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CHAPTER 6Fundamentals of NaturalEnvironmental SystemsCHAPTER PREVIEWThis chapter outlines fluid flow and material balance equations formodeling the fate and transport of contaminants in unsaturated andsaturated soils, lakes, rivers, and groundwater, and presents solutionsfor selected special cases. The objective is to provide the backgroundfor the modeling examples to be presented in Chapter 9.6.1 INTRODUCTIONIN this book, the terrestrial compartments of the natural environment arecovered; namely, lakes, rivers, estuaries, groundwater, and soils. As inChapter 4 on engineered environmental systems, the objective in this chapteralso is to provide a review of the fundamentals and relevant equations for simulatingsome of the more common phenomena in these systems. Readers arereferred to several textbooks that detail the mechanisms and processes in naturalenvironmental systems and their modeling and analysis: Thomann andMueller, 1987; Nemerow, 1991; James, 1993; Schnoor, 1996; Clark, 1996;Thibodeaux, 1996; Chapra, 1997; Webber and DiGiano, 1996; Logan, 1999;Bedient et al., 1999; Charbeneau, 2000; Fetter, 1999, to mention just a few.Modeling of natural environmental systems had lagged behind the modelingof engineered systems. While engineered systems are well defined inspace and time; better understood; and easier to monitor, control, and evaluate,the complexities and uncertainties of natural systems have rendered theirmodeling a difficult task. However, increasing concerns about human health© 2002 by CRC Press LLC
and degradation of the natural environment by anthropogenic activities andregulatory pressures have driven modeling efforts toward natural systems.Better understanding of the science of the environment, experience fromengineered systems, and the availability of desktop computing power havealso contributed to significant inroads into modeling of natural environmentalsystems.Modeling studies that began with BOD and dissolved oxygen analyses inrivers in the 1920s have grown to include nutrients to toxicants, lakes togroundwater, sediments to unsaturated zones, waste load allocations to riskanalysis, single chemicals to multiphase flows, and local to global scales.Today, environmental models are used to evaluate the impact of past practices,analyze present conditions to define suitable remediation or managementapproaches, and forecast future fate and transport of contaminants inthe environment.Modeling of the natural environment is based on the material balance conceptdiscussed in Section 4.8 in Chapter 4. Obviously, a prerequisite for performinga material balance is an understanding of the various processes andreactions that the substance might undergo in the natural environment and anability to quantify them. Fundamentals of processes and reactions applicableto natural environmental systems and methods to quantify them have beensummarized in Chapter 4. Their application in developing modeling frameworksfor soil and aquatic systems is summarized in the following sections.Under soil systems, saturated and unsaturated zones and groundwater are discussed;under aquatic systems, lakes, rivers, and estuaries are included.6.2 FUNDAMENTALS OF MODELING SOIL SYSTEMSThe soil compartment of the natural environment consists primarily of theunsaturated zone (also referred to as the vadose zone), the capillary zone, andthe saturated zone. The characteristics of these zones and the processesand reactions that occur in these zones differ somewhat. Thus, the analysisand modeling of the fate and transport of contaminants in these zones warrantdiffering approaches. Some of the natural and engineered phenomena thatimpact or involve the soil medium are air emissions from landfills, landspills, and land applications of waste materials; leachates from landfills,waste tailings, land spills, and land applications of waste materials (e.g., septictanks); leakages from underground storage tanks; runoff; atmospheric deposition;etc.To simulate these phenomena, it is desirable to review, first, the fundamentalsof the flow of water, air, and contaminants through the contaminatedsoil matrix. In the following sections, flow of water and air through the saturatedand unsaturated zones of the soil media are reviewed, followed by theirapplications to some of the phenomena mentioned above.© 2002 by CRC Press LLC
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© 2002 by CRC Press LLCModeling To
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ContentsPrefaceAcknowledgmentsFUNDA
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APPLICATIONS8. MODELING OF ENGINEER
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The contents of this book are organ
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PART IFundamentals© 2002 by CRC Pr
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The models resulting from the model
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within the grasp of only a few with
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1.2.3 STATIC VS. DYNAMICWhen a syst
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Real SystemsMathematical ModelsDete
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through several pathways. Consequen
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ange of complex environmental appli
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APPENDIX 1.1 TYPICAL USES OF MATHEM
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APPENDIX 1.2 (continued)Target Audi
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characteristics. The system is isol
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formation, inferencing, testing, va
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system-surroundings interactions ca
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2.2.4 INTERPRETATION AND EVALUATION
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to fill in where scientific theorie
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Figure 2.3 Schematic of real system
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Table 2.1 Variables, Symbols, Dimen
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∴Net diffusive inflow = -EA ∂
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in terms of the model parameters al
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Figure 2.8 Model predictions vs. me
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variables. Deterministic systems ca
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e possible, and a computational met
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or, in matrix forma 11 a 12 a 13a 2
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(a)(b)Figure 3.3 (a) Setting up Sol
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Figure 3.5 Using MATLAB ® for solv
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Another method, known as the Newton
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and so on up tof n (x 1 , x 2 , . .
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c. Second-order equation with equid
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Figure 3.9 Solution of ODE by Mathe
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over the entire step, which may be
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Hence, the original problem is now
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2∂ f f i1,j1 - f i-1,j1 - f i1,j-
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modeling, in diagnosis and troubles
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For the reach x ≥ a: C S D K
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contaminants that do not undergo an
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known as an intensive property. Oth
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Dissolved mass in sample = dissolve
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Figure 4.2 Illustration of steady s
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4.3.2.2 Dalton’s LawDalton’s La
Page 87 and 88: Table 4.2 Different Forms of Quanti
Page 89 and 90: M olesoxygenHence, K a-w = = 8 - 3
Page 91 and 92: SolutionThe flux, N, which is the d
Page 93 and 94: Figure 4.3 Illustration of the Two-
Page 95 and 96: where C s is the concentration of t
Page 97 and 98: Fraction in dissolved form = f d =
Page 99 and 100: in the air (M/L -3 ), C a is the co
Page 101 and 102: ackward reactions can expressed in
Page 103 and 104: 4.7.2 ELEMENTARY REACTIONSThe rate
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Page 107 and 108: 4.8 MATERIAL BALANCEAs indicated in
Page 109 and 110: SolutionLet M be the mass of chemic
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Page 113 and 114: APPENDIX 4.1 COMMON PARTITION COEFF
Page 115 and 116: analyzing and modeling them. The ex
Page 117 and 118: \5.2.2 HETEROGENEOUS REACTORSHetero
Page 119 and 120: CC = in -(t t 0 )k C t in0 k- C
Page 121 and 122: Worked Example 5.1A wastewater trea
Page 123 and 124: or,C L = C 0 e -(k /u)L = C 0 e -k
Page 125 and 126: HRT = 1 k (1 - )The overall HRT
Page 127 and 128: The MB equation for the above syste
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Page 131 and 132: 0 = QX - Q(X - dX) - K L (aAdz)(X -
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Page 135 and 136: This expression does not provide an
Page 137: If the WWTP used air instead of pur
Page 141 and 142: The solution to the above PDE gives
Page 143 and 144: • river 2: x = 15000.5 dmay ∴u
Page 145 and 146: These functions are valuable tools
Page 147 and 148: this problem. Once the basic “syn
Page 149 and 150: giving the condition Q > 4πRu for
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Page 153 and 154: SolutionTo be conservative, it may
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Page 157 and 158: 6.2.5 FLOW OF AIR AND CONTAMINANTS
Page 159 and 160: time-dependent volumetric flow rate
Page 161 and 162: Solution(1) The steady state concen
Page 163 and 164: As a first step in modeling a river
Page 165 and 166: where a 1,4 is the conversion facto
Page 167 and 168: © 2002 by CRC Press LLCFigure 6.8
Page 169 and 170: Figure 6.106.5 Consider the stream
Page 171 and 172: Case 4: Pulse Source in Two Dimensi
Page 173 and 174: End users often adapted these model
Page 175 and 176: to further enhance the capabilities
Page 177 and 178: are always expressed in the standar
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Page 187 and 188: Concentration [mg/L]Figure 7.3 Lake
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saving considerable model building
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dependent variable, the dependent v
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command is used to keep the plot fr
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Figure 7.10 Lake problem solved wit
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simulation. This enables, for examp
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Figure 7.13 Lake problem modeled in
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It is hoped that the above overview
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APPENDIX 7.2 EXAMPLES OF TYPES OF E
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CHAPTER 8Modeling of EngineeredEnvi
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MB on dissolved oxygen: dC od xyt=
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© 2002 by CRC Press LLCFigure 8.1
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Table 8.2 SBR Model Equations Gener
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Figure 8.4 Predicted vs. measured C
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mathematical model. First, a proces
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Figure 8.9 Pretreatment system—ef
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Figure 8.11 CMFRs in series: optimi
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Other improvements can include alte
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Figure 8.15 Model of wastewater tre
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8.5 MODELING EXAMPLE: CHEMICAL OXID
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When Mathematica ® cannot find ana
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Figure 8.20 Chemical oxidation proc
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fairly large and may not be suitabl
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where q is the mass of color adsorb
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Figure 8.29 Results of activated ca
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and d X = (µ - b)Xdtwhere b is the
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Figure 8.32 Results of bioregenerat
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under a set of known data, the stat
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MB across element on oxygen in gas
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Figure 8.38 Typical results of oxyg
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Figure 8.39 Mathematica ® script f
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entered as a function of x and y, u
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To generalize the approach, the gov
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Figure 8.44 Concentration in pore g
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modeling of a sample problem from T
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Figure 9.2 Lakes in series modeled
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Figure 9.4 Two lakes in series mode
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In this example, a two-compartment
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in the sediments, v b is the burial
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Figure 9.9 Algal growth modeled in
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Figure 9.11 Algal growth modeled in
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Once the basic model is constructed
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Figure 9.15 Graphical user interfac
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Figure 9.17 Contaminant transport v
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Figure 9.19 Contaminant transport v
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Figure 9.21 Chemical equilibrium mo
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MB on liver:MB on bones: d P2 = k 2
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Table 9.3 Model Equations in ithink
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Figure 9.25 Problem definition for
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Figure 9.28 Groundwater flow visual
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W and the second to V, in line 6. T
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Figure 9.30 Three-dimensional conto
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VerticalDispersion CoefficientsHori
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configuration of the unit world pro
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342Chemical Mass Distribution [%]11
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water quality standard of 500 mg/L
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Hence, Q π tan-1 - 1 - UL - 1Q/
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Figure 9.38d Stream lines and veloc
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BibliographyBedient P. B., Rifai, H
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Nirmalakhandan, N., Jang, W., and S
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