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Lecture 6 – Materials Balances

Lecture 6 – Materials Balances. Introduction to Environmental Engineering February 8, 2000. M.B. with a Single Material. 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

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Lecture 6 – Materials Balances

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  1. Lecture 6 – Materials Balances Introduction to Environmental Engineering February 8, 2000

  2. M.B. with a Single Material • 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 • Although there can be a transformation • We are assuming Steady-State conditions

  3. M.B. with a Single Material • [X0]=[X1] X0 X1 0 1

  4. M.B. with a Splitting Single Material • One Feed Source Separated into Two or more • [X0]=[X1] + [X2] + [X3] + …..+ [Xn] X1 X0 1 0 X2 2

  5. Combining Single Material Flow • A black box can receive numerous inputs and have one effluent X1 X0 X2

  6. Complex Processes with a Single Material • Previous Examples were simple • A True M.B. Consists of • [Accumulation] = [In] – [Out] + [Produced] – [Consumed] • Placed in either terms of Mass or Volume • Or either can be simplified to a rate

  7. Complex Processes with a Single Material • Many systems do not change with time • Therefore there is no accumulation • The M.B. is at steady-state under these conditions • 0 = [In] – [Out] + [Produced] – [Consumed]

  8. Complex Processes with a Single Material • In many problems conservation is assumed • Material of concern is not consumed or produced • M.B. becomes • 0 = [In] – [Out] + 0 - 0

  9. Complex Processes with a Single Material • 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

  10. Complex Processes with a Single Material 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 Wastewater Lake Outflow Stream Flow

  11. Complex Processes with a Single Material 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 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? steady-state, non-conservative mass balance:

  12. Complex Processes with a Single Material • 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

  13. Complex Processes with a Single Material 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.

  14. Complex Processes with a Single Material 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

  15. Homework #3 • Chapter 3: 1, 3, 5, 7, 11, 17 • Due Tuesday, February 15, 1999

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