MBBR Nitrification Denitrification Spreadsheet

Posted on August 6, 2016 by Harlan Bengtson

Where to Find an MBBR Nitrification Denitrification Spreadsheet

To obtain an MBBR Nitrification Denitrification spreadsheet, click here to visit our spreadsheet store. This Excel spreadsheet is intended for MBBR nitrification denitrification process design calculations. You can buy a convenient MBBR Nitrification Denitrification spreadsheet for a very reasonable price. This spreadsheet makes MBBR process design calculations for BOD removal, nitrification, and denitrification. including both pre-anoxic and post-anoxic denitrification processes. It is available in either U.S. units or S.I. units. Read on for information about using an MBBR process design calculations spreadsheet for nitrification and denitrification.

Background for MBBR Nitrification Denitrification Spreadsheet

The moving bed biofilm reactor (MBBR) appeared relatively recently on the wastewater treatment scene. It was developed in the 1990’s, and is now used in many countries around the world.

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 Nitrification Denitrification Spreadsheet flow diagram

MBBR Pre-Anoxic Nitrification Denitrification Flow Diagram

Example MBBR Wastewater Treatment Design Spreadsheet

An example MBBR nitrification denitrification spreadsheet is partially shown in the two images below. This Excel spreadsheet can be used to calculate the required MBBR tank volume and dimensions, based on user input media information and wastewater design flow and characteristics. 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.

MBBR Nitrification Denitrification Spreadsheet Screenshot1

Screenshot1 – Pre-anoxic Nitrification Denitrification

MMBR Nitrification Denitrification Spreadsheet Screenshot2

Screenshot2 – Pre-anoxic MBBR Nitrification Denitrification Spreadsheet

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

4. Bengtson, Harlan H., “Spreadsheets for MBBR Denitrification Design Calculations,” an Amazon Kindle ebook.

5. Bengtson, Harlan H., “Spreadsheets for MBBR Process Design Calculations,” available as an Amazon Kindle ebook or as a paperback.

Dissolved Oxygen Saturation in Water Calculator Speadsheet

Posted on November 13, 2015 by Harlan Bengtson

Where to Find a Dissolved Oxygen Saturation in Water Calculator Spreadsheet

To obtain a Dissolved Oxygen Saturation in Water Calculator Excel spreadsheet, click here to visit our spreadsheet store. Look in the Dissolved Oxygen category on the Download page. This Excel spreadsheet is intended to calculate the dissolved oxygen solubility at a specified water temperature and atmospheric pressure for water temperature of 35 to 80 degrees F and atmospheric pressure of 600 to 760 mm Hg. You can buy a convenient dissolved oxygen saturation in water calculator Excel spreadsheet for a very reasonable price. This spreadsheet calculates dissolved oxygen saturation based on user specified water temperature and atmospheric pressure. Calculations may be made in either U.S. or S.I. units. Read on for information about using a dissolved oxygen saturation in water calculator spreadsheet.

Background for Dissolved Oxygen Saturation in Water Calculator Spreadsheet

There are many tables available with values for the dissolved oxygen solubility in water over a range of water temperatures and atmospheric pressures. With an Excel spreadsheet, formulas can be derived using Excels graph plotting capability, for saturation dissolved oxygen concentration as a function of water temperature for a range of different values for atmospheric pressure. The spreadsheet can then conveniently calculate the dissolved oxygen solubility (saturation concentration) at user specified values for water temperature and atmospheric pressure. That is done in the spreadsheet being discussed here. The

Example Dissolved Oxygen Saturation in Water Calculator Excel Spreadsheet

An example dissolved oxygen saturation in water calculator Excel spreadsheet is partially shown in the image below. This Excel spreadsheet can be used to calculate the dissolved oxygen solubility in water at a specified water temperature and atmospheric pressure. This Excel spreadsheet, as well as others for wastewater treatment calculations, is available for both U.S. or S.I. units for a very reasonable price in our spreadsheet store.

References

United States Geological Survey, DOTABLES (Dissolved oxygen solubility tables), www.water.usgs.gov/software/DOTABLES/.
Bengtson, Harlan, Dissolved Oxygen Solubility in Water Calculator, an informational blog article.

Nitrification Denitrification Activated Sludge Process Spreadsheet

Posted on August 25, 2015 by Harlan Bengtson

Where to Find a Nitrification Denitrification Activated Sludge Process Excel Spreadsheet

To obtain a nitrification denitrification activated sludge process Excel spreadsheet, click here to visit our spreadsheet store. Look in the wastewater treatment category on the Download page. This Excel spreadsheet is intended for completely mixed activated sludge nitrification/denitrification calculations. You can buy a convenient nitrification denitrification activated sludge process Excel spreadsheet for a very reasonable price. This spreadsheet calculates the completely mixed aeration tank volume for BOD removal and nitrification as well as the volume for a pre-anoxic tank to achieve denitrification.. It is available in either U.S. or S.I. units. Read on for information about using a nitrification denitrification activated sludge process Excel spreadsheet.

Background for Nitrification Denitrification Activated Sludge Process Excel Spreadsheet

The activated sludge wastewater treatment process can be designed for removal of BOD (organic matter that exerts an oxygen demand in the water), or for BOD removal and nitrification, or for BOD removal, nitrification and denitrification. Nitrification is oxidation of ammonia nitrogen in the wastewater to nitrate and denitrification is removal of nitrate from the wastewater.

A flow diagram for a nitrification denitrification activated sludge process is shown below. It includes a completely mixed activated sludge aeration tank for BOD removal and nitrification as well as an anoxic basin for denitrification.

Example Nitrification Denitrification Activated Sludge Process Excel Spreadsheet

An example nitrification denitrification activated sludge process Excel spreadsheet is partially shown in the image below. This Excel spreadsheet can be used to make design calculations for a nitrification denitrification activated sludge process. This Excel spreadsheet, as well as others for 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 and Eddy, Inc, (Revised by Tchobanoglous, G, Burton, F.L., Stensel, H.D.), Wastewater Engineering, Treatment and Reuse, 4th Ed., McGraw Hill, New York, NM, 2003.

2. Bengtson, Harlan, Nitrification Denitrification Wastewater Treatment Process Spreadsheets, an informational online blog article.

MBBR Wastewater Treatment Design Spreadsheet for BOD Removal

Posted on March 24, 2015 by Harlan Bengtson

Where to Find an MBBR Wastewater Treatment Design Spreadsheet

To obtain an MBBR wastewater treatment design spreadsheet, click here to visit our spreadsheet store. This Excel spreadsheet can be used for MBBR process design calculations. You can buy a convenient MBBR wastewater treatment design spreadsheet for a very reasonable price. This spreadsheet makes MBBR process design calculations for several configurations for BOD removal and for nitrification. It is available in either U.S. or S.I. units. Read on for information about using an MBBR Wastewater Treatment Design spreadsheet.

Background for MBBR Wastewater Treatment Design Spreadsheet

The moving bed biofilm reactor (MBBR) is a relatively recently developed wastewater treatment process. It was developed in the 1990’s, but is now in use in many countries around the world.

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. It is used as a single stage process or as a two-stage or three-stage process.

Example MBBR Wastewater Treatment Design Spreadsheet

An example MBBR wastewater treatment design spreadsheet is partially shown in the image below. This Excel spreadsheet can be used to calculate the required MBBR tank volume and dimensions, based on user input media information and wastewater design flow and characteristics. 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.

References:

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

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

3. Bengtson, Harlan H,, “Spreadsheets for MBBR Process Design Calculations“, Available as an Amazon Kindle e-book and as a paperback.

4. Bengtson, Harlan H., “Biological Wastewater Treatment Process Design Calculations,” available as an Amazon Kindle e-book or as a paperback.

5. Bengtson, Harlan H. “MBBR Wastewater Treatment Processes“, an online course for PDH engineering continuing education credit.

Trickling Filter Design Calculations Spreadsheet

Posted on April 13, 2014 by Harlan Bengtson

Where to Find a Trickling Filter Design Calculations Spreadsheet using the NRC Formula

To obtain a trickling filter design calculations spreadsheet using the NRC formula, click here to visit our spreadsheet store. For use in making trickling filter design calculations with the NRC equation, you can buy a convenient trickling filter design calculations spreadsheet for a very reasonable price. This spreadsheet will use the NRC equations to calculate the trickling filter diameter needed for either a single stage or a two stage system and will calculate the estimated treatment efficiency for a specified trickling filter system, in either U.S. or S.I. units. Read on for information about a trickling filter design calculation spreadsheet that uses the NRC formula.

Trickling Filter Design Calculations Background

The trickling filter process is widely used for biological wastewater treatment all over the world. It is an attached growth biological wastewater treatment process. The aerobic microorganisms grow on a solid medium and the wastewater to be treated flows through the bed. A flow diagram for a typical single stage trickling filter wastewater treatment plant is shown in the diagram below. The diagram shows the typical flow pattern through the primary clarifier, trickling filter and secondary clarifier.

Example Trickling Filter Design Calculations Spreadsheet

A trickling filter design calculations spreadsheet is partially shown in the image below. It can be used to calculate the trickling filter diameter needed for either a single stage or a two stage trickling filter system using the NRC formula. The spreadsheet will also calculate an estimated treatment efficiency for a specified single stage or two stage trickling filter system. This Excel spreadsheet, as well as others for wastewater treatment calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

References for Further Information:

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

2. Vesilind, P.A. and Morgan, S.M., Introduction to Environmental Engineering, 2nd Edition, Belmont, CA, Brooks/Cole, 2004.

3. Bengtson, H. H., “Trickling Filter NRC Equation Spreadsheet“, a blog article at www.EngineeringExcelTemplates.com

A Spreadsheet to Calculate Oxygen Requirement Activated Sludge Process

Posted on March 27, 2013 by Harlan Bengtson

Where to Find a Spreadsheet to Calculate Oxygen Requirement Activated Sludge Process

To obtain a spreadsheet to calculate oxygen requirement activated sludge process, click here to visit our spreadsheet store. For use in calculating oxygen requirements and blower specifications, you can buy a convenient spreadsheet to calculate oxygen requirement activated sludge for a very reasonable price. This spreadsheet will calculate the oxygen requirement and blower specifications for BOD removal or for BOD removal and nitrification for specified wastewater flow and characteristics and diffuser characteristics, in either U.S. or S.I. units. Read on for information about Excel spreadsheets that can be used to calculate oxygen requirement activated sludge process parameters.

Oxygen Requirement Activated Sludge Background

The theoretical oxygen requirement for BOD removal can be approximated as ranging from 0.90 lb O2/lb BOD removed at an SRT of 5 days to 1.3 lb O2/lb BOD removed at an SRT of 20 days. This leads to the equation:

O₂ requirement in lb/day = 0.90 + [(SRT – 5)/(20 – 5)](1.3 – 0.9)(lb/day BOD removed)

A design increase factor (safety factor) is typically multiplied times the calculated oxygen requirement to get the design oxygen transfer rate. The design oxygen transfer efficiency and the air density at design conditions can then be used to calculate the design air flow rate. The blower horsepower can then be calculated from the following equation:

Blower hp = (Q_air)(ΔP)/(229*η)

Where:

Q_air is the air flow rate in cfm to be delivered by the blower
ΔP is the pressure rise across the blower in psi = outlet pressure – inlet pressure
η is the blower efficiency

If oxygen is to be provided for nitrification as well as BOD removal, then additional calculations are needed to estimate the oxygen requirement for nitrification.

Example Spreadsheet to Calculate Oxygen Requirement Activated Sludge Process

A spreadsheet to Calculate oxygen requirement activated sludge process is partially shown in the image below. It can be used to calculate the oxygen requirement and blower specifications for an activated sludge wastewater treatment system. This Excel spreadsheet, as well as others for wastewater treatment calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

References:

Bengtson, Harlan H., “Activated Sludge Oxygen Requirement,” an online blog article.
Bengtson, Harlan H., “Activated Sludge Calculations Spreadsheet: Aeration Tank Calculations,” an Amazon Kindle e-book.
Bengtson, Harlan H., “Biological Wastewater Treatment Process Design Calculations,” available as a paperback book or Amazon Kindle e-book

Sequencing Batch Reactor Design Calculation Spreadsheet

Posted on March 20, 2013 by Harlan Bengtson

Where to Find a Sequencing Batch Reactor Design Calculation Spreadsheet

To obtain a Sequencing Batch Reactor Design Calculation excel spreadsheet, click here to visit our spreadsheet store. For use in wastewater treatment design calculations, you can buy a convenient sequencing batch reactor design calculation excel spreadsheet for a very reasonable price? This spreadsheet will make calculations for BOD removal, nitrification, denitrification, and biological phosphorus removal for given information about wastewater flow rate and characteristics, in either U.S. or S.I. units. Read on for information about Excel spreadsheets that can be used for SBR design calculations.

Sequencing Batch Reactor Design Calculation Background

A typical activated sludge wastewater treatment process operates as a continuous flow process, with incoming wastewater flow coming into a primary clarifier and treated effluent continuously coming off from the secondary clarifier. A sequencing batch reactor wastewater treatment system, on the other hand, operates as a batch system. Two or more tanks are required. While one tank is receiving influent wastewater (the “fill” part of the cycle), another tank is undergoing aeration (the “react” part of the cycle), settling (the “settle” part of the cycle) and decanting of treated effluent (the “decant” part of the cycle). This is illustrated in the diagram below.

Sequencing Batch Reactor Design Calculation Applications

A sequencing batch reactor wastewater treatment system has a great deal of flexibility. It can be used for traditional BOD removal and nitrification using the four cycle components shown above. In that case there may be aeration for at least part of the fill cycle. If denitrification is to be accomplished also, then there should be no aeration during the fill cycle. If the SBR wastewater treatment system is to be designed for biological phosphorus removal as well, then an anaerobic react period is needed after the fill portion of the cycle, and an anoxic react is needed after the aerobic react part of the cycle, as shown in the diagram below.

Example Sequencing Batch Reactor Design Calculation Excel Spreadsheet

The Sequencing Batch Reactor Design Calculation excel spreadsheet partially shown in the image below can be used to make a variety of design calculations for an SBR wastewater treatment system. Based on input information about the wastewater flow rate and characteristics, as well as the treatment objectives, the spreadsheet leads the user through calculations for deciding on times for each part of the SBR cycle, tank number and size, and checks on the adequacy of the design. This Excel spreadsheet, as well as others for wastewater treatment calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

Reference:

Bengtson, Harlan H., “SBR Wastewater Treatment Plant Design Spreadsheet,” an online blog article.

Wastewater Lagoon Design Spreadsheets

Posted on November 12, 2012 by Harlan Bengtson

Where to get Wastewater Lagoon Design Spreadsheets

For wastewater lagoon design spreadsheets in either U.S. or S.I. units, click here to visit our spreadsheet store. Obtain convenient, easy to use spreadsheets for wastewater lagoon design calculations at reasonable prices. Read on for information about the use of Excel spreadsheets for wastewater lagoon design. Three types of wastewater lagoons that will be discussed next are the anaerobic lagoon, the facultative lagoon, and the maturation pond.

Anaerobic Wastewater Lagoon Design

Anaerobic lagoons are most useful for incoming wastewater with a high BOD content. If present, an anaerobic lagoon would typically be the first type of treatment, often followed by facultative and or maturation ponds. Anaerobic lagoons are deeper than facultative or maturation ponds, usually 8 to 15 ft. Anaerobic wastewater lagoon Design is usually based on volumetric loading (kg BOD/day/m³ or lb BOD/day/1000 ft³). A specified minimum hydraulic retention time may also be used.

Facultative Wastewater Lagoon Design

The classic type wastewater treatment lagoon is the facultative pond. It is aerobic at the top with an anaerobic sediment layer at the bottom. Algae growing in the lagoon are important for maintaining dissolved oxygen in the pond. There are often one or more primary facultative ponds and one or more secondary ponds. A typical three cell layout for two primary cells and one secondary cell is shown in the diagram below. A well designed and operated facultative lagoon system can provide secondary level treatment if algae are removed from the effluent. Facultative wastewater lagoon design is typically based on surface loading (kg BOD/day/ha or lb BOD/day/acre). A specified minimum hydraulic detention time is often used as a design factor also.

Maturation Wastewater Lagoon Design

A maturation pond will typically be the last type of pond in a wastewater lagoon system if it is present. There is usually little additional BOD removal in a maturation pond. Its primary function is disinfection/reduction in bacterial content. Maturation pond design is often based on required reduction in coliform bacteria with perhaps a minimum hydraulic retention time.

A Screenshot for a Wastewater Lagoon Design Spreadsheet

For a wastewater lagoon design spreadsheet with calculations in S.I. or U.S. units, or for other spreadsheets for activated sludge wastewater treatment calculations, see: www.engineeringexceltemplates.com

The Excel spreadsheet screenshot below shows part of a spreadsheet for wastewater lagoon design calculations, available at our spreadsheet store in either U.S. or S.I. units at a very reasonable price.

References

1. USEPA, Principles of Design and Operations of Wastewater Treatment Pond Systems for Plant Operators, Engineers, and Managers, EPA/600/R-11/088, August 2011.

2. Mara, D. & Pearson, H., Design Manual for Waste Stabilization Ponds in Mediterranean Countries, Lagoon Technology International Ltd, 1998.

Activated Sludge Calculations in a Solids Mass Balance Spreadsheet

Posted on March 2, 2012 by Harlan Bengtson

Where to Find a Solids Mass Balance Spreadsheet for Activated Sludge Calculations

For Excel solids mass balance spreadsheets to make activated sludge calculations calculations, click here to visit our spreadsheet store. Obtain a convenient, easy to use spreadsheet for solids mass balance activated sludge calculations for only $22.95. Read on for information about the use of an Excel spreadsheet for estimating the effect of recycle flow, BOD and TSS through solids mass balance activated sludge calculations.

Solids Mass Balance Background for Activated Sludge Calculations

Several streams from sludge treatment processes are typically recycled back into the wastewater treatment plant inflow. Examples are sludge thickener overflow, anaerobic digester supernatant, aerobic digester supernatant, centrate from centrifuge dewatering, and filtrate from filtration dewatering. The liquid flow, BOD load, and TSS load in these recycled streams contribute to the wastewater flow to be handled by the mainstream wastewater treatment processes.

An iterative solids mass balance is an organized procedure for estimating the total flow rate, BOD load, and TSS load in the recycled flows from sludge treatment and handling processes. This type of calculation is illustrated in an eight page example in Metcalf and Eddy (Reference #1). The flow diagram below shows a typical set of sludge treatment processes and recycle flows for an activated sludge plant.

Activated Sludge Calculations Influent and Effluent Inputs for Spreadsheet

General information about the wastewater influent flow and characteristics will need to be input to the spreadsheet along with information about target effluent characteristics. The screenshot below shows typical influent and effluent inputs needed.

Solids Mass Balance Activated Sludge Calculations for Each Treatment Process

The next step is solids mass balance calculations for each of the treatment processes, leading to estimates of the recycle flow rate, BOD load and TSS load for each recycle stream. For a wastewater treatment plant with the flow diagram shown above, there would need to be solids mass balance calculations for the primary clarifier, the aeration tank/secondary clarifier, the sludge thickener, the anaerobic digester, and the sludge dewatering process. The screenshot below shows typical inputs and outputs for a solids mass balance over a sludge thickener.

Similar calculations would be made for each of the wastewater treatment and sludge treatment/management processes, leading to information about recycle flow rate, BOD load, and TSS load, for each recycle stream as shown in the summary tables in the next section. After completion of the first iteration, the recycle flowrate, BOD load and TSS load are added to values for those parameters for the incoming wastewater and all of the solids mass balance calculations are repeated in a second iteration.

Summary Tables

The screenshot below shows a set of tables summarizing the results of the calculated recycles flows from the first three iterations of the activated sludge calculations. Spreadsheets are available to make this type of solids mass balance calculations in either U.S. or S.I. units at a very low cost (only $22.95) in our spreadsheet store. These spreadsheets are set up to make the solids mass balance calculations for four iterations.

References

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

2. Bengtson, Harlan H., “Activated Sludge Solids Mass Balance Spreadsheet,” an online blog article.

Activated Sludge Secondary Clarifier Design Spreadsheets

Posted on October 18, 2011 by Harlan Bengtson

Where to Find Activated Sludge Secondary Clarifier Design Spreadsheets

For an Excel spreadsheet for activated sludge secondary clarifier design calculations, click here to visit our spreadsheet store. Obtain a convenient, easy to use primary and secondary clarifier design spreadsheets for only $11.95. Read on for information about the use of an Excel spreadsheet for activated sludge secondary clarifier design calculations.

Activated Sludge Secondary Clarifier Design Parameters

The parameters typically used for activated sludge secondary clarifier design are the surface overflow rate (SOR), solids loading rate (SLR), and weir overflow rate (WOR). Activated sludge parameters are shown in the flow diagram at the right. The equations defining these three parameters are:

SOR = Q_o/A, SLR = (Q_o + Q_r)X/A, and WOR = Q_o/L, where:

Q_o = primary effluent flow rate in MGD (U.S.) or m³/d (S.I.)
A = total surface area for secondary clarifier(s) in ft²(U.S.) or m² (S.I.)
Q_r = recycle activated sludge flow rate in MGD (U.S.) or m³/d (S.I.)
X = mixed liquor activated sludge solids concentration in mg/L (U.S. or S.I.)
L = length of secondary clarifier effluent weir in ft (U.S.) or m (S.I.)

Typical values of surface overflow rate and solids overflow rate for activated sludge secondary clarifier design are shown in the tables below:

Calculation of Activated Sludge Secondary Clarifier Surface Area

The equation for calculating the needed activated sludge secondary clarifier surface area from a design SOR value with units as shown above is: A = Q_o*10⁶/SOR

The formula for calculating activated sludge secondary clarifier surface area from a design value of SLR with parameter units as shown above is: A = (Q_o + Qr)*8.34*X/SLR

An Excel Spreadsheet as an Activated Sludge Secondary Clarifier Design Calculator

The Excel spreadsheet template shown below can be used to carry out the activated sludge secondary clarifier design calculations described above. Why bother to make these calculations by hand? This Excel spreadsheet can handle primary and secondary clarifier surface area calculations and determine diameter for circular clarifier(s) or length and width for rectangular clarifier(s) and is available in either U.S. or S.I. units at a very low cost (only $11.95) in our spreadsheet store. These spreadsheets also make weir overflow calculations to aid in effluent weir design.

Reference

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