Environmental System Analysis. Kangwon National University College of Engineering Division of Geosystem and Environmental Engineering Professor Joon Hyun Kim 010-9696-6354, 033-250-6354. Class Contents and Schedule. Environmental Modeling.
Kangwon National University
College of Engineering
Division of Geosystem and Environmental Engineering
Professor Joon Hyun Kim
Fate and Transport of Pollutants in Water, Air, and Soil
-JERALD L. SCHNOOR
If we are going to live so intimately with these chemicals, eating and drinking them into the very marrow of our bones, we had better know something about their nature and power
-Rachel Carson, Silent Spring
Why should we build mathematical models of environmental pollutants?
1) To gain a better understanding of the fate and transport of chemicals by quantifying their reactions, speciation, and movement for the prediction of fate, transport, and persistence of chemicals in the environment.
2) To determine chemical exposure concentrations to aquatic organisms and/or humans in the past, present, or future.
3) To predict future conditions under various loading scenarios or management action alternatives.
(i) A clearly defined control volume.
(ii) A knowledge of inputs and outputs that cross the boundary of the
(iii) A knowledge of the transport characteristics within the control
volume and across its boundaries.
(iv) A knowledge of the reaction kinetics within the control volume.
Figure 1.1 Generalized approach for mass balance models utilizing the control-volume concept and transport across boundaries.
Classification of substances relative to their reactions in water
Q = flow rate m3d-1 I = precipitation rate md-1 A = surface area of water body, m2 E = evaporation rate md-1 ∆t = time increment, days ∆V = change in storage volume, m3
Figure 1.2 Schematic of a lake with inflows and outflows for computation of a water budget
Calculate the volume of a lake over time during a drought if the sum of all inputs is 100 m3s-1 and the outflows are 110 m3s-1 and increasing 1 m3s-1 every day due to evaporation and water demand. Initial volume of the lake is 1 × 109 m3. See Figure 1.3. (Note : Convert all units from seconds to days.)
Figure 1.3 Plot of volume versus time for hypothetical lake during a drought period
Calculate the steady-state concentration of a toxic chemical in a lake under the following conditions. Assume steady state (dC/dt = 0) and constant volume (Qin = Qout) and a degradation rate of 50 kg d-1 for the conditions such as : Cin=100μgL-1, Qin=Qout=10m3s-1, -Rxn=50kgd-1
Solution: Write the mass balance equation for the lake as a control volume
Accumulation = Inputs - Outflows ± Rxns , Accumulation = 0 at steady state Outflows = Inputs - Rxn (degradation)
O To perform mathematical modeling, four ingredients are necessary:
1) field data on chemical concentrations and mass discharge inputs
2) a mathematical model formulation
3) rate constants and equilibrium coefficients for the mathematical model
4) some performance criteria with which to judge the model
O If the model is to be used for regulatory purposes, there should be enough
field data to be confident of model results (two sets of field measurements,
one for model calibration and one for verification under somewhat
different circumstances (a different year of field measurements or an
O Model calibration involves a comparison between simulation results and
field measurements. Model coefficients and rate constants should be chosen
initially from literature or laboratory studies.
O If errors are within an acceptable tolerance level, the model is considered
calibrated. If errors are not acceptable, rate constants and coefficients must
be systematically varied (tuning the model) to obtain an acceptable
simulation. The parameters should not be "tuned" outside the range of
experimentally determined values reported in the literature.
O After you run the model, a statistical comparison is made between model
results for the state variables (chemical concentrations) and field
measurements. The model is calibrated.
Example 1.3 Calibration and Criteria Testing of a DO Model for a Hypothetical Stream
A water discharge with biochemical oxygen demand (BOD) at km 0.0 causes a depletion in dissolved oxygen in a stream (D.O. sag curve). Model calibration results are tabulated below (D.O. model) together with field measurements (D.O. field) expressed in concentration units, mg L-1. See Figure 1.4.
Determine if the model calibration is acceptable according to the following statistical criteria:
a. Chi-square goodness of fit at a 0.10 significance level (a 90% confidence level).
b. Paired t-test (difference between the mean and zero) at significance level
c. Linear least-squares regression of model results (D.O. model on x-axis) versus observed data (D.O. field data on y-axis) with r2 > 0.8.
Figure 1.4 Dissolved oxygen model calibration and comparison to field measurements.
where the observed values are the D.O. field data, and the expected values are the D.O. model results. α is the confidence level and χ02 is the chi-square distribution value for n-1 degrees of freedom. χ02=4.17 for n = 10 and α= 0.9. The value for χ02 = 4.17 was determined from a statistical table for the chi-square distribution with 9 degrees of freedom (n-1) and P = 0.10.
The table below shows that 0.1254≤4.17. Therefore the model passes the goodness of fit test at a 0.10 significance level.
di - difference between values in data pairi. The acceptance criterion for the t-test for n-1 degrees of freedom is
In D.O model the value 1.833 wart determined from a table t-values with 9 degrees of freedom and P = 0.10. The above shows
The test statistic can be calculated
The model results are found to be indistinguishable from the field data at a significance level of 0.10 from the paired t-test because 0.3699≤1.833.
Perfect model predictions would yield
Significant reactions for selected priority pollutant organic chemicals in natural waters
Figure 1.5 Periodic table and average freshwater concentration
The reservoirs of atmosphere, surface fresh waters. and living biomass are significantly smaller than the reservoirs of sediment and marine waters. The total groundwater reservoir may be twice that of fresh water. However, groundwater is much less accessible.
In Figure 1.6 the sizes of the various reservoirs, measured in number of molecules or atoms, are compared. The mean residence time of the molecules in these reservoirs is also indicated. The smaller the relative reservoir size and residence time, the more sensitive the reservoir toward perturbation.
The distribution of a pollutant in the environment is dependent on its specific properties. Of particular ecological relevance is fat solubility or lipophilicity, as lipophilic substances accumulate in organisms and the food chain. Biodegradation and chemical or photochemical decomposition decrease residence time and residual concentrations.
Figure 1.8 Transfer and transformation of pollutants in aquatic ecosystems
A substance introduced into the system becomes dispersed diluted. It can become eliminated firm the water by adsorption on particles or by volatilization. It may also be transformed chemically or biologically.
Figure 1.8: synopsis of the perspectives of aquatic ecotoxicology. Let us follow the various steps from the source to the potential ecological effects of a pollutant released into an aquatic ecosystem. The emission is measured as a flow or Input load (capacity factor; mass per unit time or mass per unit time and volume or area). The resulting concentration is a consequence of the dilution, transport, and transformation of this chemical. At any point, the water condition is characterized by the interacting physical, chemical, and biological factors.