Print version Updated: 26 November 2019 CEE 370 Environmental Engineering Principles Lecture #32 Wastewater Treatment III: Process Modeling & Residuals Reading M&Z: Chapter 9 Reading: Davis & Cornwall, Chapt 6-1 to 6-8 Reading: Davis & Masten, Chapter 11-11 to 11-12 David Reckhow CEE 370 L#32 1
Microbial Biomass in a CMFR General Reactor n n dm ∑ ∑ − − A (C Q ) (C Q ) mass balance dt = r V Ai Aj A in out i j i=1 j=1 But with CMFRs we have a single outlet concentration (C A ) and usually a single inlet flow as well C A C A Q 0 C A0 Q 0 V 2 CEE 370 L#32 David Reckhow
Batch Microbial Growth 0 0 General Reactor n n dM ∑ ∑ A − (C Q ) (C Q ) mass balance = - r V Ai Aj A i in j out dt i=1 j=1 Batch reactors are usually filled, allowed to react, then emptied for the next batch Because there isn’t any flow in a batch reactor: 1 dM C A A = - r A V dt For 1 st order V X kX biomass And: growth dC A dt = - r A 3 CEE 370 L#32 David Reckhow
Batch Microbial Growth Observed behavior Stationary Death Covered in lecture #17 Lag Exponential Growth Time 4 CEE 370 L#32 David Reckhow
Exponential Growth model Covered in lecture #17 dX ≡ µ X dt gr D&M Text where, N X = concentration of microorganisms at time t t t = time µ = proportionality constant or specific r growth rate, [time ─ 1 ] dN/dt dX/dt = microbial growth rate, [mass per volume-time] 5 CEE 370 L#32 David Reckhow
Exp. Growth (cont.) Covered in lecture #17 dX dX ≡ µ X ≡ µ dt or dt X gr gr X µ ln = t X o µ t X = X e o 6 CEE 370 L#32 David Reckhow
Substrate-limited Growth Also known as resource-limited growth THE MONOD MODEL S dX SX µ = µ ≡ µ = µ and X max S + max K S + dt K S gr S where, µ max = maximum specific growth rate, [day -1 ] S = concentration of limiting substrate, [mg/L] K s = Monod or half-velocity constant, or half saturation coefficient, [mg/L] 7 CEE 370 L#32 David Reckhow
Monod Kinetics Covered in lecture #17 0.5*µ m K S 8 CEE 370 L#32 David Reckhow
Substrate Utilization & Yield Related to growth by Y, the yield coefficient Mass of cells produced H&H, Fig 11-38, pp.406 per mass of substrate utilized dX ∆ X dt ≡ = Y dS ∆ S dt Just pertains to cell growth dX dS = Y dt dt gr 9 CEE 370 L#32 David Reckhow
Microbial Growth dX dS = Y dt dt gr Monod kinetics in a chemostat (batch reactor) Substitute for dS µ dS XS dX SX = ≡ µ = µ X max max S + + dt K S dt Y K S gr S & Divide by Y XS Where = e r k su + K S dS/dt = r su = actual substrate utilization rate S e k = maximum substrate utilization rate = μ max /Y S = concentration of substrate (S e in H&H) K S = half-saturation constant Y = cell yield = dX/dS 10 CEE 370 L#32 David Reckhow
Death Bacterial cells also die at a characteristic first order rate with a rate constant, k dX = − k X d dt d This occurs at all times, and is independent of the substrate concentration 11 CEE 370 L#32 David Reckhow
Overall model: chemostat Combining growth and death, we have: dX dX dX = + dt dt dt net gr d SX = µ − k X See: M&Z equ 9.3 max d + K S S And in terms of substrate utilization dX dS ≡ ÷ Y dt dt gr dX dS = − Y k X d dt dt net 12 CEE 370 L#32 David Reckhow
Activated Sludge Flow Schematic Conventional X o Q+ Q r Q X X e Effluent S o Aeration S S Basin Settling Influent Tank V,X Q r X r Return activated sludge 13 Q w X r S Waste activated sludge CEE 370 L#32 David Reckhow
Efficiency & HRT Efficiency of BOD removal ( ) − S S 100 % = E o S o Hydraulic Retention Time, HRT (Aeration Time) Same as retention time in DWT (t R ) V θ = Actual HRT is a bit different Q Isn’t used as much in design V θ = act + Q Q R 14 CEE 370 L#32 David Reckhow
SRT – solids retention time & R SRT: Primary operation and design parameter How long does biomass stay in system XV XV θ = ≈ ( ) See: M&Z equ 9.10 c − + Q Q X Q X Q X w e w r w r Typically equals 5-15 days Q Recycle Ratio = r R Q Values of 0.25-1.0 are typical 15 CEE 370 L#32 David Reckhow
F:M Ratio and volumetric loading Food-to-Microorganism Ratio (F/M) ∗ F Q BOD = ∗ M V X F QS = o M&Z equ 9.16 M XV Typical values are 0.2-0.6 in complete mixed AS BOD volumetric Loading QS = o Loading V Typically 50-120 lb BOD/day/1000ft 3 tank volume 16 CEE 370 L#32 David Reckhow
Act. Sludge: Biomass Model dX dX dX = + Steady State mass balance on biomass dt dt dt net gr d dX dX SX = 0 = − − + = µ − V QX Q X Q X V k X max d + o e e w r K S dt dt S batch From chemostat model Incorporating the chemostat model gets: dX SX = = − − + µ − V 0 QX Q X Q X V k X o e e w r max d + dt K S S And simplifying SX − + + = µ − QX Q X Q X V k X o e e w r max d + K S S Finally, we recognize that the amount of solids entering with the WW (i.e., X o ) and leaving in the treated effluent (i.e., X e ) is quite small and can be neglected 17 CEE 370 L#32 David Reckhow
Biomass Model II So it becomes SX = µ − Q X V k X w r max d + K S S And rearranging Q X S 1 = µ − ≈ w r k θ max d + VX K S c S Earlier equation for SRT XV XV θ = ≈ ( ) c − + Q Q X Q X Q X w e w r w r 18 CEE 370 L#32 David Reckhow
Act. Sludge: Substrate Model Steady state mass balance on substrate µ dS XS = max S + dt Y K S dS dS = 0 = − − + V QS Q S Q S V o e w From chemostat model dt dt batch Substituting and noting that Q e =Q-Q w µ XS = − + − QS QS Q S Q S V max o w w + Y K S S And further simplifying µ XS ( ) − = Q S S V max o + Y K S S 19 CEE 370 L#32 David Reckhow
Merging the biomass & substrate models If we divide the previous equation by V and X ( ) − µ µ Q S S S XS ( ) − = = Q S S V max o max o + Y K S + VX Y K S S S Multiply both sides by Y ( ) − YQ S S S = µ o M&Z equ 9.8 max + VX K S S Now insert the LH term into the 1 Q X S = = µ − w r k earlier equation based on biomass max d θ + VX K S c S ( ) − 1 Q X YQ S S = = − w r o k M&Z equ 9.9 d θ VX VX c 20 CEE 370 L#32 David Reckhow
Combined model II Now recognize that Q/V is the reciprocal of the HRT ( ) − 1 1 Y S S = θ − o k d θ X c 21 CEE 370 L#32 David Reckhow
Question All else being equal, as SRT goes up: Settleability goes down 1. F/M goes down 2. Waste sludge return ratio must go down 3. Endogenous respiration becomes less 4. important Sludge yield increases 5. 22 CEE 370 L#32 David Reckhow
Aeration: Loadings Food-to-Microorganism Where Q=WW flow Ratio (F/M) V=volume of aeration tank X=MLVSS=mixed liquor ∗ F Q BOD = volatile suspended solids ∗ M V X (biomass concentration) X e =VSS e = suspended solids in Sludge Age or mean cell wastewater effluent residence time ( ɵ c ) X W =VSS w = suspended solids in waste sludge Q w = flow of waste sludge VX θ = SS is sometimes used instead ( ) ( ) c + X Q X Q of VSS e e W W VX ≈ X Q W W 23 CEE 370 L#32 David Reckhow
Operating Criteria Loading, biomass, retention time, etc H&H, Table11-4, pp.395 24 CEE 370 L#32 David Reckhow
Activated Sludge Mixed liquor Return Activated sludge 1. Surface aerators 2. Bubble diffusers 25 CEE 370 L#32 David Reckhow
Updated: 26 November 2019 CEE 370 Environmental Engineering Principles Lecture #32b Wastewater Treatment IIIb: Process Modeling & Residuals Reading: M&Z Chapter 9.11 Other Reading: Davis & Cornwall, Chapt 6-1 to 6-8 and Davis & Masten, Chapter 11-11 to 11-12 David Reckhow CEE 370 L#32 26
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