Mass Balance Concepts

Concept of Mass Balance

• A fundamental scientific concept is the law of conservation of matter.
• In the absence of significant mass-to-energy conversion, the total mass of substances entering a reaction equals the total mass of the products.
• The law of conservation underlies the concept of mass balance (material balance), useful in environmental technology, even without chemical reactions.
• Mass balance calculations are crucial in designing and operating water, sewage, air, and solid waste treatment processes.
• Treatment systems involve physical, chemical, and biochemical processes in reactors (vessels or tanks).
• Specific reactions or processes are called unit processes.
• Input must equal output, summarized as "what goes in must go out."
• Otherwise, accumulation = input − output.
• Composition changes in the reactor over time indicates an unsteady-state operation.
• A steady-state operation assumes constant rates of input/output and completely mixed reactor composition.

Types of Operation

• Unsteady-state operation involves changes in the material's composition in the reactor over time.
• Steady-state operation assumes constant input/output rates and composition within a completely mixed reactor.

Applying Mass Balance

• The concept of mass (material) balance determines the concentration of mixed solution discharged from a tank under steady-state conditions.
• For a tank where two pipes with salt solutions enter and one pipe carries the mixture out:
  • Pipe 1: Concentration c₁ mg/L, flow rate Q₁
  • Pipe 2: Concentration c₂ mg/L, flow rate Q₂
  • Pipe 3: Carries mixture out of tank
• The total amount of salt entering the tank must equal the total amount leaving it
• If the salt neither decays nor reacts, the salt concentration remains constant.
• The total mass of salt entering the tank must equal the total mass of salt leaving.
  • Input equals output.
• Known salt concentrations and flow rates in pipes 1 and 2 enables calculation of the salt concentration in pipe 3 using a mass balance equation.
  • Where Q3 = Q1 + Q2
• Concentration (mg/L) x volume flow rate (L/d) equals mass flow rate (mg/d).
  • mg/L x L/d = mg/d
• Volume flow rate is expressed in liters per day (L/d) with a time interval of 1 day assumed.
• C₁ x Q₁ equals the mass of salt entering the vessel in 1 day from the first pipe.
• C₂ x Q₂ equals the mass of salt entering the tank from the second pipe.
• Total mass of salt entering the tank in tons/day is the "input" and must equal the sum from the two pipes:
  • input = c₁ x Q₁ + c₂ x Q₂
• Total mass of salt leaving the tank equals the product of the mixture's salt concentration (c₃) and its volume flow rate leaving the tank (Q3)
  • Then output = c₃ x Q₃ or, Q3 = Q1 + Q2
  • Because mass balance applies here and output = input
• For the concept of mass or material balance: output equals input.
• You can solve the previous equation for c₃ by dividing both sides by (Q₁ + Q₂)
  • C₃ = (c₁ x Q₁ + c₂ x Q₂)/(Q₁ + Q₂)

Chemical Parameters of Water Quality

• Dissolved Oxygen
• Biochemical Oxygen Demand
• Nitrification
• Chemical Oxygen Demand
• Solids
• Hardness
• Iron, Manganese, Copper, and Zinc
• Fluorides
• Chlorides
• Chlorine Residual
• Sulfates
• Nitrogen
• Phosphorus
• Acidity, Alkalinity, and pH
• Toxic and Radioactive Substances
• Radionuclides
• Contaminants of Emerging Concern

Dissolved Oxygen (DO)

• Critical parameter for water quality in streams, rivers, and lakes.
• It is used extensively in biological wastewater treatment facilities.
• Can be introduced by mixing air (or pure oxygen) with sewage to promote aerobic decomposition.
• Higher dissolved oxygen concentration means better water quality.
• In general, the less of other substances in the water, the better the water quality.
• DO is determined by several methods:
  • Using standard wet chemistry methods of analysis
  • Using membrane electrode meters in the lab or the field.
• Oxygen's solubility is only slight in water.
• Aquatic organisms, plus bacteria, compete for the available dissolved oxygen.
• If much organic material exists in the water, bacteria will use up the DO very rapidly.
• Oxygen solubility depends on temperature:
  • Changes in water temperature significantly affect DO concentrations.
  • Oxygen solubility decreases as water temperature increases.
• Aquatic environments are classified by DO concentrations:
  • Healthy waters: DO concentrations are 80% or higher of saturation levels, supporting a diverse population.
  • Hypoxia occurs: When DO declines to less than 30% saturation, and most fish cannot thrive.
• Oxygen depletion in natural bodies of water from sewage and plant nutrients causes pollution.
• Anaerobic conditions, where DO concentration is zero or very close to zero in water and wastewater.
• Dissolved oxygen does not directly affect public health
  • Has an objectionable taste if drinking water has very little or no oxygen.
• Dissolved oxygen plays a part in the corrosion or rusting of metal pipes
  • Important factor in the operation and maintenance of water distribution networks.

Biochemical Oxygen Demand

• One of the most used terms in water quality and pollution control technology
• Microbes "demand" oxygen to fuel biochemical reactions, called the biochemical oxygen demand.
• Bacteria and microorganisms use organics for food.
• As microorganism metabolize the materials, they consume oxygen (DO)
  • Organics break down into simpler compounds (CO2 and H2O).
  • Microbes use the energy they released for growth and reproduction.
• Organic waste from sewage indicates a major type of water pollutant.
• BOD measures the total amount of biodegradable organics (pollution):
  • The more organics in the water, the higher the BOD by the microbes.
• BOD measures the strength of sewage
  • One of the most important parameters for pollution control plants.
    • Strong sewage has high organic concentration and BOD
    • Weak sewage (low BOD) needs less treatment.

Ultimate BOD

• Definition: The amount of oxygen used to completely decompose or stabilize all of the biodegradables in a given volume of water - BODL
  • Usually 20+ days to reach
• BOD is generally expressed in terms of mg/L of oxygen
• Expressing the BODL can be calculated:
  • For example, if 1 liter of municipal sewage needs 300 mg of oxygen for decomposition, BODL would be expressed as 300mg/L.
• Industrial wastewater examples may require much higher amounts of oxygen to complete waste stabilization
  • For example, BODL of 1500 mg/L indicates much stronger waste than domestic sewage.
  • The BOD value is a function of time.
• At beginning of BOD test (time = 0), no oxygen will have been consumed, and the BOD = 0
• As each day goes by, oxygen is consumed, and the BOD increases.
• Ultimately the BODL is reached, and the organics are completely decomposed.
• The BOD curve can be expressed mathematically:
  • BODt = BODL x (1 - 10^-kt)
  • BODt = BOD at any time t, mg/L
  • BODL = ultimate BOD, mg/l
  • k = a constant representing the BOD reaction rate
  • t = time in days
• The constant k represents the rate of oxygen consumption.
• The value of this rate constant depends on:
  • temperature
  • type of organic material
  • type of microbes exerting the BOD.
• The common value for k is 0.15/d for typical domestic sewage at 20° C.
• Higher temperatures increases the decomposition rate:
  • However, the BODL remains the same.
• The rate of the BOD reaction has direct relationship with temperature.
• The parameter of BOD5 estimates the organic content in water or wastewater
• Two-thirds of the BODL is usually exerted in the first 5 days of decomposition.
• Indicator of sewage pollution is if BOD5 values rise above 10 mg/L.
• Clean water surfaces usually have BOD5 or 1 mg/L.
• The BOD5 parameter serves as the amount of dissolved oxygen used by microbes in 5 d to decompose organic substances at 20°C.
  • It is due to naturally occurring organics from animal wastes and decaying leaves

BOD Tests

• Standard 300-mL glass BOD bottles perform BOD test
• The test measures the 5-day BOD value of a water sample
  • This tests by taking two measurements:
    • The first measurement is the initial
    • The second measurement is after a 5 day dark incubation at 20°C.
    • The BOD5 is the difference between the two DO measurements.
• A sample tested initially at 8.0 mg/L DO gets incubated in a BOD bottle for a 5 d at 20° C
  • The DO measures at 4.5 mg/L after the incubation.
  • The BOD is the amount of oxygen consumed (or the difference between the readings).
  • This makes BOD5 become equal to 3.5 mg/L.
• To measure the sewage, the sample needs to be first diluted in the BOD bottle.
• The dilution method done in computation of BOD5 in a 300-mL BOD bottle with the formula given
  • Where DO0 = initial DO at t = 0
  • DO5 = DO at t = 5 d
  • V = sample volume, mL
• Given a 6.0-mL sample of wastewater that diluted to 300 mL with distilled water:
  • The DO reading determines that initial DO is 8.5 ml/L and DO after 5 days at 20° is 5 mg/L.
  • The wastewater's BOD5 becomes 180 mg/L
    • BOD5 = [(8.5-5.0) x 300]/ 6.0 = 180mg/L
  • The BODL becomes 260 mg/L given a dilution rate constant k=0.1 mg/L

Nitrification

• Ultimate carbonaceous BOD is labelled as the ultimate BOD after 8 days from the BOD curve
• Bacteria primarily act on carbon substances during the first or so week of decomposition.
• As carbonaceous material is depleted, a different bacteria group proceeds - nitrifying bacteria which is the type of bacteria used in the process called Nitrification.
• Nitrification: ammonia becomes nitrite and nitrate (ionic nitrogen forms)