Fundamental Concepts for Environmental Processes Flow Reactors IX. Sedimentation A. Uses of...

University Curriculum Development for Decentralized Wastewater Treatment Fundamental Concepts for Environmental Processes

Kenimer et al. Page i

Fundamental Concepts for Environmental Processes

Suggested Course Materials

Ann Kenimer, Julie Villeneuve, Sarah Shelden Associate Professor, Graduate Assistant, Undergraduate Technician

Department of Biological and Agricultural Engineering Texas A&M University

August 2004

FINAL


Kenimer, et. al. Page ii

NDWRCDP Disclaimer This work was supported by the National Decentralized Water Resources Capacity Development Project (NDWRCDP) with funding provided by the U.S. Environmental Protection Agency through a Cooperative Agreement (EPA No. CR827881-01-0) with Washington University in St. Louis. These materials have not been reviewed by the U.S. Environmental Protection Agency. These materials have been reviewed by representatives of the NDWRCDP. The contents of these materials do not necessarily reflect the views and policies of the NDWRCDP, Washington University, or the U.S. Environmental Protection Agency, nor does the mention of trade names or commercial products constitute their endorsement or recommendation for use. CIDWT/University Disclaimer These materials are the collective effort of individuals from academic, regulatory, and private sectors of the onsite/decentralized wastewater industry. These materials have been peer-reviewed and represent the current state of knowledge/science in this field. They were developed through a series of writing and review meetings with the goal of formulating a consensus on the materials presented. These materials do not necessarily reflect the views and policies of University of Arkansas, and/or the Consortium of Institutes for Decentralized Wastewater Treatment (CIDWT). The mention of trade names or commercial products does not constitute an endorsement or recommendation for use from these individuals or entities, nor does it constitute criticism for similar ones not mentioned. Acknowledgements The authors wish to acknowledge and thank Jennifer Brogdon, Nancy Deal, Stan Fincham, Mark Gross, and James Kreissl for time and effort spent reviewing these module materials.


Kenimer, et. al. Page iii

Citation of Materials The educational materials included in this module should be cited as follows: Kenimer, Ann L., J. Villeneuve and S. Shelden. 2005. Fundamental Concepts Text. in (M.A. Gross and N.E. Deal, eds.) University Curriculum Development for Decentralized Wastewater Management. National Decentralized Water Resources Capacity Development Project. University of Arkansas, Fayetteville, AR. Kenimer, Ann L., J. Villeneuve and S. Shelden. 2005. Fundamental Concepts: Water Quality - Power Point Presentation. in (M.A. Gross and N.E. Deal, eds.) University Curriculum Development for Decentralized Wastewater Management. National Decentralized Water Resources Capacity Development Project. University of Arkansas, Fayetteville, AR. Kenimer, Ann L., J. Villeneuve and S. Shelden. 2005. Fundamental Concepts: Stoichiometry - Power Point Presentation. in (M.A. Gross and N.E. Deal, eds.) University Curriculum Development for Decentralized Wastewater Management. National Decentralized Water Resources Capacity Development Project. University of Arkansas, Fayetteville, AR. Kenimer, Ann L., J. Villeneuve and S. Shelden. 2005. Fundamental Concepts: Biology - Power Point Presentation. in (M.A. Gross and N.E. Deal, eds.) University Curriculum Development for Decentralized Wastewater Management. National Decentralized Water Resources Capacity Development Project. University of Arkansas, Fayetteville, AR. Kenimer, Ann L., J. Villeneuve and S. Shelden. 2005. Fundamental Concepts: Units - Power Point Presentation. in (M.A. Gross and N.E. Deal, eds.) University Curriculum Development for Decentralized Wastewater Management. National Decentralized Water Resources Capacity Development Project. University of Arkansas, Fayetteville, AR. Kenimer, Ann L., J. Villeneuve and S. Shelden. 2005. Fundamental Concepts: Mass Balance - Power Point Presentation. in (M.A. Gross and N.E. Deal, eds.) University Curriculum Development for Decentralized Wastewater Management. National Decentralized Water Resources Capacity Development Project. University of Arkansas, Fayetteville, AR. Kenimer, Ann L., J. Villeneuve and S. Shelden. 2005. Fundamental Concepts: Fluids - Power Point Presentation. in (M.A. Gross and N.E. Deal, eds.) University Curriculum Development for Decentralized Wastewater Management. National Decentralized Water Resources Capacity Development Project. University of Arkansas, Fayetteville, AR. Kenimer, Ann L., J. Villeneuve and S. Shelden. 2005. Fundamental Concepts: Reactions - Power Point Presentation. in (M.A. Gross and N.E. Deal, eds.) University Curriculum Development for Decentralized Wastewater Management. National Decentralized Water Resources Capacity Development Project. University of Arkansas, Fayetteville, AR. Kenimer, Ann L., J. Villeneuve and S. Shelden. 2005. Fundamental Concepts: Sedimentation - Power Point Presentation. in (M.A. Gross and N.E. Deal, eds.) University Curriculum Development for Decentralized Wastewater Management. National Decentralized Water Resources Capacity Development Project. University of Arkansas, Fayetteville, AR.


Kenimer, et. al. Page iv

Fundamental Concepts for Environmental Processes Suggested Course Materials

Table of Contents

Overview..........................................................................................1 Agenda .............................................................................................2

Outline……………………………………………………………..3 Goals ..............................................................................................4 Learning Objectives .........................................................................5 Prerequisites.....................................................................................6 Evaluation Form...............................................................................7 Problem Sets ....................................................................................8 Problem Sets with Solutions ..........................................................12 Additional Materials: Field Activities...................................................................22 In-class Activities...............................................................23 In-class Activities with Solutions ......................................25 Lecture Notes for Select Topics: Overview of Water Quality....................................28 Fluid Mechanics.....................................................35 Mass Balance .........................................................39 First Order Reactions .............................................42 Sedimentation ........................................................45


Kenimer et al. Page 1

Fundamental Concepts for Environmental Processes Overview This module presents, at a rudimentary level, concepts that are required for full understanding of processes and technologies common to decentralized wastewater treatment. This module is aimed at students from non-engineering backgrounds or with limited prior exposure to wastewater treatment methodologies. Suggested prerequisite courses for this module include freshman chemistry, freshman biology, and college algebra. The material contained in this module is likely not appropriate for students who have completed previous courses in wastewater treatment or are from engineering disciplines. Concepts covered in this module dovetail into other curriculum modules where the concepts are covered in greater detail and depth. Where greater coverage of topics is desired, instructors are encouraged to identify related modules for additional study. Module materials include a text for student use, slide presentations, lecture notes, and various problem sets for use in and out of the classroom. If used in its entirety, this module will require approximately 12 to 15 hours of course time. Instructors are encouraged to use only those topics in this module that serve the needs of their student body. To facilitate selective use of module concepts, lecture notes, slides, and problem sets are divided according to their relative topic.



Fundamental Concepts for Environmental Processes Agenda The materials in this module are intended to be used cafeteria-style such that instructors will select only those topics required to prepare their students for further study of decentralized wastewater treatment. Since each instructor will customize the fundamental topics covered to suit their particular needs, no single agenda could address the myriad possible permutations. Should an instructor choose to cover all the fundamental concept topics included in this module, the following agenda is suggested. This suggested agenda assumes a four week period with three 50 minute class periods per week. Week 1 Class 1: Application of fundamental concepts to decentralized wastewater treatment.

Introduction to water quality characteristics including resources for additional information

Class 2: Water quality characteristics including organic compounds, dissolved oxygen, and oxygen demand

Class 3: Water quality characteristics including nutrients, microbial organisms, salts, metals, and other water quality parameters

Week 2 Class 1: Stoichiometry concepts including mass, moles, and molecular weight; balancing

chemical equations; and limiting reagents Class 2: Biological concepts including organisms and oxygen, temperature and growth, and

toxicity Class 3: Units concepts including systems of units, unit conversions, and dimensional

homogeneity Week 3 Class 1: Mass balance concepts including conservation of mass, examples of mass balance

principles, types of processes, and using concentrations and percent composition Class 2: Mass balance concepts including setting up and solving mass balance problems Class 3: Mass balance concepts including instructor and student solved mass balance

problems Week 4 Class 1: Fluid mechanics concepts including flow rate, continuity, and head Class 2: Reaction concepts including reaction types, hydraulic retention time, and reactor

relationships Class 3: Sedimentation including sedimentation types, Stoke’s Law, and application to

settling basins



Fundamental Concepts for Environmental Processes Module Outline I. Introduction A. Application of Fundamental Concepts II. Overview of Water Quality A. Resources B. Organic Compounds C. Dissolved Oxygen D. Oxygen Demand 1. Biochemical Oxygen Demand (BOD) 2. Chemical Oxygen Demand (COD) 3. Carbonaceous Oxygen Demand (CBOD) and Nitrogenous Oxygen Demand (NBOD) 4. Other Measures of Organic Materials E. Solids F. Nutrients 1. Problems Associated with Nutrients 2. Nitrogen 3. Phosphorus G. Microbial Organisms 1. Problems Associated with Microorganisms H. Salts I. Metals J. Other Water Quality Parameters 1. Turbidity 2. Hardness 3. Alkalinity 4. pH III. Stoichiometry A. Mass, Moles, and Molecular Weight 1. Mass 2. Moles 3. Molecular Weight B. Balancing Chemical Equations C. Limiting Reagents IV. Biological Concepts A. Importance of Biology to Decentralized Systems B. Organisms and Oxygen C. Temperature and Biomass Growth D. Toxicity V. Units A. Unit Systems 1. International System of Units 2. U.S. Customary System B. Converting Units C. Dimensional Homogeneity VI. Mass Balance A. Conservation of Mass



B. Examples of the Mass Balance Principle C. Types of Processes D. Using Concentrations E. Using Percent Composition F. A Cookbook Procedure for Setting Up Mass Balance Problems VII. Fluid Mechanics A. Flow Rate B. Continuity C. Handy Area Equations D. Head VIII. Reactions A. Reaction Types B. Hydraulic Retention Time C. Types of Reactors 1. Batch Reactors 2. Continuously Stirred Tank Reactors 3. Plug Flow Reactors IX. Sedimentation A. Uses of Sedimentation B. Types of Sedimentation C. Influencing Factors 1. Particle Factors 2. Fluid Factors D. Determining Sedimentation Rates with Stoke's Law 1. Typical Values for ρ and µ E. Application to Settling Basins



Fundamental Concepts for Environmental Processes Goals This course module aims to provide students with limited prior education in wastewater treatment or from non-engineering backgrounds with a basic understanding of select fundamental concept topics and how those topics relate to decentralized wastewater treatment.



Fundamental Concepts for Environmental Processes Learning Objectives 1. Upon completing this module, students will have a fundamental understanding of concepts

pertinent to wastewater treatment that will enable them to more fully understand processes used for wastewater treatment, disposal, and reuse.

2. After completion of this module students should be prepared for more in-depth study

available in other curriculum modules.



Fundamental Concepts for Environmental Processes Prerequisites 1. Freshman chemistry, freshman biology, college algebra 2. This module is likely not appropriate for students from engineering disciplines or with prior

courses in wastewater treatment



Fundamental Concepts for Environmental Processes Evaluation Form Name: ______________________________ We are requesting your assistance in reviewing the modules developed through the On-Site Consortium curriculum project. Please complete the following form while reviewing the materials With a rating scale of 1 (Disagree) to 5 (Agree), please respond to the following questions:

Review of printed materials: Disagree Agree

The text completely covers the topic area. 1 2 3 4 5 The visuals completely cover the topic area. 1 2 3 4 5

The discussion notes completely cover the topic area. 1 2 3 4 5

Review of learning objectives: I gained a better understanding of fundamental concepts related to decentralized wastewater treatment. 1 2 3 4 5 I gained a better understanding of how to apply fundamental concepts to decentralized wastewater treatment systems. 1 2 3 4 5 I gained a better understanding of how these concepts help describe system function and performance. 1 2 3 4 5 What specific recommendations would you provide for the text. __________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ What specific recommendations would you provide for the visuals.________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ What specific recommendations would you provide for the notes. _________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Please give specific constructive comments on the topic/module. __________________________ ______________________________________________________________________________



Fundamental Concepts for Environmental Processes Problem Sets Overview of Water Quality A sample of water was analyzed for solids content. 0.25 L of sample was filtered through a 2.000 g filter paper. 10 % of the filtrate was placed in a crucible that weighed 30.000 g. After drying, the total weight of the filter and crucible are 2.150 g and 30.050 g, respectively. After ashing, the filter paper and crucible weigh 2.050 g and 30.009g, respectively. Calculate the solids concentrations of the following:

a) TSS and VSS b) TDS and VDS A 0.15 L sample of water has an initial dissolved oxygen level of 8.35 mg/L. After five days in incubation in a 300 mL BOD bottle, the dissolved oxygen level has decreased to 4.09 mg/L. Calculate the BOD5. A small industrial plant discharges wastewater into a stream. The plant discharge has a flow rate of 0.2 m3/s and a BODu concentration of 40 mg/L. The stream receiving the discharge has a flow rate of 1.3 m3/s and a BODu of 6 mg/L. Downstream of the discharge point, the velocity in the stream is 0.15 m/s. Assuming no other sources of BOD enter the stream, what is the BODu remaining in the stream 10 km downstream of the plant discharge? Use k = 0.23 1/day. Fluid Mechanics A mixing tank receives wastewater from two inlet lines. The first inlet has an i.d. of 8 in and a flow velocity of 2 ft/s. The second inlet has an i.d. of 12 in and a flow velocity of 2.5 ft/s. The mixed water leaves the tank through a 16 in i.d. pipe. What is the flow velocity in the outlet pipe? Flow is carried in a triangular channel at a velocity of 2 ft/s. The channel is 2 ft deep and has a top width of 12 ft. The flow in the channel is 1 ft deep. What is the flow rate in the channel? A pipe flowing full carries water at 20°C from a reservoir in 12 inch ID pipe at a rate of 3 ft/s. Some of the flow branches off to a cooling system while the remaining flow continues on for treatment in 10 inch ID pipe at 2 ft/s. What diameter pipe (inches) is necessary to deliver water to the cooling system at 1 ft/s?



Two triangular streams merge to form one larger channel with a rectangular cross-section. The diagram showing the characteristics of the streams follows, where w is stream width, d is flow depth, and v is flow velocity:

Stream 3: w = 2 m d = 0.75 m v = 1.5 m/s

Stream 2: w = 3 m d = 0.5 m

Stream 1: w = 2 m d = 0.5 m v = 1.5 m/s

Determine the flow velocity in stream 2. Conservation of Mass A stream with a 50 mg/L concentration of some chemical flows at 0.75 m3/s. What is the mass flow rate in g/s of the chemical? The oxygen concentration in a 2L bottle of water is 5.0 mg/L. What is the mass (in g) of O2 in the bottle? Wet sludge with a solids content of 30% by weight is placed in a drying bed until it reaches a solids content of 80%. If 5 tons of wet sludge are placed in the bed:

a) how much dried sludge is removed, and b) how much water (by weight) is lost?

Water with a solids concentration of 50 mg/L passes through a sand filter at a flow rate of 2 m3/s. Effluent from the filter has a solids concentration of 8 mg/L. At what rate do solids accumulate on the sand filter? Two pipes, Pipe A and Pipe B, join and flow into Pipe C. Pipe A has a flow of 0.1 m3/s and a concentration of 5 mg/L and Pipe B has a flow of 0.3 m3/s and a concentration of 9 mg/L. What is the concentration of the flow in Pipe C?



Many larger wastewater treatment plants use activated sludge systems to remove organic material from wastewater. This process generates lots of solids that then must be removed in clarifiers. In one system, a flow of 500 m3/day enters a clarifier with a solids concentration of 10,000 mg/L. Of the water entering the clarifier, 90 % leaves as treated effluent. That effluent carries 0.1 % of the solids. The remaining water and solids leave the clarifier as waste sludge. Determine: a) What is the solids concentration in the treated effluent? b) How many kilograms of dry solids exit the system in waste sludge every day? Water entering a septic tank has a maximum flow of 0.025 m3/min, a concentration of solids of 200 mg/L, and a concentration of organic material of 150 mg/L. Approximately 60 % of the solids and 30 % of the organics are retained in the septic tank.

a) What are the mass rates of solids and organic material exiting the tank? b) What are the effluent concentrations of solids and organic material?

Water enters a settling pond from two rectangular channels. The first influent flow has a depth of 0.2 m, a width of 1 m, a velocity of 0.5 m/s, and a concentration of 500 mg/L. The second influent flow has a depth of 0.15 m, a width of 1.5 m, a velocity of 0.75 m/s, and a concentration of 400 mg/L. A single rectangular channel carries effluent from the pond. If 95% of the incoming solids are retained in the pond, what is the solids concentration of the effluent? First Order Reactions Calculate the hydraulic residence time for a plug flow reactor that has a volume of 1150 gal and a flow rate in of 25 gal/hour. A batch reactor is used to break down organic materials in a wastewater. The initial concentration is 500 mg/L and the reaction rate is 0.5 1/d. What is the concentration after:

a) 1 day, and b) 1 week?

What size (volume) tank would you need to treat waste water at a flow rate of 30 m3/hr from a concentration of 1.75 mg/L to a final concentration of 0.75 mg/L? k = 0.25d-1. Do for both CSTR and Plug Flow reactors. Wastewater flow from a food processing operation is passed through two reactors in series (i.e. all flow passes through the first reactor then the second). The reactors are used to reduce the concentration of Constituent X, which has an initial concentration of 1000 mg/L. A constant flow of 80 ft3/hr is processed by the reactors. The first reactor has a volume of 4000 ft3 and is equipped with an agitator to keep the fluid well-mixed. The second reactor has a volume of 6000 ft3 and provides no mixing of fluids. If the reaction rate coefficient for Constituent X is 0.5 1/day, what is the concentration of Constituent X in the effluent of the second reactor?



Sedimentation Calculate the diameter and depth (in m) of a circular sedimentation basin for a design flow of 3800 m3/d based on an critical velocity of 0.00024 m/s and a detention time of 3 hours. Water entering a wastewater treatment plant is passed through a grit chamber. The flow rate is 0.12 m3/s and the chamber surface area is 48 m2. What is the smallest diameter particle (give particle diameter in mm) that will be completely retained in the grit chamber? Assume the particles are mineral and that the water temperature is 15 °C. Two pipes carry mineral solids having a particle size distribution as shown below into a grit chamber. Pipe 1 has an inside diameter of 0.20 m, a flow velocity of 0.6 m/s, and a solids concentration of 400 mg/L. Pipe 2 has an inside diameter of 0.10 m, a flow velocity of 0.8 m/s, and a solids concentration of 700 mg/L. If the tank has a surface area of 2.8 m2, what is the approximate accumulation (storage) rate of solids in the tank as kg/hr? Assume a water temperature of 20 C.

Particle Size Range, mm

% Composition

> 2.00 10 1.00 - 2.00 14 0.50 - 1.00 27 0.25 - 0.50 28 0.10 - 0.25 13

< 0.10 8



Fundamental Concepts for Environmental Processes Problem Sets With Solutions Overview of Water Quality A sample of water was analyzed for solids content. 0.25L of sample was filtered through a 2g filter paper. 10% of the filtrate was placed in a crucible that weighed 30g. After drying, the total weight of the filter and crucible are 2.15g and 30.050g, respectively. After ashing, the filter paper and crucible weigh 2.05g and 30.009g, respectively. Calculate the solids concentrations of the following:

a) TSS and VSS b) TDS and VDS

TSS = 25.0

00.215.2 − = ∗ = 6001000 Lmg

VSS = 25.0

05.215.2 − *1000 = 400 Lmg

TDS = 025.0

)000.30050.30( − *1000 = 2000 L

mg

VDS = 025.0

)009.30050.30( − *1000 = 1640 L

mg

A 0.15 L sample of water has an initial dissolved oxygen level of 8.35 mg/L. After five days in incubation in a 300 mL BOD bottle, the dissolved oxygen level has decreased to 4.09 mg/L. Calculate the BOD5.

BOD5 =

300150

)09.435.8( − = 8.52 L

mg



A small industrial plant discharges wastewater into a stream. The plant discharge has a flow rate of 0.2 m3/s and a BODu concentration of 40 mg/L. The stream receiving the discharge has a flow rate of 1.3 m3/s and a BODu of 6 mg/L. Downstream of the discharge point, the velocity in the stream is 0.15 m/s. Assuming no other sources of BOD enter the stream, what is the BODu remaining in the stream 10 km downstream of the plant discharge? Use k = 0.23 1/day.

m& BOD p = 0.2 s

m3

* 40 3mg = 8

sg

m& BOD p = 1.3 s

m3

* 6 3mg = 7.8

sg

BOD = )3.12.0(

)8.78(

+

+ = 10.533 L

mg

t =

sm

m

15.0

)1000*10(= 66667s = 18.52 hr = 0.7716 d

BODt = 10.533 (1 – e -0.23*0.7716) = 1.713 Lmg

Fluid Mechanics A mixing tank receives wastewater from two inlet lines. The first inlet has an i.d. of 8 in and a flow velocity of 2 ft/s. The second inlet has an i.d. of 12 in and a flow velocity of 2.5 ft/s. The mixed water leaves the tank through a 16 in i.d. pipe. What is the flow velocity in the outlet pipe?

q1 = 2 ∗4π (

128 )2 = 0.6981cfs

q2 = 2.5 ∗ 4π (

1212 ) 2 = 1.9635cfs

vout = 6616.2 = 1.906 sft

4π (

1216 )2



Flow is carried in a triangular channel at a velocity of 2 ft/s. The channel is 2 ft deep and has a top width of 12 ft. The flow in the channel is 1 ft deep. What is the flow rate in the channel?

q = ½ (6∗ 1)∗ 2 = 6 cfs A pipe flowing full carries water at 20°C from a reservoir in 12 inch ID pipe at a rate of 3 ft/s. Some of the flow branches off to a cooling system while the remaining flow continues on for treatment in 10 inch ID pipe at 2 ft/s. What diameter pipe (inches) is necessary to deliver water to the cooling system at 1 ft/s?

qin = 3 ∗4π (

1212 ) 2 = 2.3562 cfs

qout = 2 ∗4π (

1210 )2 = 1.0908 cfs

Acool = sft1

2654.1= 1.2654 ft2

d = 1.269 ft = 15.23 in



Two triangular streams merge to form one larger channel with a rectangular cross-section. The diagram showing the characteristics of the streams follows, where w is stream width, d is flow depth, and v is flow velocity:

Stream 2: w = 3 m d = 0.5 m

Stream 1: w = 2 m d = 0.5 m v = 1.5 m/s Stream 3:

w = 2 m d = 0.75 m v = 1.5 m/s

Determine the flow velocity in stream 2.

( )

( )

( ) sm 2.00

0.5 3 21

0.75 - 2.25 v

sm 2.25 1.5 0.75 2 q

sm 0.75 1.5 0.5 2

21 q

2

3

3

3

1

=∗

=

=∗∗=

=∗∗=

Conservation of Mass A stream with a 50 mg/L concentration of some chemical flows at 0.75 m3/s. What is the mass flow rate in g/s of the chemical?

sg 37.5 0.75 50 m =∗=&

The oxygen concentration in a 2L bottle of water is 5.0 mg/L. What is the massing of O2 in the bottle? m

� = 5.0 * 2 = 10mg = 0.01g



Wet sludge with a solids content of 30% by weight is placed in a drying bed until it reaches a solids content of 80%. If 5 tons of wet sludge are placed in the bed:

c) how much dried sludge is removed, and d) how much water (by weight) is lost?

lb 6250 3750 - 10000 lost -water

lb 3750 0.8

3000 sludge-dry

lb 3000 0.30 2000 5 solids

m

m

m

==

==

=∗∗=

Water with a solids concentration of 50 mg/L passes through a sand filter at a flow rate of 2 m3/s. Effluent from the filter has a solids concentration of 8 mg/L. At what rate do solids accumulate on the sand filter?

sg 84 16 - 100 acc.-solids

sg 16 2 8 out -solids

sg 100 2 50 in-solids

m

m

m

==

∗=

=∗=

&

&

&

Two pipes, Pipe A and Pipe B, join and flow into Pipe C. Pipe A has a flow of 0.1 m3/s and a concentration of 5 mg/L and Pipe B has a flow of 0.3 m3/s and a concentration of 9 mg/L. What is the concentration of the flow in Pipe C?

( ) lmg 8

0.3 0.1sg 3.2

sg 3.2 2.7 0.5

sg 2.7 9 0.3

sg 0.5 0.1 5

CC

Cm

Bm

Am

=+

=

=+=

=∗=

=∗=

&

&

&



Many larger wastewater treatment plants use activated sludge systems to remove organic material from wastewater. This process generates lots of solids that then must be removed in clarifiers. In one system, a flow of 500 m3/day enters a clarifier with a solids concentration of 10,000 mg/L. Of the water entering the clarifier, 90 % leaves as treated effluent. That effluent carries 0.1 % of the solids. The remaining water and solids leave the clarifier as waste sludge. Determine: a) What is the solids concentration in the treated effluent? b) How many kilograms of dry solids exit the system in waste sludge every day? Mass balance of water: Water entering system = 500 m3/day Water leaving as treated effluent = 0.90 * 500 = 450 m3/day Water leaving with sludge = 500 - 450 = 50 m3/day Mass balance of solids: Solids entering system = 500 * 10,000 = 5,000,000 g/day Solids exiting system with treated effluent = 0.001 * 5,000,000 = 5,000 g/day Solids leaving with sludge = 5,000,000 - 5000 = 4,995,000 g/day = 4995 kg/day Solids concentration in effluent = 5000/450 = 11.11 mg/L Water entering a septic tank has a maximum flow of 0.025 m3/min, a concentration of solids of 200 mg/L, and a concentration of organic material of 150 mg/L. Approximately 60 % of the solids and 30 % of the organics are retained in the septic tank.

c) What are the mass rates of solids and organic material exiting the tank? d) What are the effluent concentrations of solids and organic material?

( )

( )

lmg 105

0.0252.625 out -orgsC

lmg 80

0.0252 out -solidsC

mg 2.625 .3 - 1 3.75 out -BOD

mg 2 .6 - 1 5 out -solids

mg 3.75 150 0.025 in-org

mg 5 200 0.025 in-solids

m

m

m

m

==

==

==

=∗=

=∗=

=∗=

&

&

&

&



Water enters a settling pond from two rectangular channels. The first influent flow has a depth of 0.2 m, a width of 1 m, a velocity of 0.5 m/s, and a concentration of 500 mg/L. The second influent flow has a depth of 0.15 m, a width of 1.5 m, a velocity of 0.75 m/s, and a concentration of 400 mg/L. A single rectangular channel carries effluent from the pond. If 95% of the incoming solids are retained in the pond, what is the solids concentration of the effluent?

( ) ( ) ( )

( )( )( )

( )

( )( ) ( )( ) lmg 21.86

75.1.5 .15 5.1 .25.875 C

sg 5.875 67.5 50 0.05

sg 67.5 40075.01.5 0.15

sg 50 500 0.5 1 0.2

006m

2m

1m

=∗+∗

=

+=

=∗=

=∗=

&

&

&

First Order Reactions Calculate the hydraulic residence time for a plug flow reactor that has a volume of 1150 gal and a flow rate in of 25 gal/hour.

hr 46 25

1150 ==θ

A batch reactor is used to break down organic materials in a wastewater. The initial concentration is 500 mg/L and the reaction rate is 0.5 1/d. What is the concentration after:

c) 1 day, and d) 1 week?

lmg 15.10 e 500 Cl

mg 303.3 e 500 C

0.5(7)-7

0.5(1)-1

==

==



What size (volume) tank would you need to treat waste water at a flow rate of 0.30 m3/hr from a concentration of 1.75 mg/L to a final concentration of 0.75 mg/L? k = 0.25l/d. Do for both CSTR and Plug Flow reactors.

3m 24.40 24 3.389 0.30 v 3.389d 0 1.75e 0.75

PFR

338.4m 24 5.33 hr

3m .30 v d 5.33 0

0.250 11.75 0.75

CSTR

0025-

=∗∗===

=∗∗==

+=

Wastewater flow from a food processing operation is passed through two reactors in series (i.e. all flow passes through the first reactor then the second). The reactors are used to reduce the concentration of Constituent X, which has an initial concentration of 1000 mg/L. A constant flow of 80 ft3/hr is processed by the reactors. The first reactor has a volume of 4000 ft3 and is equipped with an agitator to keep the fluid well-mixed. The second reactor has a volume of 6000 ft3 and provides no mixing of fluids. If the reaction rate coefficient for Constituent X is 0.5 1/day, what is the concentration of Constituent X in the effluent of the second reactor?

lmg 102.67 e 489.8 2C

d 3.125 hr 75 80

6000 20

lmg 489.8

24500.5 1

1000 1C

hr 50 80

400010

0.5(3.125)- ==

===

=

+

=

==



Sedimentation Calculate the diameter and depth (in m) of a circular sedimentation basin for a design flow of 3800 m3/d based on an critical velocity of 0.00024 m/s and a detention time of 3 hours.

15.28m d m 2.6 depth

m 183 3600 24 0.00024

3800

m 475 243 3800 Vol

2

3

==

=∗∗

=Α

=∗=

Water entering a wastewater treatment plant is passed through a grit chamber. The flow rate is 0.12 m3/s and the chamber surface area is 48 m2. What is the smallest diameter particle (give particle diameter in mm) that will be completely retained in the grit chamber? Assume the particles are mineral and that the water temperature is 15 °C.

mm 0.056 d10x 1.14 18

9.81 d )9992650(0025.0

sm 0.0025

480.12 sV

3-

2

=∗

−=

==



Two pipes carry mineral solids having a particle size distribution as shown below into a grit chamber. Pipe 1 has an inside diameter of 0.20 m, a flow velocity of 0.6 m/s, and a solids concentration of 400 mg/L. Pipe 2 has an inside diameter of 0.10 m, a flow velocity of 0.8 m/s, and a solids concentration of 700 mg/L. If the tank has a surface area of 2.8 m2, what is the approximate accumulation (storage) rate of solids in the tank as kg/hr? Assume a water temperature of 20 C.

Particle Size Range, mm

% Composition

> 2.00 10 1.00 - 2.00 14 0.50 - 1.00 27 0.25 - 0.50 28 0.10 - 0.25 13

< 0.10 8

m& 1 = 0.0188 ∗ 400 = 7.5398 sg

q2 =0.8 ∗ 4π (0.1)2 = 0.0063

sm3

m& 2 = 700 0.0063 = 4.398 ∗sg

tot = 11.938 m&sg

q tot = 0.0188 + 0.0063 = 0.251 s

m3

Vc = 0251.0 = 0.009 sm

2.8

dc = 3

2

10118

81.9)9982650(−∗

−

x

d = 0.009

dc = 0.10mm 92% captured

m& acc = 11.938 ∗ 0.92 = 10.98 sg



Fundamental Concepts for Environmental Processes Additional Materials: Field Activities Grocery Store Tour Goal: Visit and tour a local grocery store to discuss how daily operations influence the quantity and quality of wastewater generated by the operation. Suggested Contact: Store manager Required Time: 3 hours on site Suggested Activities on Site: • Examine the parking lot and access alleys around the store to determine whether the store is

on municipal sewer service or on a decentralized treatment facility. • Look for on-site pretreatment devices such as grease traps. Discuss operation and

maintenance of these technologies. • Examine the density of development around the store and discuss how it likely influences

wastewater treatment options. • Inquire about water supply for the business. Does the store use a municipal or private water

source? • Visit various areas of the store, such as the bakery or deli, and ask about water use and waste

disposal in those operations. How do those activities influence wastewater quantity and quality from the business?

• Ask students to estimate the equivalent number of homes that would generate wastewater loads similar to the business.

Decentralized Wastewater Treatment Facility Tour Goal: Discuss how fundamental concepts covered in this module relate to the facility observed. Suggested Contact: Land owner or facility manager Required Time: 2 to 3 hours on site Suggested Activities on Site • Discuss the types of water use in the area and how that would influence wastewater

characteristics. • Examine the wastewater treatment technologies on the site. Discuss how fundamental

concepts such as mass balance, fluid mechanics, reactions, or sedimentation play a role in the treatment process.

• Examine local soils, drainage, and topography. Discuss how these factors impact system layout and design.



Fundamental Concepts for Environmental Processes Additional Materials: In-Class Activities The following problems are recommended for use in the classroom. Students may be instructed to work in small groups to develop their solutions. As students work on the problems, the instructor has an opportunity to visit with student groups to answer any questions. Solutions may be shared with the class as the activity ends to provide immediate feedback to students regarding their work. These activities each require approximately 15 minutes of class time to complete. Water Quality--Solids A 100 mL water sample is examined for solids concentrations. The sample is filtered and the solids filtered out and the filtrate are dried and then ashed. The tare, dried, and ashed weights are shown below. Determine the total suspended solids, volatile suspended solids, and total dissolved solids concentrations. Filtered Solids Filtrate Tare Weight 2.000 g 50.000 g Dried Weight 2.300 g 50.045 g Ashed Weight 2.100 g 50.023 g Water Quality--BOD 5 mL of wastewater is placed into a 300 mL BOD bottle and diluted. The DO concentration in the sample before incubation is 6.5 mg/L. The sample is incubated 5 days and the final DO is found to be 2.8 mg/L.

a) What is the BOD5? b) If the reaction rate coefficient is 0.24 1/d, what is the ultimate BOD? c) What is the BOD15?

Fluid Mechanics a) Water in a trapezoidal ditch travels at 0.75 ft/s. The cross-sectional area of flow has a bottom

width of 5 ft, a top width of 8 ft, and a depth of 1 ft. What is the flow rate in the channel? b) Water flows in an 10 in i.d. pipe at 1.8 ft/s. The pipe narrows to a 8 in i.d. What is the flow

velocity in the narrower section? Conservation of Mass A belt press is used to remove excess water from wastewater biosolids. Wet sludge having 40% solids by weight enters the belt press at a rate of 1000 lb/hr. The pressed sludge is 80% solids by



weight. What is the mass rate of the pressed sludge and what is the mass rate of the separated water? First Order Reactions A reactor receives wastewater having a constituent concentration of 500 mg/L. A discharge concentration of 200 mg/L is desired. If the flow rate is 3 m3/d and the reaction rate coefficient is 3 1/d, what volume should the reactor be if it is:

a) a continuous flow, stirred tank reactor and b) a plug flow reactor.

Sedimentation Determine the settling velocity of a particle having a diameter of 0.25 mm and a density of 2650 kg/m3 in 10 °C water. Sedimentation A settling basin must trap all sediment greater than 0.2 mm in size. The sediment is mineral (ρ = 2650 kg/m3). The water temperature is 30 ºC and the flow rate is 500 m3/d. What tank surface area is needed?



Fundamental Concepts for Environmental Processes Additional Materials: In-Class Activities With Solutions Water Quality--Solids A 100 mL water sample is examined for solids concentrations. The sample is filtered and the solids filtered out and the filtrate are dried and then ashed. The tare, dried, and ashed weights are shown below. Determine the total suspended solids, volatile suspended solids, and total dissolved solids concentrations. Filtered Solids Filtrate Tare Weight 2.000 g 50.000 g Dried Weight 2.300 g 50.045 g Ashed Weight 2.100 g 50.023 g

Lmg3000

Lg3

1.0)000.2300.2(TSS ==

−=

Lmg2000

Lg2

1.0)100.2300.2(VSS ==

−=

Lmg450

Lg45.0

1.0)000.50045.50(TDS ==

−=

Water Quality--BOD 5 mL of wastewater is placed into a 300 mL BOD bottle and diluted. The DO concentration in the sample before incubation is 6.5 mg/L. The sample is incubated 5 days and the final DO is found to be 2.8 mg/L.

a) What is the BOD5? b) If the reaction rate coefficient is 0.24 1/d, what is the ultimate BOD? c) What is the BOD15?

Lmg222

3005

)8.25.6(BOD5 =−

=

Lmg07.737BOD

eBOD222

u

524.0u

=

= ×−



Lmg9.716)e1(07.737BOD 1524.0

15 =−= ×−

Fluid Mechanics

a) Water in a trapezoidal ditch travels at 0.75 ft/s. The cross-sectional area of flow has a bottom width of 5 ft, a top width of 8 ft, and a depth of 1 ft. What is the flow rate in the channel?

b) Water flows in a 10 in i.d. pipe at 1.8 ft/s. The pipe narrows to an 8 in i.d. What is the flow velocity in the narrower section?

cfs875.412

)85(75.0vAq =

×

+==

sft81.2

128

4

982.0Aqv

cfs982.01210

48.1Avq

22

2

2

11

=

π

==

=

π

==

Conservation of Mass A belt press is used to remove excess water from wastewater biosolids. Wet sludge having 40% solids by weight enters the belt press at a rate of 1000 lb/hr. The pressed sludge is 80% solids by weight. What is the mass rate of the pressed sludge and what is the mass rate of the separated water?

hrlb40040.01000m insolids

.=×=−

hrlb500

8.0400m outgeslud

.==−

hrlb5005001000m outwater

.=−=−



First Order Reactions A reactor receives wastewater having a constituent concentration of 500 mg/L. A discharge concentration of 200 mg/L is desired. If the flow rate is 3 m3/d and the reaction rate coefficient is 3 1/d, what volume should the reactor be if it is:

c) a continuous flow, stirred tank reactor and d) a plug flow reactor.

3m5.135.0

d5.031

500200

=×=∀

=θθ+

=

3

3

m92.03305.0

d305.0e500200

=×=∀

=θ= θ−

Sedimentation Determine the settling velocity of a particle having a diameter of 0.25 mm and a density of 2650 kg/m3 in 10 °C water.

sm0429.0

)1031.1(18)81.9()00025.0)(10002650(v 3

2

x =×

−= −

Sedimentation A settling basin must trap all sediment greater than 0.2 mm in size. The sediment is mineral (ρ = 2650 kg/m3). The water temperature is 30 ºC and the flow rate is 500 m3/d. What tank surface area is needed?

sm0453.0

)1096.7(18)81.9()0002.0)(9962650(v 4

2

x =×

−= −

2

sm127.0

)3600)(24(0453.0500

vqA ===



Fundamental Concepts for Environmental Processes Additional Materials: Lecture Notes for Select Topics Overview of Water Quality References • Two publications are widely used as the principal “cookbooks” for water and wastewater

analysis: • Standard Methods for the Analysis of Water and Wastewater. American Water Works

Association and the American Public Health Association. Published about every two years.

• EPA Standard Methods. US Environmental Protection Agency. • These references contain information regarding which analytical tests are appropriate for

what types of questions or problems along with step-by-step analytical procedures. • In many cases these references also provide information on how to handle and preserve

samples to provide the best possible analyses. Solids • Associated problems include:

Mass deposition - filling of storage areas; blockage of ditches, channels, degrades fish spawning areas Increased turbidity - light penetration to aquatic vegetation, feeding habits of sight-hunting fish, unappealing appearance (Brazos River) Interference with Mechanical Systems - plugs, filters & sprinkler heads, complicates water treatment, erodes equipment High TDS typically associated with high salts concentrations—taste problems in public drinking water supplies (local tap water)

• Solids descriptions typically include:

Total Solids (TS) - material remaining after evaporation of sample liquid

Total Volatile Solids (TVS) - material lost after total solids are ashed (organics that are burned off at 550 ºC)



Total Fixed Solids (TFS) - material (mineral basis) left after total solids are ashed

TS = TVS + TFS

Total Suspended Solids (TSS) - dried solids caught during filtration through a 1.5 µm filter

Total Dissolved Solids (TDS) - dried solids passing through filter

TS = TSS + TDS

Volatile Suspended and Volatile Dissolved Solids (VSS/VDS) Fixed Suspended and Fixed Dissolved Solids (FSS/FDS)

• Measured as the mass of solids per known volume of water:

Sm m

volt c=

−

Where S = solids concentration, mg/L mt = total mass of solids and container, mg mc = mass of container, mg vol = volume of liquid sample, L Example A 100 mL sample is filtered through a 2 g filter paper. The resulting dried weight is 2.075 g. What is the TSS concentration?

LmgL

mgmgvol

mmTSS ct /7501.0

20002075=

−=

−=

The solids are then ashed yielding a total weight of 2.025 g. What are the FSS and VSS concentrations?

LmgL

mgmgFSS /2501.0

20002025=

−=

VSS = TSS - FSS = 750 mg/L - 250 mg/L = 500 mg/L

Nutrients • Generally consists of macro nutrients N-P-K, primarily N and P, naturally occurring (without

human influence) in surface waters at low level concentrations N=0.3 mg/L, P=0.05 mg/L



Eutrophication • Excess nutrients act as fertilizer to aquatic plants -> increased productivity • Added organic matter eventually decays -> odors and decreased DO • Thick vegetation also interferes with swimming and boating. Decaying matter may foul

beaches. • High "concentrations" of suspended material inhibit light penetration to submerged aquatic

vegetation (just like turbidity from sediment) • Limiting nutrient - the least abundant in relation to plant needs. Plants will establish until one

is used up - when it is unavailable, development is impaired other nutrients go unused. • As P becomes more abundant, much more productivity is allowed if P is the limiting nutrient

Nitrogen • Commonly reported Nitrogen forms include:

Nitrate (NO3-N) - greatest oxidation state, inorganic Nitrite (NO2-N) - inorganic Ammonia (NH3-N) - least oxidation state Organic N - nitrogen bound in organic compounds (proteins, urea, etc.) Total Kjeldahl Nitrogen (TKN) - total organic nitrogen and ammonia Total nitrogen - sum of all forms

• Ammonia=0.2 mg/L may be toxic to fish, especially trout • NO2,NO3 - may cause methemoglobinemia (blue baby), reduced oxygen carrying

capacity in blood - high nitrate waters should be avoided by pregnant women and children under 6mo - 1yr (10 mg/L)

• Nitrogen readily changes forms depending on ambient conditions

Phosphorus • Typically reported forms:

orthophosphates (ortho-P) - reactive phosphorus, available without prior oxidation, most available to plants

condensed (poly) phosphates - become reactive with preliminary oxidation or acid hydrolysis

organic phosphorus - bound in organic matter which must be destroyed (by digestion) before phosphorus becomes reactive



total phosphorus (TP) – the sum of all of the above

Microbial Organisms (Pathogens) • Common descriptors:

Fecal coliform counts - number of colonies formed after filtering sample • Pathogenic - generally considered a surface water problem but some question movement to

groundwater. Example: Contaminated oyster beds, Cryptosporidium problem in Milwaukee, pfisteria in Chesapeake Bay estuaries

Salts • Saline conditions may limit usefulness of water for municipal, industrial, or agricultural

applications. • Accumulation of Na leads to soil dispersion -> structure breakdown, decreased infiltration,

possible toxicity, greater suspension in water • Can be a particular problem in irrigated areas Metals • Nontoxic - taste, staining, biological growth -- odors • Toxic - bioaccumulation, population disturbance Hardness • Concentration of multivalent cations (usually measured as equivalent amounts of calcium

carbonate)—mostly calcium, magnesium, iron, and manganese • Hard water leaves scale in pots, pipes, hot-water heaters, also requires increased amounts of

soap for washing and bathing • Soft water has fewer of these cations and suds and lathers easily with soap—may seem

difficult to remove soap residue



Dissolved Oxygen (DO) • Amount of molecular oxygen dissolved in water • Important in sustaining aquatic life • Maximum possible DO level decreases as temperature increases, so DO stress is greatest

during the day in summer months • Measured by meter and probe Oxygen Demand • Referred to as the amount of oxygen consumed in the aerobic oxidation

(breakdown/metabolism) or organic substances • Use of DO during metabolism of organic constituents depletes the DO supply available for

aquatic life—may result in fish kills • Measurement of oxygen demand is considered an indirect measure of the amount of organic

material in water—changes in DO are measured instead of a direct measurement of the organic concentration

Biochemical Oxygen Demand (BOD) • Amount of oxygen used during the aerobic biochemical breakdown of organics • Relies on microbial and natural chemical processes for breakdown—similar to what happens

in natural water resources • Usually conducted over a 5-day period (yields BOD5). A microbial seed and nutrients for

bacterial growth may be added to ensure proper breakdown • DO is measured at the start of the test and again after the incubation period • BOD measurements detect the amount of BOD degraded over the incubation time (BOD

consumed). • After incubation, some BOD will remain in the sample (BOD remaining). • The amount of BOD detected increases as the amount of incubation time increases until the

ultimate BOD is detected (you’ve broken down everything that will degrade naturally) • BOD consumed + BOD remaining = ultimate BOD



• BOD is determined from laboratory measurements as:

BODDO DO

VV

i f

s

b

=−

Where BOD = biochemical oxygen demand, mg/L (BOD consumed) DOi = initial DO concentration, mg/L DOf = final DO concentration, mg/L Vs = volume of sample, L Vb = volume of the BOD bottle, L • The term Vs/Vb allows for sample dilution when organic concentrations are high Example 30 mL of a wastewater are placed in a 300 mL BOD bottle. The sample is diluted to fill the bottle. The DO concentrations at the beginning and the end of the 5-day incubation period are 7.3 mg/L and 1.8 mg/L, respectively. What is the BOD?

BODDO DO

VV

mg Li f

s

b

5

7 3 1830300

55=−

=−

=. .

/

• BOD breakdown over time, in an incubated sample or elsewhere, follows the batch reaction

equation:

BOD BOD erem ukt= −

Where BODt = BOD remaining at time t, mg/L BODu = ultimate BOD concentration, mg/L k = reaction rate coefficient, 1/d t = time, d or, expressed in terms of BOD consumed:

BOD BOD econ ukt= − −( )1

Example The BOD5 of a wastewater was determined to be 250 mg/L. If the reaction coefficient was 0.23 1/d, what is the ultimate BOD?



The BOD5 value is BOD consumed over 5 days, so use the BOD consumed equation BOD BOD et u

kt= − −( )1 250 1 0 23 5= − −BOD eu ( )( . )( ) BODu= 365.84 mg/L What is BOD3? Again, BOD3 is a measure of consumed BOD, so use the second equation BOD e mg l3

0 23 336584 1 182 34= − =−. ( ) . /. ( ) What is the BOD remaining at 3 days? BODrem = BODu - BOD3 = 365.84 - 182.34 = 183.5 mg/L Chemical Oxygen Demand • The equivalent amount of oxygen needed to break down organic matter under strong

oxidizing agents • Breaks down more of the organic materials than a natural process would because of the

strong chemicals used—hence COD ≥ BOD • Much faster to perform than BOD testing since an incubation period is not required • Does not match as closely the behavior of the waste in a natural situation—toxic or non-

biodegradable compounds can be oxidized by COD analysis that would not show up in a 5-day BOD analysis

Organic Materials Indirect Measurement • BOD and COD both provide an indirect measurement of organic material in water • The higher the BOD or COD concentrations, the higher the concentration of organic material Total Organic Carbon (TOC) • The amount of carbon bound in organic constituents (does not include carbonates)



• Special instrumentation has been developed for this analysis—organics are oxidized and the

resulting CO2 is measured • Quick and easy to run if machinery is available—the equipment is very expensive Oil and Grease • Measurement of the oily or greasy component of water without determining the actual

chemical constituency of the greasy substance • Measures amount of material which can be extracted using a specific solvent • Sometimes listed as fats, oils, and grease (FOG) Man-Made Organics • May provide toxic at high concentrations—recall bioaccumulation • May yield taste and odor problems



Fluid Mechanics Importance • Describes the movement of fluids into, through, and out of systems used for environmental

control Fluids • Refers to any non-solid materials including both liquids and gasses • The flow of liquids is easier to predict because they are “noncompressible,” meaning that

their density doesn’t change when they are put under pressure Flow Rate • The flow rate of a fluid may be determined using the velocity of flow and the cross-sectional

area of flow (area through which the flow moves)

q = vA

q = flow rate, volume per unit time, cfs m3/s gpd v = flow velocity, length per time, ft/s m/s A = cross-sectional area, length squared, ft2 m2

Continuity • This is really a mass balance of fluid • If we look it as a continuous mass balance, based on mass flow rate,

Fluid mass rate = flow rate times density

M�

= qρ

• If we assume no storage, then what goes in must come out

M�

in = M�

out

qinρout = qoutρout



• For liquids, ρ is typically constant, so ρin = ρout

qin = qout

Ainvin = Aoutvout Handy Area Equations d = diameter A = Area w = width wt = width at water surface wb = width at bottom of channel Circle: pipes (based on inside diameter)

Ad

=π 2

4

Rectangle: rectangular channels A = wd

Trapezoid: trapezoidal channels

Aw w db t=

+( )2

Triangle: triangular channels

Aw dt=2

Example Flow in a 4 inch i.d. (inside diameter) pipe has a velocity of 2 ft/s. What is the flow rate?

q = vA

v = 2 ft/s

Ad

ft= =

=π π2

2

2

4

4124

0 087.

q = 2(0.087) = 0.175 cfs



Example Water entering a settling tank is carried at 0.5 m/s in a rectangular channel 2m wide by 0.3m deep. This same flow rate exits the tank in a channel measuring 3m wide by 0.3 m deep. What is the flow velocity in the exit channel?

AiVi=AeVe

Ai=2m x 0.3m = 0.6m2 Vi=0.5 m/s

Ae= 3m x 0.3m = 0.9m2

0.6m2 x 0.5 m/s = 0.9 m2 Ve Ve = 0.33 m/s



Mass Balance Who Cares? • Key component of “process” operations (distribution, blending, mixing, sorting, separating,

etc.) • Allows us to determine the movement of materials through a process (water, solids, carbon,

nutrients)—what comes in, how much goes out, how much is retained in the treatment system

• Allows us to determine the efficiency of a treatment process (efficiency—how much of the

incoming material was captured and or transformed during treatment) Conservation of Mass • Conservation of Mass—mass is neither created or destroyed (excluding nuclear reactions) • For any system, mass that enters the system is either removed or accumulates within the

system:

input - output = accumulation • A system may have multiple inputs and/or outputs • Inputs or Outputs can be gaseous and yet are still part of the mass balance • Inputs and outputs may be mixed, reacted and/or combined (e.g. inputs to bread dough mixer

are flour, water, sugar and yeast, they are still outputs, but no longer individual) • Material may change phase and form and may combine or may separate, but the mass of each

individual component remains constant. (Phase Change) • Examples of multiple inputs and phase change include combustion: Inputs: fuel (let’s assume an organic that burns completely) oxygen Outputs: carbon dioxide water mineral ash



Types of Processes • Batch—results in a fixed amount of output, process conducted one-at-a-time-- brewing beer • For batch processes, mass balance is based on weight, mass, or volume:

stored mass = input mass - output mass • Continuous (rate)—flow of material is continuous—blending soft drinks • For continuous processes, mass balance is based on mass or volume flow rate (mass per unit

time, frequently using the variable m�

or M�

, or volume per unit time):

rate of storage = rate of input - rate of output Using Concentrations Many of the processes we use will be based on movement of air or liquid through the treatment process Sometimes instead of a mass, you’ll get a flow rate or flow volume and an average concentration To determine mass or mass flow rate, simply use:

mass flow rate (mass/time) = concentration (mass/volume) x flow rate (volume/time)

mass (mass) = concentration (mass/volume) x flow volume (volume) Using % Compositions Sometimes very concentrated solutions (slurries) will be described as having % composition by weight (typically % solids by weight) Multiply the fraction composition (% = value/100) by the total weight of the slurry constituent mass = total mass * fraction composition water mass = total mass - constituent mass For example 100 kg of slurry with 30% solids would have 30 kg solids and 70 kg water



Cookbook Procedure for Setting Up Mass Balance Problems 1. Identify the system and define the system boundaries—you choose based on your needs. 2. Determine whether the process is batch or continuous. 3. Determine whether the materials involved change form or composition. 4. Identify all inputs and outputs—diagram as needed. 5. Identify known quantities of mass or flow rates. 6. Identify unknown quantities and assign a variable to each. 7. Use mass balance equations to determine unknowns and solve. Example A sedimentation tank receives 2000 m3/d water containing 200 mg/L solids. Water leaves the tank at the same flow rate but with a solids content of 20 mg/L. What is the solids accumulation rate in the tank? Hints: Mass flow rate = fluid flow rate* concentration, mg/L = g/m3 System: sedimentation tank Process: continuous Inputs: water and solids Outputs: water and solids Storage: solids Solids accumulation = Sa Input rates: Water = 2000 m3/d Solids = 2000 m3/d*200g/m3 = 400,000 g/d = 400 kg/d Output rates: Water = 2000 m3/d Solids = 2000 m3/d*20g/m3 = 40,000 g/d = 40 kg/d Storage rate: unknown, use Sa Mass balance: Sa = Solids in - solids out = 400 kg/d - 40 kg/d = 360 kg/d



Example A solids slurry is 20% solids by weight. Five tons of this slurry are placed in a drying bed. After drying, the material is 80% solids by weight and all the material is removed. How much dried material was generated? How much water was lost in drying? System: drying bed Process: batch Inputs: water, solids Outputs: water left in material, water lost during drying, solids Storage: none Input quantities: solids = 0.20(5 tons) = 1 ton water = 5 tons - 1 ton = 4 tons Mass balance of solids: Solids in = solids out (no storage for this problem) Solids out = 1 ton Total mass of material generated = 0.8(Total) = 1 ton = 1.25 tons Mass of water in material = 0.2(1.25) = 0.25 tons Mass of water lost = 4 tons - 0.25 tons = 3.75 tons



First Order Reactions Importance • Basis for many of the processes important to environmental engineering technology

• Degradation of organic compounds • Transformation of air quality compounds

• Drives concentration of some environmentally important compounds

• Dissolved oxygen in streams • Volatilization of compounds into the air

Terms • Reactants—the original compounds prior to the reaction • Products—the compounds formed by the reaction • Reaction rate—speed at which the process takes place • Reactors—systems used to facilitate the reaction—usually designated as a type of tank Reaction Types • Irreversible—reactants form a product which cannot return to the original state—Process

cannot operate backwards • Reversible—Process works in both directions—Rate of process may be different depending

on the direction (Faster forming product than returning to original reactants) Hydraulic Retention Time • The amount of time, on average, that flow spends in the reactor • Treatment increases with greater retention times, but costs for treatment also rise (lower flow

rates or larger tanks) • Must find proper balance between desired treatment levels and treatment costs (i.e. use the

lowest retention time that provides the required treatment)



• Also called hydraulic residence time, HRT, θ

θ =VolQ

.

Vol = volume of the reactor tank, volume Q = fluid flow rate, volume per time

Batch Reactors • Reactants are placed in a reactor and mixed well, products are removed after reaction • Reactant concentrations depend on time • No flow into or out of the reactor during the reaction process

C C eA Aokt= −

CA = Concentration at time t, mass per unit volume Cao = Concentration at start of reaction, mass per unit volume k = reaction rate coefficient, one over time t = time since reaction started, time

Continuous Flow Stirred Tank (CFST) Reactors • Well-mixed reactors in which there is a continuous flow in and out

CCkA

Ao=+( )θ 1

θ = hydraulic retention time, time

Plug Flow Reactors (PFR) • Continuous flow through the reactor, but no stirring

C C eA Aok= − θ



Example Water with 200 mg/L of a degradable compound is passed through a reactor. The flow rate through the reactor is 500 m3/d and the reactor has a volume of 250 m3. The reaction rate coefficient for the 2 1/d. What is the exiting concentration for a batch reactor after 1 day? C C eA Ao

kt= − CA = 200 (mg/L) e(-2x1) = 27.1 mg/L for a CFST reactor? θ = Vol/Q = 250 (m3)/500 (m3/day) = 0.5 d

CCk

mg LAAo=+

=× +

=( ) ( . )

/θ 1

20005 2 1

100

for a PFR? C C eA Ao

k= − θ CA = 200 e(-2x0.5) = 73.6 mg/L



Sedimentation Definition • Gravitational accumulation of solids (particles) at the bottom of a fluid (air or water) • Essentially settling of solid particles Where is Sedimentation Used? • Removal of solids from drinking water

• Most water sources, especially surface water, have some solids that must be removed prior to consumption

• Removal of solids from waste waters

• Settling of solids in a septic tank

• Settling of solids in a primary lagoon

• Solids removal at a treatment plant • Settling of solids from air emissions

• Dust deposition near a feed lot • Removal of solids from runoff water

• Sedimentation basins at construction sites

• Solids deposition in stock tanks Types of Sedimentation • Discrete Settling—individual particles settle independently, low solids concentration • Flocculant—Concentration is great enough to cause individual particles to stick together and

form flocs. Flocs settle unhindered.



• Hindered—Particle concentration is great enough to inhibit water movement between

particles during settling, water must move through spaces between particles • Compression—Particles settle by compressing mass below Influencing Factors • Particle factors—size, density, shape, to some extent electrical charge

• Size—bigger particles settle faster than smaller

• Density—denser particles settle faster than less dense

• Shape—spherical particles settle faster than large, flat particles

• Charge—some particles (clays) carry an electric charge which interacts with polarity of water

• Fluid factors—flow velocity, density, viscosity

• Flow velocity—particles settle faster when there is no fluid movement, velocity causes turbulence that keeps particles suspended (greater velocity allows suspension of larger, denser particles)

• Fluid density—determines amount of buoyancy (weight of displaced water), denser

fluids provided greater buoyancy and slower settling

• Fluid viscosity—(fluid thickness) greater drag from thicker fluid Determining Sedimentation Rate • Stoke’s Law—applies to spherical particles settling in a very quiet fluid (usually won’t apply

to gasses)

18µg)dρ(ρ

v2

wpp

−=

where: vp = particle settling velocity (m/s or ft/s), ρp = particle density (kg/m3 or lb/ft3) ρw = fluid density (kg/m3 or lb/ft3) d = particle diameter (m or ft), g = gravitational acceleration (9.81 m/s2 or 32.2 ft/s2)



µ= fluid viscosity (kg/m·s or lb/ft·s) • Typical values for ρ and µ

• Particle densities for mineral sediments (mineral fraction of soil) ρp = 2650 kg/m3

• Water densities at 20 ºC

ρw = 998 kg/m3 µ = 1.01 x 10-3 kg/m·s or 0.00101 kg/m·s

Example Determine the settling velocity for a 0.5mm particle with a density of 2000 kg/m3 in 20 ºC water.

ρp = 2000 kg/m3 ρw = 998 kg/m3 d = 0.5mm = 0.0005 m g = 9.81 m/s2 µ = 0.00101 kg/m·s

0.14m/ss)kg/m18(0.00101

)9.81m/s(0.0005m)(998)kg/m(2000v23

p =⋅

−=

Application to Settling Basins • The surface area of a settling tank or basin needed to trap particles of a given size and density

can be determined using Stoke’s Law. • The critical settling velocity is set equal to the settling velocity of the smallest particle to be

trapped. • The overflow rate (similar to a vertical velocity) is equal to the flow rate into the tank divided

by the surface area (just like Q = VA) • Setting the overflow rate equal to the critical settling velocity will allow time for capture of

the smallest particles of interest

AQvOFR c ==

where OFR = the overflow rate (m/s or ft/s) vc = the critical settling velocity (m/s or ft/s)



Q = the flow rate into the basin (m3/s or cfs) A = the surface area of the basin (m2 or ft2) Example A flow has 2000 kg/m3 particles ranging in size from 0.2 mm to 1.5 mm. The flow rate into a settling basin is 2,000,000 m3/d. How large a tank is needed to capture particles 0.5 mm and larger? The temperature is 20 ºC. We need vp for 0.5mm particles which we will use as the critical velocity. From the previous example, we know that vp = 0.14 m/s for a 0.5mm particle with a 2000 kg/m3 density

A/3600)/d(1/24)(12,000,000m0.14m/sv

3

c ==

A = 165 m2

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