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An Alterna)ve Mathema)cal Model for Oxygen Transfer Evalua)on in Clean
Water
John He, PE, BCEE, Process Engineer – Kruger Inc.
NC AWWA-‐WEA Annual Conference, Nov. 18, 2014
Energy Consump)on for WWTP
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Aera)on process consumes more energy than other processes by far, so reducing energy consump)on during aera)on is usually the best ini)al step to minimize energy cost.
Goals To learn the theory to understand oxygen transfer and aera5on process in clean water
To evaluate the accuracy of the standard method for oxygen transfer efficiency test
To present an alterna5ve mathema5cal model including more parameters than standard method.
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Nomenclature OTR = Oxygen Transfer rate in clean water SOTR = Oxygen transfer rate in standard condi)on in clean water OTE = Oxygen transfer efficiency in clean water SOTE = Oxygen transfer efficiency in standard condi)ons in clean water KLa = Liquid-‐side mass transfer coefficient (Measured in clean water tests) α = Alpha factor, ra)o of process -‐ to clean water mass transfer = αSOTE/SOTE or = KLa in process water / KLa in clean water
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Standard condi+ons are defined as 20 °C, I atm, zero salinity, zero DO in water
Theory – Two Film Theory Oxygen transfer and transfer of other sparingly soluble gases can be modeled using the two film theory (Lewis and Whitman’s paper in 1924)
OTR = KLa*(DOSat-‐DO)*V Where: KLa = Liquid-‐side mass transfer coefficient (hr-‐1) DO = dissolved oxygen in water (kg O2/m3) DOSAT = dissolved oxygen in water at satura)on (kg O2/m3) V = Water Volume (m3) The OTR is the actual mass of oxygen transferred per unit )me and it is the key process variable for process design
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Oxygen Transfer Efficiency Oxygen transfer efficiency is defined as follows:
OTE = (O2,IN -‐ O2,OUT)/O2,IN
Where: O2,IN and O2,OUT are mass flow rates In order for manufacturers to provide equipment without bias for site specific condi)ons, it is common to report OTE at standard condi)ons. SOTE =SOTR/Oxygen In Standard Condi)on
SOTR = KLa*Ѳ(20-‐t)*Csat,20*V
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Standard Oxygen Transfer Procedure Step 1: Analyze DO measurement data to es5mate volumetric mass transfer coefficient
Step 2: Once KLɑ value at site condi5ons is determined by Eq. 2, the SOTR can be readily calculated by the following equa5on:
Step 3: Oxygen In from Blowers
ACFM (Measured) ICFM (Adiaba5c Eq.) SCFM (Universal Gas Law) Oxygen Mass Rate Step 4: SOTE = SOTR/Oxygen Mass rate x 100%
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)C-(C×αK=dtdC
t∞L
( )( ) ( )0t∞
0∞L t-t
1×
C-CC-C
In=αK
( ) V×C×θ×αK = SOTR 20 S,t-20
L
A Typical DO Concentra)on Curve
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0
2
4
6
8
10
12
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00
DO
(mg/
L)
Time (min)
Standard Model -‐ Assump5ons Water in the tank is completely mixed The overall oxygen transfer is only from air bubbles, oxygen transfer from water surface is not taken into considera5on Equilibrium DO concentra5ons are the same everywhere in the tank, the effect of SWD on DO satura5on concentra5on is not taken into considera5on The effect of tank geometry on KLa is also not taken into considera5on.
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Reality
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Water in the tank is not completely mixed – the degree of mixing depends on tank geometry and diffuser floor coverage Oxygen transfer from air phase is inevitable DO satura5on concentra5on varies with sta5c pressure
Modified Standard Model #1
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Oxygen transfer exists in two phases – water surface and gas bubble surface In order to describe two oxygen transfer in two phases, the following formula is proposed:
Where: KLɑs is volumetric mass transfer coefficient (T-‐1) at water surface CSC is the satura)on concentra)on at site temperature and atmospheric, which is equal to C∞
Ct is the dissolved oxygen at )me t.
( )tSCsLst∞L C-CαK+)C-(C×αK=dtdC
Modified Standard Model #1 -‐ 2
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Integra5on and re-‐arrangement of Eq. yields: Where: ξ= KLa × CSC + KLsas × CSC λ= -‐ KLa -‐ KLsas, C0 is DO concentra5on at 5me zero.
( )( ) ( ) λ=
00
t
t-t1
×C×λ+ξξ+λ×C
ln
Modified Standard Model #1 -‐ 3
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If the ini5al DO concentra5on is 0 mg/L at 5me zero, the above Eq. becomes:
When system is at the steady state condi5on, C(t) CSC, the above Eq. can be simplified as:
KLas can be measured in field and in lab and it can also be calculated. Note is ra5o of total water surface area (As) to total tank volume (V), KLs is air-‐water transfer coefficient
( )( ) λ
ξ=
0
t
t-t1
×ξ+λ×C
ln
( )0sLSL
sLS t-t=a K+aK
a K×2ln ×λ
Modified Standard Model #2
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This is a model that combines Standard Model and Modified Model #1
Where Zd is side water depth to aera5on system (L), Z is side water depth (L), Co* is dissolved equilibrium concentra5on (mg/L).
( ) ( )tSCsL*0
d
L C-CαK+)dzC-z(C×ZαK
=dtdC
Modified Standard Model #2 -‐ 2
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DO equilibrium concentra5on, Co* can be es5mated by following equa5on (McWhirter and Huper, 1989):
Where y = kmol O2/kmol N2 in gas phase PWV (atm) is water vapor pressure P (atm) is atmospheric pressure, 0.266 (kmol O2/kmol N2) at z = 0 when the bubbles released from the diffusers.
( ) [( )
]0.266y
P-110.33
Z-Z+P-P
×C=zCWV
dWV
SC*0 ×
Modified Standard Model #2 -‐ 3
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Integra5on of above Eq. yields:
In order to solve above Eq., Co* must be computed. Because y must be determined to be able to calculate C0* in Equa5on 8, and y is also depth dependent, it makes the computa5on of Eq. extremely complicated.
( ) ( )tSCsLt*0
0d
L C-CαK+)dzC-zCZαK
=dtdC ∫ s
Z
Modified Standard Model #2 -‐ 4
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Because at the steady state condi5on, C(t) CSC and , the above Eq. can be simplified as:
Re-‐arrangement of this Eq. gives:
0→dtdC
( ) 0=)dzC-z(CZαK
t*0
Z
0d
L ∫
( ) dt*0
Z
0L Z)dzC-z(CαK ∫ ×=
Field Oxygen Transfer Test
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DO Concentra5on Curve Over Time
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0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0
2
4
6
8
10
12
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00
DO
(mg/
L)
Time (min)
DO Probe #1 DO Probe #2 DO Probe #3 % of DO Saturation
% D
O S
atur
atio
n C
once
ntra
tion
Results Comparison
20 0
5
10
15
20
25
30
35
40
KLa
Liq
uid-
side
mas
s tra
nsfe
r co
effic
ient
(KL
a, h
r-1)
Methods
Standard Modified Standard #1 Modified Standard #2
Results Comparison -‐ 2
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0
200
400
600
800
1000
1200
KLa
SOT
R (l
b/hr
)
Methods
Standard Modified Standard #1 Modified Standard #2
Take-‐home messages
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Standard method oversimplified the oxygen transfer process by assuming surface oxygen transfer is negligible Standard method oversimplified the oxygen transfer process by assuming DO Equilibrium DO concentra5ons are independent of SWD In order to get comparable results, all inves5ga5ons must use the same method at the same condi5ons.
