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

2. 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

3. Modeling and Environmental Engineering …the environmental engineering equivalent of building a bridge to nowhere. (Thomann and Mueller 1987, p. ix) http://www.zen39641.zen.co.uk/ps/

4. …the environmental engineering equivalent of building a bridge that falls down. (Thomann and Mueller 1987, p. ix) http://www.jansenkiener.com/Bridge%20Engineering.htm Modeling and Environmental Engineering

5. …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

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

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

8. Soaking Rain

9. Dream Car

10. CMF Reactor

11. Control Volume

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

13. First Order Kinetics Radioisotope Decay k = 0.036 yr -1 t 0.5 = 19.25 yr lnC t = -k∙t + lnC 0

14. Temperature and Kinetics Theta Function

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

16. CMF Reactor with first order decay

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

18. 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

20. BATCH Reactor with first order decay

21. BATCH Reactor with first order decay

22. Batch Reactor in Pipe

34. PFR = Train of Batch Reactors To Water Quality

35. CMF Reactor and, at steady state

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

37. 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  1 1 2 1 1   CCe t kt  F H G I K J  F H G I K J  2 1 1  Time-Variable Response time concentration

38. Response Time Wastewater Treatment Grit removal, 0.5 hr 1°, 2° settling, 1-2 hr Activated sludge, 4-8 hr Anaerobic digestion, 15-30 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)

39. SS CMF Application to Lakes where W = Q∙Cin, i.e. the loading

40. SS CMF Application to Lakes

41. PF-CMF Comparison: Reactor Efficiency

42. PF-CMF Comparison: Sensitivity to Spikes

43. Mass Transport CMF Reactor Saginaw Bay Lake Huron PF Reactor

44. Advection and Diffusion advection alone diffusion alone advection plus diffusion

45. Diffusion

46. 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 3 4 56 3’ 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

47. 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