Dr. Martin T. AuerMTU Department of

Civil & Environmental Engineering

Mass Balance, Kinetics & Reactors

Plug FlowReactor

Completely-MixedFlow Reactor

Reactor Analogs – Natural Systems

Mille Lacs LakeMinnesota

Fox RiverWisconsin

Reactor Analogs – Engineered Systems

Plug FlowReactor

Completely-MixedFlow Reactor

Resin-BasedWater Softener

WastewaterPrimary Clarifier

Soaking Rain

Dream Car

CMF Reactor

Control Volume

CMF Reactor

with first order decay

in

dCV Q C Q C V k Cdt

For many years, Allied Chemical and its ancestors produced soda ash … a chemical used to soften water and in the manufacture of glass, soap, and paper. The raw materials were two locally abundant minerals:

CaCO NaCl Na CO CaCl3 2 3 2

and the products were soda ash (Na2CO3) and calcium chloride (CaCl2) waste. The wastes were deposited in 2000 acres of lagoons along the banks of 9 Mile Creek. The waste continually leaks from the lagoons into the creek, making the water highly ‘salty’.

Chloride in 9 Mile Creek

Chloride in 9 Mile Creek

up up in inmb

up in

C Q C QC

Q Q

BATCH Reactor

with first order decay

in

dCV Q C Q C V k Cdt

dCk C

dt

BATCH Reactorwith first order decay

dCk C

dt

Distance or TimeTime (yr)

Co

nc

en

tra

tio

n 0k t

tC C e

Batch Reactor in Pipe

Batch Reactor in Pipe

Batch Reactor in Pipe

Batch Reactor in Pipe

Batch Reactor in Pipe

Batch Reactor in Pipe

Batch Reactor in Pipe

Batch Reactor in Pipe

Batch Reactor in Pipe

Batch Reactor in Pipe

Batch Reactor in Pipe

Batch Reactor in Pipe

PFR = Train of Batch Reactors

Distance or TimeTime (yr)

Co

nc

en

tra

tio

n

To Water Quality

CMF Reactor

in

dCV Q C Q C V k Cdt

ss in

QC C

Q V k

and, at steady state

Change in Cssco

ncen

trat

ion

time

Css,1

Css,2

C C et ss

k t FHG

IKJ

1

1

C C e C et ss

k t

ss

k t F

HGIKJ

FHG

IKJ

FHG

IKJ

1

1

2

1

1

C C et ss

k t F

HGIKJ

FHG

IKJ

2

1

1

Time-Variable Response

time

conc

entr

atio

n

Response Time

95%

ln 0.051

tk

Wastewater Treatment

Grit removal, 0.5 hr1°, 2° settling, 1-2 hrActivated sludge, 4-8 hr Anaerobic digestion, 15-30 d

95%

31

tk

Drinking Water Treatment

Rapid mix, <1 minFlocculator, 30 minDisinfection, 15 min

Rate Coefficients

‘fast’ k, 30 yr-1

‘slow’ k, 0.03 yr-1

Natural Systems

Onondaga Lake (0.25 yr)Lake Ontario (8 yr)Lake Michigan (136 yr)Lake Superior (179 yr)

SS CMFApplication to Lakes

· · ·dP

V W Q P V k Pdt

where W = Q∙Cin, i.e. the loading

· · ·dP

V W Q P V k Pdt

v Vk and A

H H

· · · ·dP

V W Q P v A Pdt

@ ,·

WSS P

Q v A

SS CMFApplication to Lakes

PF-CMF Comparison: Reactor Efficiency

PF-CMF Comparison: Sensitivity to Spikes

Mass Transport

CMF Reactor8 8

SaginawBay

LakeHuron

PF Reactor

Advection and Diffusion

advectionalone

diffusionalone

advectionplusdiffusion

Diffusion

PCBs

PCBs are a family of chemical compounds formed by the addition of chlorine to biphenyl (C12H10). There are 10 substitution positions where chlorine may be added, leading to a possible 209 unique chemical compounds termed congeners.

23

4

5 6

3’2’

4’

6’ 5’

ClnH(10-n)

Congeners have been assigned numbers (1209) and are also classified by the positions occupied by chlorine. Referencing the substitution positions in the figure above, three examples are:

Congener 1: 2-Chlorobiphenyl

Congener 101: 2,2’,4,5,5’-Pentachlorobiphenyl

Congener 209: Decachlorobiphenyl

Example 4.14 PCBs in Lake Superior

Dr. Perlinger’s research groupsampling on Lake Superior aboardthe U.S. EPA research vesselLake Guardian.

air

water