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Environment Engineering I

AnNajah National University Civil Engineering Department. Environment Engineering I. Chapter Three. Materials Balance. Dr. Amal Hudhud Dr. Abdel Fattah Hasan. Introduction. Materials and Energy Balance:

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Environment Engineering I

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  1. AnNajah National University Civil Engineering Department Environment Engineering I Chapter Three Materials Balance Dr. Amal Hudhud Dr. Abdel Fattah Hasan

  2. Introduction Materials and Energy Balance: • A key tool in achieving a quantitative understanding of the behavior of Environmental Systems. • Accounts for the flow of energy and material into and out of Environmental Systems. • Models Production, transport, and fate of Pollutants and Energy in the Environment.

  3. Conservation of Matter • Matter (without nuclear reaction) can neither be created nor destroyed • Its Mathematical form is called: Materials Balance or Mass Balance • For an environmental system: Accumulation = Input – Output Env. System: River, Pond, Pollution Control Device...etc.

  4. Conservation of Energy • Energy (without nuclear reaction) can neither be created nor destroyed • Its Mathematical form is called: Energy Balance

  5. Control Volume (CV) • CV: boundaries to the system as imaginary blocks around the process or part of the process so the calculations are made as simple as possible. CV River in Output Input LAKE Accumulation River out

  6. Useful Relations • Density (ρ) [M/L3] = Mass [M]/Volume [L3] • Mass (M) = Density (ρ) x Volume (V) • Mass Flow Rate [M/T] = ρ[M/L3] x Q [L3/T] • Concentration of Component A (CA) [M/L3] = Mass of A [M]/Volume [L3] • Mass Flow Rate of Component A [M/T]= CA [M/L3] x Q [L3/T]

  7. Mass Balance In Min [M/T] Qin [L3/T] CAin [M/L3] Out Mout [M/T] Qout [L3/T] CAout [M/L3] Accumulation = Input – Output Output Input Accumulation dM/dt

  8. Mass Balance When No Accumulation in the System ( dM/dt = 0) : Steady State Conditions:

  9. Mass Balance for Component A In Min [M/T] Qin [L3/T] CAin [M/L3] Out Mout [M/T] Qout [L3/T] CAout [M/L3] Accumulation = Input – Output Output Input Accumulation dM/dt

  10. Mass Balance for Component A For Steady State Conditions:

  11. Efficiency In Min [M/T] Qin [L3/T] CAin [M/L3] Out Mout [M/T] Qout [L3/T] CAout [M/L3] When Qin = Qout Output Input Accumulation dM/dt

  12. State of Mixing • Two Extreme cases (Models): • 1. No Mixing 2.Complete Mixing Continuous Stirred Tank Reactor (CSTR) OR Continuous Mixed Flow Reactor (CMFR) Plug Flow Reactor (PFR) C inside reactor = Cout

  13. Including Reactions • Conserved Substances: Substances do not undergo chemical, biological or radioactive transformations. • In case of transformations, Mass Balance will become: • Accumulation Rate = Input Rate – Output Rate ± Transformation Rate

  14. Kinetics • r: Rate of Transformation or Reaction Rate • r is used to describe the rate of formation or disappearance of a substance or chemical species. • These time dependent reactions are called: Kinetic Reactions.

  15. So, r = - k Cn • k: reaction rate constant • C: concentration of substance • n: exponent or reaction order • For first order reactions: The rate of loss of the substance is proportional to the amount of substance present at any given time t. • So, r = - K C = dC/dt (units of k; s-1 or d-1)

  16. By Integration: • Co: Initial Concentration • Rearranging:

  17. Mass Balance for CSTR • For completely CSTR (CMFR), with 1st order reaction, Mass Balance for Environmental Systems will be rewritten as: • For steady state conditions (dCA/dt = 0 and Qin = Qout): • Define Q as residence time in the CSTR = V/Q

  18. Mass Balance for PFR • For PFR, No mix with fluid ahead or behind • Taking a CV for a differential element of the fluid….. • Mass Balance: • For 1st order reactions:

  19. Define Q as residence time in PFR = V/Q • Integration of the above equation: Also, u: sped of flow, L: system length, A: x-sectional area of PFR

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