Environmental Science and Engineering Toolbox

Transcription

1 Environmental Science and Engineering Toolbox 1. Material balances 2. Energy balances 3. Equilibrium relations 4. Rate equations Reactions Mixing and transport Growth 5. Design for pollution control and prevention 6. Statisticsti ti 7. Risk assessment 8. Policy, law, and ethics Media Air Water Ground Introduction to Mass and Energy Balances Mass and energy are conserved. They cannot be created or destroyed. This allows us to track materials and energy in the environment. Pollutants and energy must go somewhere. An individual chemical species may react and take a different form. For example, elemental mercury may react to form monomethylmercury (HgCH 3 ) but the amount of the element Hg does not change in that chemical process. 1

2 Units of Measurement The large and the small common prefixes Quantity Prefix Symbol 10-9 nano n 10-6 micro 10-3 milli m 10-2 centi c 10 3 kilo k 10 6 mega M 10 9 giga G tera T Units - Concentrations in Liquids (Water) Usually mass of substance per unit volume of mixture: mg or g per liter (L) of mixture or per cubic meter (m 3 ). Alternatively, mass of substance per mass of mixture: parts per million (ppm by weight) or parts per billion (ppb by wt.). For dilute solutions in water, 1 mg/l = 1 g/m 3 = 1 ppm (by wt.) 1 g/l = 1 mg/m 3 = 1 ppb (by wt.). Examples: 1 ppm is about the same as one drop added to 15 gallons. 1 ppb is about the same as one drop in a large backyard swimming pool (70 m 3 ). 2

3 Units - Concentrations in Solids (Coal) Usually mass of substance per mass of mixture: g/g or ng/g or parts per million (ppm by weight) or parts per billion (ppb by wt.). Sample Elkhor/Hazard Pittsburgh Illinois 6 Wyodak Wyodak Ohio 5,6,7 ND Lignite Description low S bit med S bit high S bit PRB PRB high S bit lignite ANALYSIS (As Received): Carbon Hydrogen Oxygen Nitrogen Sulfur Ash Moisture Total Hg, ug/g Cl, ug/g ** Br, ug/g Cl/Br **Not measured Coal analyses taken from DOE Toxics program Units - Concentrations in Gases (Air) Usually in volumetric terms: volume of gaseous pollutant x 10 6 volume of mixture volume of gaseous pollutant x 10 9 volume of mixture volume of gaseous pollutant x volume of mixture ppm (by volume) = ppmv ppb (by volume) = ppbv ppt (by volume) = pptv Frequently in mass per unit volume: g/m 3 or mg/m 3 or ng/m 3. The relationship between volumetric and mass per volume depends on pressure, temperature, and the molecular weight of the pollutant. The ideal gas equation establishes that relationship. 3

4 Units - Concentrations in Gases (Air) The Ideal Gas Equation m PV nrt or PV RT M n = number of moles of gas, kmol T = absolute temperature, K P = absolute pressure, kpa R = universal gas constant = kj/(kmol K) = (kpa m 3 )/(kmol K) V = volume, m 3 M = molecular or atomic weight of gas, kg/kmol m = mass of gas, kg, where m = nm Units - Concentrations in Gases (Air) Example. The ambient concentration of elemental mercury in the atmosphere of the Northern Hemisphere is about 0.4 pptv. Calculate the concentration as ng/m 3 at temperature 300 K and pressure 1 atm. mpol RT Vpol npolrt / P Vpol Mpol P mpol RT ppt V V V V V M P mix mix mix mix mix pol kg m pptm P kPa kmol kg x10 V RT m K kmol K pol pol mix RT kpam 12 1 kg = 10 ng and our final concentration is 3 m 3 ng 4

5 Mercury in the Atmosphere Observed atmospheric total gaseous mercury (TGM) concentrations over the Atlantic Ocean in 1994 [Slemr, 1996] (left panel) and 1996 [Temme etal., 2003] (right panel) are shown in black circles. The error bars represent the standard deviation of the observations within a grid box. Simulations are shown by solid lines. Source: Sarah A. Strode, et al., Department of Atmospheric Sciences, University of Washington, Seattle, Washington, USA (2006). Material Balances Universal Balance Equation for Any Extensive Property Accumulation = transport + generation Integrated form: final initial amount amount amount amount amount amount entering leaving generated consumed Rate form: rate of rate of rate of rate of rate of change transport in transport out generation consumption $ entering Checking account $ leaving with some rate of interest 5

6 Material Balances rate of change rate at which rate at which of mass of water water enters water leaves in lake lake lake Mass entering Great Salt Lake Mass leaving At steady state, rate of change of mass of water = 0 in lake This is a poor assumption for the Great Salt Lake. Steady State Material Balances Number of students at U: 29,012 (stock = M) Rate of graduation: 6,997 per year (flow = F) rate of change rate at which rate at which 0 of enrollment students enter students leave F = students entering, yr -1 M = number of students attending F = students leaving, yr -1 mean residence stock M 29,000 students = = = = 4.1 yr -1 time of flow F 7,000 students yr students This equation holds only if the system is well mixed. 6

7 Steady Material Balances (Global Hg Cycle) Flows in 10 3 kg/y Stocks in 10 3 kg 4000 anthr ropogenic Land 2000 l/ regional eposition loca de Estimated residence time Air (5000) in atmosphere 98% Hg 0, 2% Hg p 2000 stocks 5000x10 3 kg = 1 y Hg p Hg 0 3 flows 5000x10 kg/y deposition Hg 2+ Estimated residence time in marine mixed layer 3 stocks 10800x10 kg 3 = 5 y flows 2200x10 kg/y Global Marine (mixed layer, 10,800) 200 Hg 0 CH 3 Hg CH 3 HgCH 3 Source: Adapted from Mason, R.P. Fitzgerald, W.F. and Morel, M.M The Biogeochemical Cycling of Elemental Mercury: Anthropogenic Influences. Geochem. Cosmochim. Acta, 58(15): Hg 2+ Hg p sedimentation Unsteady Material Balances Entering flow Flow rate Q = IV Concentration C a Box volume V Well mixed Concentration C Leaving flow Flow rate Q = IV Concentration C rate of rate of rate of rate of rate of change transport in transport out generation consumption dc V QCa QCSkVC dt at time < 0, C = C 0 V = box volume, m 3 C = concentration, mg/m 3 S = rate at which pollutant is generated, mg/hr Q = IV = total flow rate out of the box, m 3 /hr k = reaction rate coefficient for consumption, hr -1 7

8 Energy Balances The law of conservation of energy applied to a control volume Energy entering with mass Heat transfer Control volume or system Energy leaving with mass Work transfer Time rate of change net rate of energy rate of rate of of energy within = crossing boundary + energy entering - energy exiting system as work and heat with mass with mass Mass and Energy Balances Use mass and energy balances to estimate the mercury emissions from a 1000 MW e coal-fired power plant Data: Higher heating value of coal (HHV) = 29.3x10 6 J/kg (as received) = 12,600 Btu/lbm Concentration of Hg in coal [Hg] = 0.1 g/g (as received) Overall efficiency of power plant = 0.3 = Efficiency = desired result required input overall W electrical HHV m coal overall boilerthermalgenerator The efficiencies are determined by experiment. 8

9 Mass and Energy Balances Solve for mass flow rate of coal: m coal 6 Welectrical 1000x10 J/s kg J/kg 0.3 s 6 HHV overall x Solve for mass flow rate of Hg: μghg kgcoal 4 μg mhg Hg mcoal x10 kg coal s s Change units to give mass flow rate of Hg per year: m Hg 9 4 μg s 10 kg kg 1.14x s yr 1μg yr Conclusions (1) Our calculation to estimate the mercury flow rate may be off by a factor of two but it is more useful than no calculation at all. (2) Simple calculations involving units and material and energy balances can help clarify discussions of policy, regulation, risk assessment, and law. (3) Simple calculations can help detect errors and half truths. (4) Simple models based on material and energy balances will allow you to explore the consequences of assumptions, policies, and regulations. (5) Mathematics is a global language and can help avoid confusion. 9