plate clarifier design spreadsheet.  An inclined plate lamella clarifier obtains more settling area for the same footprint by using a set of inclined plates in the clarifier as illustrated in the following schematic diagram for a lamella inclined plate clarifier.

Lamella Inclined Plate Clarifier Design SpreadsheetPotential values for some of the design parameters for a lamella inclined plate clarifier are shown in the following table:

Potential Values for Design Parameters:

lamella inclined plate clarifier design parameter valuesThe source for the values in the above table is: www.wikivisually.com/wiki/Lamella_clarifier

Example Lamella Inclined Plate Clarifier Design Spreadsheet

An example Lamella Inclined Plate clarifier design spreadsheet is partially shown in the image below.  .  This Excel spreadsheet can be used to calculate the required plate area and module dimensions based on several user input values.  This Excel spreadsheet, as well as others for water and wastewater treatment calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

lamella inclined plate clarifier deisgn spreadsheetReferences:

1. Metcalf & Eddy, Inc, (Revised by Tchobanoglous, G, Burton, F.L, Stensel, H.D.), Wastewater Engineering, Treatment and Reuse, 4th Ed., New York, NY, 2003.

2. Metcalf & Eddy, Inc, (Revised by Tchobanoglous, G, Burton, F.L, Stensel, H.D.), Wastewater Engineering, Treatment and Resource Recovery, 5th Ed., New York, NY, 2014.

3. Bengtson, Harlan H.,  “Lamella Inclined Plate Clarifier Design,” an online blog article.

MBBR MBR SBR Spreadsheets

Where to Find MBBR MBR SBR Spreadsheets

To obtain MBBR MBR SBR spreadsheetsclick here to visit our spreadsheet store. You can buy your choice of several different MBBR MBR SBR spreadsheets as a convenient MBBR-MBR-SBR spreadsheet bundle or Excel spreadsheets for wastewater treatment design for MBBR wastewater treatment, MBR wastewater treatment or SBR wastewater treatment for very reasonable prices.  This Excel spreadsheet bundle include process design calculations for MBBR wastewater treatment processes, MBR wastewater treatment processed, SBR wastewater treatment processes.   These Excel spreadsheets are available in either U.S. units or S.I. units.  Read on for more information about MBBR MBR SBR Spreadsheets.

MBBR processes in Wastewater Treatment Spreadsheet Bundles

MBBR wastewater treatment process design spreadsheets are included in all of the MBBR-MBR-SBR spreadsheet bundle mentioned above.  The MBBR wastewater treatment process is quite flexible.  It is used for domestic and industrial wastewater treatment and can be designed for BOD removal alone or in combination with nitrification or with nitrification and denitrification.  It is used as a single stage process or as a two-stage or three-stage process.

The diagram below shows the general configuration of a Pre-anoxic nitrification denitrification MBBR wastewater treatment process.  Denitrification can also be carried out in a Post-Anoxic nitrification denitrification process.

MBBR MBR SBR Spreadsheets MBBR Flow Diagram

Figure 1. MBBR Wastewater Treatment Flow Diagram for Pre-Anoxic Deniitrification

MBR Processes in Wastewater Treatment Spreadsheet Bundles

A membrane bioreactor wastewater treatment system (MBR) can provide a compact alternative to the conventional activated sludge process. The MBR process uses filtration through a membrane instead of secondary clarification, so it produces a very high quality effluent.  Primary clarification is not typically used in a membrane bioreactor wastewater treatment system.  Fine screening is needed as a minimum pretreatment, and depending upon wastewater characteristics, coarse screening and grit removal may be needed also. The diagram below shows a general flow diagram for a MBR wastewater treatment system for BOD removal and nitrification.

MBBR MBR SBR Spreadsheet - MBR Process Flow DiagramFigure 2. MBR Wastewater Treatment Flow Diagram for BOD Removal and Nitrification

Currently the membrane module is typically immersed in the aeration tank as shown in the flow diagram.  Denitrification can also be carried out by adding a preanoxic tank before the aeration tank.

 References:

1. McQuarrie, J.P. and Boltz, J.P., Moving Bed Bio-film Reactor Technology: Process Design and Performance, Water Environment Research, Vol 83, No 6, June 2011.

2. Bengtson, Harlan, “MBBR-MBR-SBR Spreadsheet Bundle,” an online blog article

3. Bengtson, Harlan, “MBR Wastewater Treatment Process Design,” an online blog article

3. Bengtson, Harlan H., “Biological Wastewater Treatment Process Design Calculations,” available as an Amazon Kindle ebook or as a paperback.

Wastewater Treatment Spreadsheet Bundles

Where to Find Wastewater Treatment Spreadsheet Bundles

To obtain wastewater treatment spreadsheet bundlesclick here to visit our spreadsheet store. You can buy your choice of several different convenient wastewater treatment excel spreadsheet bundles  for a very reasonable prices.  These Excel spreadsheet bundles include process design calculations for MBBR wastewater treatment processes, MBR wastewater treatment processed, SBR wastewater treatment processes, activated sludge design calculations, and several other wastewater treatment processes.  These Excel spreadsheets are available in either U.S. units or S.I. units.  Read on for more information about these wastewater treatment spreadsheet bundles.

Available Wastewater Treatment Spreadsheet Bundles

The wastewater treatment spreadsheet bundles available from the EngineeringExcelTemplates.com DOWNLOADS page are “Biological-Secondary Wastewater Treatment Bundle“,  “Nitrification and Denitrification Bundle“, “Wastewater Treatment Complete Spreadsheet Bundle“. and “MBBR-MBR-SBR Spreadsheet Bundle”.

Descriptions of these spreadsheet bundles and descriptions of the spreadsheets included in each of them are available through the links in the previous paragraph.

MBBR processes in Wastewater Treatment Spreadsheet Bundles

MBBR wastewater treatment process design spreadsheets are included in all of the wastewater treatment spreadsheet bundles described above.  The MBBR wastewater treatment process is quite flexible.  It is used for domestic and industrial wastewater treatment and can be designed for BOD removal alone or in combination with nitrification or with nitrification and denitrification.  It is used as a single stage process or as a two-stage or three-stage process.

The diagram below shows the general configuration of a Pre-anoxic nitrification denitrification MBBR wastewater treatment process.  Denitrification can also be carried out in a Post-Anoxic nitrification denitrification process.

MBBR process in wastewater treatment spreadsheet bundles

Figure 1. MBBR Wastewater Treatment Flow Diagram for Pre-Anoxic Deniitrification

MBR Processes in Wastewater Treatment Spreadsheet Bundles

A membrane bioreactor wastewater treatment system (MBR) can provide a compact alternative to the conventional activated sludge process. The MBR process uses filtration through a membrane instead of secondary clarification, so it produces a very high quality effluent.  Primary clarification is not typically used in a membrane bioreactor wastewater treatment system.  Fine screening is needed as a minimum pretreatment, and depending upon wastewater characteristics, coarse screening and grit removal may be needed also. The diagram below shows a general flow diagram for a MBR wastewater treatment system for BOD removal and nitrification.

MBR flow diagram from Wastewater Treatment Spreadsheet BundlesFigure 2. MBR Wastewater Treatment Flow Diagram for BOD Removal and Nitrification

Currently the membrane module is typically immersed in the aeration tank as shown in the flow diagram.  Denitrification can also be carried out by adding a preanoxic tank before the aeration tank.

 References:

1. McQuarrie, J.P. and Boltz, J.P., Moving Bed Bio-film Reactor Technology: Process Design and Performance, Water Environment Research, Vol 83, No 6, June 2011.

2. Bengtson, Harlan, “MBBR Denitrification Design Spreadsheet,” an online blog article

3. Bengtson, Harlan, “MBR Wastewater Treatment Process Design,” an online blog article

3. Bengtson, Harlan H., “Biological Wastewater Treatment Process Design Calculations,” available as an Amazon Kindle ebook or as a paperback.

Partially Full Pipe Flow Viscous Liquid Spreadsheet

Where to Find a Partially Full Pipe Flow Viscous Liquid Spreadsheet

To obtain a Partially Full Pipe Flow Viscous Liquid Spreadsheet, click here to visit our spreadsheet store.  This Excel spreadsheet is intended for calculating the flow rate. required diameter, depth of flow, or pipe slope for partially full flow of a viscous liquid in a circular pipe . You can buy a convenient partially full pipe flow viscous liquid spreadsheet for a very reasonable price.  It is available in either U.S. units or S.I. units.  Read on for background information about a partially full pipe flow viscous liquid spreadsheet

Background for a Partially Full Pipe Flow Viscous Liquid Spreadsheet

For information about making calculations for partially full flow of water in a circular pipe, see the post, Partially Full Pipe Flow Calculations Spreadsheet .   That post describes the use of the Manning Equation, which can only be used for the flow of water.  For flow of a liquid with viscosity and/or density different from water, the Darcy-Weisbach Equation should be used.  The parameters and equations for calculating them for partially full pipe flow are shown in the diagram below for flow at a depth greater than the pipe diameter.

Partially Full Pipe Flow Viscous Liquid Spreadsheet Diagram           Figure 1. Parameters and Equations for More Than Half Full Flow

The definition of hydraulic radius and the Darcy-Weisbach equation as applied to partially full pipe flow are shown below.

Partially Full Pipe Flow Viscous Liquid Spreadsheet Equations

 Example Partially Full Pipe Flow Viscous Liquid Spreadsheet

An example partially full pipe flow viscous liquid spreadsheet is partially shown in the image below.  .  This Excel spreadsheet can be used to calculate the pipe flow rate, required diameter, depth of flow or pipe slope for partially full pipe flow of a viscous liquid.   This Excel spreadsheet, as well as others for pipe flow and open channel flow calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

Partially Full Pipe Flow Viscous Liquid Spreadsheet ScreenshotReferences

1. Bengtson, Harlan H.,  Uniform Open Channel Flow and The Manning Equation, an online, continuing education course for PDH credit.

2. Steel, E.W. & McGhee, T.J., Water Supply and Sewerage, 5th Ed., New York, McGraw-Hill Book Company, 1979

3. Bengtson, H.H., “Manning Equation Partially Filled Circular Pipes,”  An online blog article

4. Bengtson, H.H., “Partially Full Pipe Flow Calculations with Spreadsheets“, available as an Amazon Kindle e-book and as a paperback.

Broad Crested Weir Calculations Spreadsheet


Where to Find a Broad Crested Weir Calculations Spreadsheet

To obtain a Broad Crested Calculations Spreadsheetclick here to visit our spreadsheet store.  This Excel spreadsheet is intended for calculating the flow rate over the weir for free flow over the weir or for submerged flow.  . You can buy a convenient broad crested weir calculations spreadsheet for a very reasonable price.  It is available in either U.S. units or S.I. units.  Read on for background information about a broad crested weir calculations spreadsheet

Background for a Broad Crested Weir Calculations Spreadsheet

Figure 1, below shows a longitudinal section of a broad crested weir with free flow over the weir.

Broad crested weir calculations spreadsheetFigure 1. Longitudinal Section of a Broad Crested Weir with Free Flow over the Weir

The flow over a broad crested weir is referred to as free flow if the depth of water flowing immediately downstream of the weir is lower than the weir crest (the top of the weir), as shown in Figure 1.  The broad crested weir calculations spreadsheet being described here can calculate the flow rate over the weir for user specified values of the depth of flow upstream of the weir, y1, the length of the weir crest, L, (typically equal to the width of channel in which the broad crested weir is placed), and the value to be used for the weir coefficient, C.  The equation used for this calculations is:

broad crested weir calculations spreadsheetA similar calculation can be made for submerged flow over the broad crested weir, in which the depth of flow immediately downstream of the weir is greater than the height of the weir.  Submerged flow over a broad crested weir is shown in Figure 2 below.

broad crested weir calculations spreadsheetAlso the required upstream head above the weir crest can be calculated for a given flow rate over the weir for either free flow over the weir or submerged flow

Example Broad Crested Weir Calculations Spreadsheet

An example broad crested weir calculations spreadsheet is partially shown in the image below.  .  This Excel spreadsheet can be used to calculate the flow rate over the weir or to calculate the required upstream head over the weir for a given flow rate. These calculations can be made for free flow over the weir or for submerged flow over the broad crested weir.  This Excel spreadsheet, as well as others for open channel flow measurement calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

broad crested weir calculation spreadsheet screenshot

References:

1. Federal Highway Administration,  Publication No. FHWA-HIF-12-018, Hydraulic Design Series Number 7, Hydraulic Design of Safe Bridges, April 2012.2

2. Bengtson, Harlan H.,  “ Spreadsheet for Broad Crested Weir Calculations,” an online blog article.

SBR Denitrification Calculations Spreadsheet

Where to Find an SBR Denitrification Calculations Spreadsheet

To obtain an SBR Denitrification Calculations Spreadsheet, click here to visit our spreadsheet store.  This Excel spreadsheet is intended for making design calculations for either pre-anoxic or post-anoxic denitrification in a sequencing batch reactor. You can buy a convenient SBR denitrification calculations spreadsheet for a very reasonable price.  It is available in either U.S. units or S.I. units.  Read on for background information about sequencing batch reactor denitrification process design calculations.

Background for an SBR Denitrification Calculations Spreadsheet

The sequencing batch reactor is a batch type, fill and draw alternative to the continuous flow activated sludge process for biological wastewater treatment, including BOD removal, nitrification and denitrification.  The typical components of a sequencing batch reactor operating cycle for BOD removal and nitrification are shown in the diagram below.

Typical SBR Cycle for SBR denitrification calculations spreadsheetAt least two tanks are typically used.  In that case, the length of the fill period would be equal to the sum of the times for the react, settle and decant periods.  Thus one tank would be filling while the other tank was going through the react, settle and decant periods and then the roles would be reversed.

In order to achieve denitrification, an anoxic period must be added.  A typical sequencing batch reactor cycle for a post-anoxic denitrification process is shown in the figure below.  A mixed anoxic react period is included after the aerobic react period.

post-anoxic SBR operating cycle for SBR denitrification calculations spreadsheetFor a pre-anoxic denitrification SBR process, some or all of the fill period would be anoxic and there would be no anoxic react period after the aerobic react period.

 Example SBR Denitrification Calculations Spreadsheet

An example SBR denitrification calculations spreadsheet is partially shown in the image below.  This Excel spreadsheet can be used to set the times for the different parts of the SBR operating cycle, calculate the required tank size and check on the adequacy for nitrification and for denitrification.  This Excel spreadsheet, as well as others for wastewater treatment process design calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

screenshot for SBR denitrification calculations spreadsheet

References:

1. Metcalf & Eddy, Inc, (Revised by Tchobanoglous, G, Burton, F.L, Stensel, H.D.), Wastewater Engineering, Treatment and Reuse, 4th Ed., New York, NY, 2003.

2. Metcalf & Eddy, Inc, (Revised by Tchobanoglous, G, Burton, F.L, Stensel, H.D.), Wastewater Engineering, Treatment and Resource Recovery, 5th Ed., New York, NY, 2014.

3. Bengtson, Harlan H.,  “Sequencing Batch Reactor Denitrification Calculations,” an online blog article.