BOD Modeling "L" is modelled as a simple 1st order decay: - PDF document

CEE 577 Lecture #13 10/23/2017 Updated: 23 October 2017 Print version Lecture #13 BOD and Deoxygenation (Chapra, L20) Dave Reckhow (UMass) CEE 577 #13 1 BOD Modeling "L" is modelled as a simple 1st order decay: dL   k L 1 dt Which leads to:  1  k t L L e o    And combining with: BOD y L L t t o t     ( 1 ) We get: k t BOD y L e 1 t t o Dave Reckhow (UMass) CEE 577 #13 2 1

CEE 577 Lecture #13 10/23/2017 Temperature Effects Temperature Dependence  Chemist's Approach: Arrhenius Equation (ln )  d k E a 2 dT RT a a   ( 293 )/ 293 E T RT k k e a a a o T 293 K a  Engineer's Approach: Often we use:  =1.047    20 o T C k k for CBOD T 20 o C Dave Reckhow (UMass) CEE 577 #13 3 NBOD Nitrogeneous BOD (NBOD)          Nitrosomonas 15 . NH O NO H O H 3 2 2 2 1        Nitrobacter NO O NO 2 2 3 2 2 moles oxygen/1 mole of ammonia 4.57 grams oxygen/gram ammonia-nitrogen Like CBOD, the NBOD can be modelled as a simple 1st order decay: N dL   N k L N dt Dave Reckhow (UMass) CEE 577 #13 4 2

CEE 577 Lecture #13 10/23/2017 NBOD cont.  The model is then:      1 N k t NBOD L e N t o  where:        N 4 . 57 L NBOD org N NH N  Nitrifiers 3 o u  very slow generation time (~1 day)  sensitive to low D.O.  NBOD may be very important for non ‐ nitrified, but otherwise highly treated waters Dave Reckhow (UMass) CEE 577 #13 5 Typical Municipal WW Charact. Typical Wastewater U.S. EPA Discharge Typical Characteristics, mg/L Standards, mg/L Concentrations in Parameter except pH except pH Lakes or Streams, mg/L except pH BOD 5 150-300 30 2-10 Total Suspended Solids 150-300 30 2-20 COD 400-600 N/A 5-50 D.O. 0 4-5 4-Sat. NH 3 -N 15-40 * <1 NO_ 3 0 * <1 pH 6-8 6-9 6-8 Dave Reckhow (UMass) CEE 577 #13 6 3

CEE 577 Lecture #13 10/23/2017 BOD Model   L L    U k L   r t x   k k k Settling rate r d s  v s Decomposition rate in the stream H  L t  0   k xU  L L e r o Dave Reckhow (UMass) CEE 577 #13 7 Estimating the k’s 1.4 1.2 k s +k d k d 1 0.8 Deep Stream Ln L Shallow Stream 0.6 0.4 0.2 0 0 2 4 6   1047 . t* = x/U Where: C=0.2 for unstable bottoms  0 434 .   C H      C=0.3 for rocky bottoms , 0 8 k H ft   d 8   , 8 k C H ft d Dave Reckhow (UMass) CEE 577 #13 8 4

CEE 577 Lecture #13 10/23/2017 Typical DO Sag Curve 12 Saturation D.O. 10 Critical D.O. (mg/L) 8 Recovery Zone Distance 6 Critical Concentration 4 2 Decomposition Reaeration Dominates Dominates 0 -2 0 2 4 6 8 Distance Downstream (miles) Dave Reckhow (UMass) CEE 577 #13 9 Updated: 23 October 2017 Print version Lecture #22 (Distributed Systems, time variable. Dye Studies) Chapra, L10 5

CEE 577 Lecture #13 10/23/2017 Plug Flow (time variable)  Simulating accidental spill, tracer studies   c c    U kc   t x  when a spill causes a concentration of c o at x=0 and t=0 *   kt c c e Where: t * =x/U o Refer to Example 10.1 David Reckhow CEE 577 #22 11 Moving vs. Fixed frame of reference x1 x2 x3 t=0 t=1 t=2 David Reckhow CEE 577 #22 12 6

CEE 577 Lecture #13 10/23/2017 The random walk: a normal distribution 0.018 0.016 0.014 Relative Frequency 0.012 0.010 0.008 0.006 0.004 0.002 0.000 u-3s u-2s u-s u u+s u+2s u+3s 68.3% 95.4% 99.7% David Reckhow CEE 577 #22 13 Spill Models m A c  Dispersion and advection   2  m x Ut  Equ# 10.24 ( , )  p 4 c x t Et e Et  in Chapra 2  a normal distribution with:  x Ut   2 Et David Reckhow CEE 577 #22 14 7

CEE 577 Lecture #13 10/23/2017 Recall from our discussion on Longitudinal Dispersion (~Lecture #9)  From Fischer et al., 1979 m/s m 2 s -1 Width (m) 2 2 U B  0 011 . E * HU Mean depth (m) Where the Shear Velocity is: *  U gHS David Reckhow CEE 577 #22 15 Over length, at a single time Empirical Method   2 Over time, E t l x at a specific  2 2  2 location U   l t E x 2 2  From Dye Study data t t   2 2 U  t  Method of moments  2 t    2 2 2 U  td tu E  x 2 t t d u   2 = variance of the concentration ‐ time curve t 0 . 01   t ‐ bar = time of travel to the centroid of the curve stdt   The first moment about the origin gives: 0 t t 0 . 01  where t 0.01 is the time at which concentration has  sdt decreases to 1% of the peak 0 David Reckhow CEE 577 #22 16 8

CEE 577 Lecture #13 10/23/2017 Empirical Method (cont.)  And the 2nd moment about the centroid gives: t 0 . 01  2 st dt    2 2 0 ( ) t t 0 . 01  sdt 0  For discrete data these become:       2   2   st t st st t st 2 2        2 t t t       s t s s t s Compare to T&M equ 10.32 Compare to T&M equ 10.33 David Reckhow CEE 577 #22 17 Dye Studies (cont.)  Single point method  Use of peak concentration (c p ) and time to reach peak (t p )   M   0 . 5 c t p  p 2 A E x  plot c p vs (t p ) ‐ 0.5 to get a slope that is a function of E x  see sample problem 2.6 in T&M (pg. 78) David Reckhow CEE 577 #22 18 9

CEE 577 Lecture #13 10/23/2017 Homework #4  Velocity  dispersion coefficient David Reckhow CEE 577 #22 19 USGS Guidelines: Input  The USGS recommends the following volume or mass of Rhodamine WT ‐ 20% dye: cfs Miles downstream Peak 0 . 93   Q x   4   3 . 4 10 m concentration V x S dye   p U desired at distance “x” Liters ft/sec  2 . 62 W V dye dye lb David Reckhow CEE 577 #22 20 10

CEE 577 Lecture #13 10/23/2017 USGS Guidelines: Sampling  Duration of dye cloud as a function of travel time to peak, and average channel width ‐ depth ratio (B/H). David Reckhow CEE 577 #22 21  To next lecture Dave Reckhow (UMass) CEE 577 #13 22 11