CE5504 – Surface Water Quality Modeling CE5504 Surface Water Quality Modeling Lab 1. Modeling 101.

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CE5504 – Surface Water Quality Modeling CE5504 Surface Water Quality Modeling Lab 1. Modeling 101

discovery application fate and transport decision support integration Surface Water Quality Engineering

Reactor Analogs CE5504 – Surface Water Quality Modeling Plug Flow Reactor (rivers) Completely-Mixed Flow Reactor (lakes, bays, nearshore) Mille Lacs Lake, Minnesota Fox River, Wisconsin

The Reactor Analog for Lakes CE5504 – Surface Water Quality Modeling Completely Mixed Flow Reactor CMFR

The Mass Balance CE5504 – Surface Water Quality Modeling CMF Reactor Characteristics completely mixed (C out = C) constant volume (Q in = Q out )

The Mass Balance CE5504 – Surface Water Quality Modeling Control Volume the system about which the mass balance will be computed.

The Mass Balance CE5504 – Surface Water Quality Modeling Kinetics growth decay RXN

The Mass Balance CE5504 – Surface Water Quality Modeling Kinetics 0 order reactions rate is not a function of concentration C t = C 0 - k∙t k, mg·L -1 ·d -1

The Mass Balance CE5504 – Surface Water Quality Modeling Kinetics 1 st order reactions rate is a function of concentration lnC t = -k∙t + lnC 0 or C t = C 0 ·e -k·t k, d -1

Writing the Mass Balance CE5504 – Surface Water Quality Modeling RXN 1 st order decay

At Steady State CE5504 – Surface Water Quality Modeling RXN 1 st order decay 0 At steady state, the source terms are equal to the sink terms and there is no net change in mass within the control volume.

Time Variable (analytical solution) CE5504 – Surface Water Quality Modeling flushing out building in

Time to Steady State Variable CE5504 – Surface Water Quality Modeling Noting that the hydraulic retention time,  = V/Q and (Chapra, Sec. 3.3) or, for 95% or

Variability in  and k CE5504 – Surface Water Quality Modeling Lake  (years) Superior179 Michigan136 Ontario 8 Onondaga 0.25 Materialk (yr -1 ) Organic C36.5 Atrazine1.0 PCB0.05 Chloride 0

Review CE5504 – Surface Water Quality Modeling 1.Can you see any limitations to the analogs in Slide 3? 2.Can you identify 2 additional source terms for lakes in Slide 4? 3.Discuss the completely mixed and constant volume assumptions in Slide 5. 4.Develop an example of an inappropriately-defined control volume in Slide 6. 5.Provide some additional examples of growth and decay in Slide 7. 6.Show how a system acts to bring itself to steady state; see Slide In lab - a.Determine half-lives of selected chemical species. b.Compare response times of lake/chemical couplets. c.Calculation of steady state concentrations. d.Time variable solutions: kinetics and step function response.