Dr. Martin T. Auer MTU Department of Civil & Environmental Engineering Mass Balance, Kinetics & Reactors

Some concepts and definitions Sustainability In our every deliberation we must consider the impact of our decisions on the next seven generations. Iroquois Confederacy We seek to meet the needs of the present without compromising the ability of future generations to meet their own needs. World Commission on Environment and Development, 1987 Modeling: an alternative to build and measure, providing a more rational basis for making water quality control decisions, such a basis to include a defensible, credible, predictive framework, within the larger framework of cost-benefit analysis. Definition: a mathematical model is an idealized formulation that represents the response of a physical system to external stimuli. Chapra 1997, p. 10

Modeling and Environmental Engineering …the environmental engineering equivalent of building a bridge to nowhere. (Thomann and Mueller 1987, p. ix)

…the environmental engineering equivalent of building a bridge that falls down. (Thomann and Mueller 1987, p. ix) Modeling and Environmental Engineering

…the question is not will a system will respond, but rather when and to what extent. (Cooke et al. 1999) and, as engineers, we might add ‘ at what cost ’ ? Modeling and Environmental Engineering

Plug Flow Reactor Completely-Mixed Flow Reactor Reactor Analogs – Natural Systems Mille Lacs Lake Minnesota Fox River Wisconsin

Reactor Analogs – Engineered Systems Plug Flow Reactor Completely-Mixed Flow Reactor Resin-Based Water Softener Wastewater Primary Clarifier

Soaking Rain

Dream Car

CMF Reactor

Control Volume

Zero Order Kinetics Oxygen in Dollar Bay Zero Order k = 0.13 mg∙L -1 ∙d -1 C t = -k∙t + C 0

First Order Kinetics Radioisotope Decay k = yr -1 t 0.5 = yr lnC t = -k∙t + lnC 0

Temperature and Kinetics Theta Function

Temperature and Kinetics WWTP Nitrification Effluent Ammonia Load (MT∙d -1 ) J F M A M J J A S O N D

CMF Reactor with first order decay

Sonora River at Arizpe, Mexico Image courtesy of Agustin Robles Morua

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: CaCONaClNaCOCaCl 3232  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

BATCH Reactor with first order decay

BATCH Reactor with first order decay

Batch Reactor in Pipe

PFR = Train of Batch Reactors To Water Quality

CMF Reactor and, at steady state

Change in C ss concentration time C ss,1 C ss,2

CCe tss kt    F H G I K J  1 1  CCeCe t kt kt  F H G I K J   F H G I K J   F H G I K J    CCe t kt  F H G I K J  F H G I K J   Time-Variable Response time concentration

Response Time Wastewater Treatment Grit removal, 0.5 hr 1°, 2° settling, 1-2 hr Activated sludge, 4-8 hr Anaerobic digestion, d Drinking Water Treatment Rapid mix, <1 min Flocculator, 30 min Disinfection, 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 CMF Application to Lakes where W = Q∙Cin, i.e. the loading

SS CMF Application to Lakes

PF-CMF Comparison: Reactor Efficiency

PF-CMF Comparison: Sensitivity to Spikes

Mass Transport CMF Reactor Saginaw Bay Lake Huron PF Reactor

Advection and Diffusion advection alone diffusion alone advection plus diffusion

Diffusion

PCBs PCBs are a family of chemical compounds formed by the addition of chlorine to biphenyl (C 12 H 10 ). There are 10 substitution positions where chlorine may be added, leading to a possible 209 unique chemical compounds termed congeners ’ 2’ 4’ 6’5’ Cl n H (10-n) Congeners have been assigned numbers (1  209) 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 group sampling on Lake Superior aboard the U.S. EPA research vessel Lake Guardian. air water