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Lecture 3 – Materials Balances

Lecture 3 – Materials Balances. Introduction to Environmental Engineering Lecture3 Dr. Jawad Al-rifai. The accounting of all mass in a chemical/Environmental process is referred to as a mass (or material) balance . ‘day to day’ operation of process for monitoring operating efficiency

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Lecture 3 – Materials Balances

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  1. Lecture 3 – Materials Balances Introduction to Environmental Engineering Lecture3 Dr. Jawad Al-rifai

  2. The accounting of all mass in a chemical/Environmental process is referred to as a mass (or material) balance. • ‘day to day’ operation of process for monitoring operating efficiency • Making calculations for design and development of a process i.e. quantities required, sizing equipment, number of items of equipment Paul Ashall, 2008

  3. Conservation of Mass – mass is neither created nor destroyed • Mass Flow – therefore mass flowing into a box will equal the flow coming out of a box • Black box – schematic representation X0 X1 0 1 M.B. with a Single Material

  4. One or more effluent • One or more Feed Source / influent X1 X1 X0 1 X0 0 X2 X2 2 [Accumulation]= [In]– [Out] +[Produced] – [Consumed] M.B. with a Splitting Single Material

  5. Steady state • The rate of input= rate of out put, mass rate of accumulation is Zero • Conservation: In many problems conservation is assumed • Material of concern is not consumed or produced • No chemical, biological or radioactive decay • Ex. Salt in Sewer & stream • M.B. equation • 0 = [In] – [Out] + 0 - 0 [In]= [Out] State of Mixing-Steady State

  6. 2. Reactions/ loss process dM/dt = [d(in)/dt – d(out)/dt]+ r r=-KVCn • K; reaction rate constant; S-1 or d-1 • C: Concentration of substances • n: reaction order • V: volume • - Indicate disappearance of substances The reaction rate is often complex function of T, P [Accumulation]= [In]– [Out] + [Produced] – [Consumed] State of Mixing- Reactions/ loss process

  7. General Rules for solving M.B. Problems • Draw the system as a diagram • Add the available information • Draw a dotted line around the component being balanced • Decide material to be balanced • Write the basic M.B. equation • If only one missing variable, solve • If more that one unknown, repeat the procedure Complex Processes with a Single Material

  8. A completely mixed lake receives two inflows: natural stream flow 0.1 m3/s, wastewater discharge 0.054 m3/s and has a constant volume of 2 x 106 m3. Given: • 1)the wastewater has 20 mg/L NH3-N • 2)stream has 1 mg/L NH3-N bacteria in the lake convert NH3 to NO3- by a process called nitrification. -rN = k*CN where k = a first-order rate constant = 0.03 day-1 and CN = concentration of ammonia-nitrogen mg/L FIND: lake and outflow NH3-N Assume steady-state, non-conservative mass balance: Ammonia is very toxic to fish, 1 mg/L NH4-N. Does the amount of natural nitrification in the lake allow wastewater discharge of 20 mg/L ammonia-N? Example

  9. QW*CNW + QN*CNN - QTCN - V*k*CN = 0 • where QW = wastewater flow, = 0.054 m3/s • CNW = wastewater ammonia-N = 20 mg/L • QN = stream flow = 0.1 m3/s • CNN =stream ammonia-N = 1 mg/L • QT = lake outflow = QW +QN = 0.154 m3/s • CN = lake and outflow ammonia-N = ? • V = lake volume = 2 x 106 m3 • t = 150 days Complex Processes with a Single Material

  10. find CN: by rearranging mass balance: QTCN + V*k*CN = QW*CNW + QN*CNN CN (QT + V*k) = QW*CNW + QN*CNN Divide everything by QT; CN (1 + V/ QT *k) = (QW*CNW + QN*CNN)/ QT CN =[ 1 / (1+ (V/QT)*k)]*[(QWCNW + QN*CNN)/QT]  CN = [ 1/(1+ (t)*k)]*[(QW*CNW + QN*CNN)/QT] CN = [1 /(l +(150d * 0.03d-1))]*[(0.054m3/s*20 mg/L + 0.1 m3/s*1 mg/l)/0.154m3/s] CN = 1.4 mg/L ammonia-nitrogen 1.4 mg/L ammonia-N > 1 mg/L standard. Complex Processes with a Single Material

  11. Aside:What is the detention time of water in the lake (Hydraulic Residence Time)? • Define detention time, t in the book: t = V/Q = volume/flow rate = time 2 x 106 m3/(0.1 m3/s + 0.054 m3/s)*(1 day/86,400 s) = 150 days Complex Processes with a Single Material

  12. Sequence of operations/steps repeated according to a cycle • Batch cycle time • Batch size Batch cycle Paul Ashall, 2008

  13. Recycle of unreacted material reactor Separation & purification product Fresh feed (reactants, solvents, reagents, catalysts etc) Typical simple flowsheet arrangement waste Byproducts/coproducts Paul Ashall, 2008

  14. wash water/solvent solid feed suspension Mass balance filtration/centrifuge filtrate waste water Paul Ashall, 2008

  15. 5000 kg DM water F1 Water 300 kg API 448 kg Impurity 5 kg Impurity 55 kg Water 2600 kg API 450 kg Filtration Water 7300 kg Impurity 50 kg API 2kg Paul Ashall, 2008

  16. water/evaporated solvent product feed Mass balance - drier Paul Ashall, 2008

  17. A + B A + B S + B S Mass balance – extraction/phase split A – feed solvent; B – solute; S – extracting solvent Paul Ashall, 2008

  18. feed raffinate E1 solvent extract Example (single stage extraction; immiscible solvents) Paul Ashall, 2008

  19. exit gas stream feed solvent feed gas stream Mass balance – absorption unit waste solvent stream Paul Ashall, 2008

  20. E – evaporator; C – crystalliser; F – filter unit F1 – fresh feed; W2 – evaporated water; P3 – solid product; R4 – recycle of saturated solution from filter unit W2 R4 E C F F1 P3 Multiple units Paul Ashall, 2008

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