Diffusion models of environmental transport:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Lewis
2000
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 183 S. graph. Darst. |
| ISBN: | 1566704146 |
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MARC
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Diffusion |x Mathematical models | |
| 650 | 4 | |a Environmental chemistry |x Mathematical models | |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
1 ENVIRONMENTAL TRANSPORT MODELING............................................................................1
1.1 Introduction.........................................................................................................................................1
2 PRELIMINARIES.................................................................................................................................5
2.1 Equilibrium between environmental phases...................................................................................5
2.1.1 Chemical equilibrium in air-water phases...........................................................................................5
2.1.2 Chemical equilibrium in water-organic liquid phases.........................................................................6
2.1.3 Chemical equilibrium in the air-water-soil phases..............................................................................7
2.2 DlFEUSION AND THE DIFFUSION COEFFICIENT...........................................................................................9
2.2.1 Diffusion in free phases.......................................................................................................................9
2.2.2 Effective diffusion coefficient in a porous medium.......................................................................... 10
2.3 ADVECTION AND THE SURFACE MASS TRANSFER COEFFICIENT............................................................... 11
2.3.1 Laminar flow boundary layer theory and turbulent flow mass transfer............................................. 11
2.3.2 Penetration theory............................................................................................................................. 12
2.4 Mass balance and transport equations........................................................................................12
References.................................................................................................................................................15
3 DIFFUSION IN A SEMI-INFINITE SYSTEM................................................................................17
3.1 Introduction.......................................................................................................................................17
3.2 Analysis summary..............................................................................................................................17
3.2.1 Case 1: Semi-infinite region with uniform initial concentration and zero concentration at the
surface...............................................................................................................................................17
3.2.2 Case 2: Semi-infinite region with uniform initial concentration and mass transfer or reaction at
the surface......................................................................................................................................... 18
3.2.3 Case 3: Semi-infinite region with uniform initial concentration capped by a finite layer with a
different uniform initial concentration, and zero concentration at the surface..................................20
3.2.4 Case 4: Semi-infinite region with uniform initial concentration, zero concentration at the
surface, and first-order decay............................................................................................................21
3.2.5 Case 5: Semi-infinite region with uniform initial concentration, mass transfer or reaction at the
surface, and first-order decay............................................................................................................22
3.2.6 Case 6: Semi-infinite region with uniform initial concentration capped by a finite layer with a
different uniform initial concentration, zero concentration at the surface, and first-order decay......23
3.3 Numerical Evaluation......................................................................................................................25
3.4 Development.......................................................................................................................................25
3.4.1 Laplace transformation method.........................................................................................................25
3.4.2 Principle of superposition..................................................................................................................29
3.4.3 Variable transformation for first-order decay....................................................................................30
References.................................................................................................................................................32
4 DIFFUSION IN A FINITE LAYER...................................................................................................33
4.1 Introduction.......................................................................................................................................33
4.2 Analysis summary..............................................................................................................................33
4.2.1 Case I: Finite layer with arbitrary initial concentrations, zero concentration at the surface, and
zero flux at the base...........................................................................................................................34
4.2.2 Case 2: Finite layer with uniform initial concentration, zero surface concentration, and zero flux
at the base..........................................................................................................................................35
4.2.3 Case 3: Finite layer with arbitrary initial concentrations, mass transfer or reaction at the surface,
and zero flux at the base....................................................................................................................36
4.2.4 Case 4: Finite layer with uniform initial concentration, mass transfer or reaction at the surface.
and zero flux at the base....................................................................................................................37
4.2.5 Case 5: Finite layer with arbitrary initial concentrations, zero concentration at the surface, zero
flux at the base, and first-order decay...............................................................................................38
Contaminant Transport in Soils and Sediments
4.2.6 Case 6: Finite layer with uniform initial concentration, zero surface concentration, zero flux at
the base, and first-order decay...........................................................................................................39
4.2.7 Case 7: Finite layer with arbitrary initial concentrations, mass transfer or reaction at the surface,
zero flux at the base, and first-order decay........................................................................................40
4.2.8 Case 8: Finite layer with uniform initial concentration, mass transfer or reaction at the surface,
zero flux at the base, and first-order decay........................................................................................41
4.3 Numerical evaluation......................................................................................................................42
4.3.1 Evaluation of the initial condition integral........................................................................................42
4.3.2 Cases 1 and 2: zero surface concentration.........................................................................................44
4.3.3 Cases 3 and 4: surface mass transfer.................................................................................................44
4.3.4 Determining transcendental function roots........................................................................................45
4.4 Development.......................................................................................................................................46
4.4.1 Separation of variables......................................................................................................................46
4.4.2 Solution to the temporal problem......................................................................................................46
4.4.3 Solution to the spatial problem..........................................................................................................46
4.4.4 Variable transformation for first-order decay....................................................................................51
References.................................................................................................................................................52
5 DIFFUSION IN A TWO-LAYER COMPOSITE SYSTEM............................................................53
5.1 Introduction.......................................................................................................................................53
5.2 Analysis summary..............................................................................................................................53
5.2.1 System dynamics and general solution for a two-layer composite....................................................53
5.2.2 System eigenfunctions and eigenvalues............................................................................................55
5.2.3 Case I: Two-layer finite system with arbitrary initial concentrations, zero concentration at the
surface, and zero flux at the base.......................................................................................................56
5.2.4 Case 2: Two-layer finite system with arbitrary initial concentrations, mass transfer or reaction at
the surface, and zero flux at the base.................................................................................................58
5.3 Numerical Evaluation......................................................................................................................60
5.3.1 Concentration calculation..................................................................................................................61
5.3.2 Surface flux calculation.....................................................................................................................62
5.3.3 Range of significance for eigenvalues...............................................................................................62
5.3.4 Determination of eigenvalues in range..............................................................................................63
5.3.5 Eigenfunction evaluation...................................................................................................................65
5.3.6 Normalization integral evaluation.....................................................................................................65
5.3.7 Initialization integral evaluation........................................................................................................65
5.4 Development.......................................................................................................................................67
5.4.1 Separation of variables......................................................................................................................67
5.4.2 Solution to the temporal problem......................................................................................................67
5.4.3 Solution to the spatial problem..........................................................................................................67
5.4.4 Initial conditions................................................................................................................................72
5.4.5 Variable transformation for first-order decay....................................................................................74
Ri! LRENCFS ................................................................................................................................................. 75
6 DIFFUSION IN A THREE-LAYER COMPOSITE SYSTEM........................................................77
6.1 Introduction.......................................................................................................................................77
6.2 Analysis summary..............................................................................................................................77
6.2.1 System dynamics and general solution for a three-layer composite..................................................77
6.2.2 System eigenfunctions and eigenvalues............................................................................................79
6.2.3 Case I: Three-layer finite system with arbitrary initial concentrations, zero concentration at the
surface, and zero flux at the base.......................................................................................................81
6.2.4 Case 2: Three-layer finite system with arbitrary initial concentrations, mass transfer or reaction
at the surface, and zero flux at the base.............................................................................................84
6.3 Numerical Evaluation......................................................................................................................87
6.3.1 Concentration calculation..................................................................................................................87
6.3.2 Surface flux calculation.....................................................................................................................88
6.3.3 Range of significance for eigenvalues...............................................................................................89
6.3.4 Determination of eigenvalues in range..............................................................................................90
6.3.5 Eigenfunction evaluation...................................................................................................................92
6.3.6 Normalization integral evaluation.....................................................................................................92
6.3.7 Initialization integral evaluation........................................................................................................92
6.3.8 General numerical evaluation comments..........................................................................................93
6.4 DEVELOPMENT.......................................................................................................................................93
6.4.1 Separation of variables......................................................................................................................93
6.4.2 Solution to the temporal problem......................................................................................................94
6.4.3 Solution to the spatial problem..........................................................................................................94
6.4.4 Initial conditions.............................................................................................................................. 104
6.4.5 Variable transformation for first-order decay.................................................................................. 106
References...............................................................................................................................................107
7 ADVECTION-DIFFUSION MODELS............................................................................................109
7.1 Introduction.....................................................................................................................................109
7.2 Analysis summary............................................................................................................................109
7.2.1 Case 1: Semi-infinite region with uniform initial concentration with a constant concentration
boundary condition.......................................................................................................................... 109
7.2.2 Case 2: Semi-infinite region with uniform initial concentration with a constant flux boundary
condition.......................................................................................................................................... 1 10
7.2.3 Case 3: Semi-infinite region with uniform initial concentration with a boundary condition given
by a finite-timed pulse at a constant concentration......................................................................... 110
7.2.4 Case 4: Semi-infinite region with uniform initial concentration with a boundary condition given
by a finite-timed pulse at a constant flux......................................................................................... I 11
7.2.5 Case 5: Semi-infinite region with uniform initial concentration capped by a finite region of a
different uniform initial condition, with a constant concentration boundary condition.................. 1 1 1
7.2.6 Case 6: Semi-infinite region with uniform initial concentration capped by a finite region of a
different uniform initial condition, with a constant flux boundary condition.................................. 1 12
7.2.7 Case 7: Semi-infinite region with uniform initial concentration capped by a finite region of a
different uniform initial condition, with a boundary condition given by a finite-timed pulse at a
constant concentration..................................................................................................................... 1 13
7.2.8 Case 8: Semi-infinite region with uniform initial concentration capped by a finite region of a
different uniform initial condition, with a boundary condition given b a finite-timed pulse at a
constant flux.................................................................................................................................... 113
7.3 Numerical Evaluation....................................................................................................................114
7.4 Development.....................................................................................................................................114
References...............................................................................................................................................117
8 VOLATILE LIQUID EVAPORATION.......................................................................................... 119
8.1 Introduction.....................................................................................................................................119
8.2 Analysis Summary...........................................................................................................................119
8.2.1 Case 1: Evaporation and vapor diffusion through soil sediment with uniform initial liquid
saturation, with zero vapor concentration at the surface................................................................. I 19
8.2.2 Case 2: Evaporation and vapor diffusion through soil sediment with uniform initial liquid
saturation, with a vapor mass transfer boundary condition at the surface....................................... 120
8.2.3 Case 3: Evaporation and vapor diffusion through soil sediment with uniform initial liquid
saturation below a finite clean capped region, with zero vapor concentration at the surface.......... 121
8.2.4 Case 4: Evaporation and vapor diffusion through soil/sediment with uniform initial liquid
saturation below a finite clean capped region, with a vapor mass transfer boundary condition at
the surface....................................................................................................................................... !--
8.3 Numerical Evaluation...................................................................................................................123
8.4 Development..................................................................................................................................... 123
8.4.1 Case 1: Evaporation and vapor diffusion through soil sediment with uniform initial liquid
saturation, with zero vapor concentration at the surface................................................................ 123
Contaminant Transport in Soils and Sediments
8.4.2 Case 2: Evaporation and vapor diffusion through soil/sediment with uniform initial liquid
saturation, with a vapor mass transfer boundary condition at the surface....................................... 124
8.4.3 Case 3: Evaporation and vapor diffusion through soil/sediment with uniform initial liquid
saturation below a finite clean capped region, with zero vapor concentration at the surface..........125
8.4.4 Case 4: Evaporation and vapor diffusion through soil/sediment with uniform initial liquid
saturation below a finite clean capped region, with a vapor mass transfer boundary condition at
the surface....................................................................................................................................... 125
REFERENCES............................................................................................................................................... 126
9 DIFFUSION WITH TIME-DEPENDENT PARTITION COEFFICIENTS................................127
9.1 Introduction.....................................................................................................................................127
9.2 Mathematical Analysis..................................................................................................................127
9.3 Analysis Summary...........................................................................................................................129
9.3.1 Case 1: Diffusion in a thin layer with time-dependent soil-air partition coefficient, zero surface
concentration, a no-flow bottom boundary condition, and constant initial conditions....................129
9.3.2 Case 2: Diffusion time-dependent partition coefficient, zero surface concentration, no flow
bottom boundary, and arbitrary initial conditions........................................................................... 133
9.3.3 Case 3: Diffusion in a thin surface boundary layer with time-dependent soil-air partition
coefficient, zero surface concentration, a constant concentration source at the lower boundary,
and constant initial conditions.........................................................................................................134
9.4 Variable transformations on a variety of time-dependent air-soil partition coefficient
functions........................................................................................................................................... 140
9.4.1 Constant soil-air partition coefficient..............................................................................................140
9.4.2 Linear soil-air partition coefficient..................................................................................................140
9.4.3 Exponential soil-air partition coefficient.........................................................................................141
9.5 Development.....................................................................................................................................142
9.5.1 Transformation of variables............................................................................................................142
9.5.2 Separation of variables.................................................................................................................... 142
9.5.3 Time-dependent boundary condition............................................................................................... 145
References...............................................................................................................................................148
10 CONSTANT FLUX LIQUID EVAPORATION.............................................................................149
10.1 Introduction..........................................................................................................................149
10.2 Analysis and Development..................................................................................................149
References...............................................................................................................................................151
APPENDIX...............................................................................................................................................153
A. Error function.................................................................................................................................153
B. Laplace transformation................................................................................................................155
C. ROOTS OF TRANSCENDENTAL EQUATIONS............................................................................................ 158
D. Predicting the diffusion coefficients vapors...........................................................................160
E. Predicting the diffusion coefficient in liquids...........................................................................162
F. SAMPLE CALCULATIONS OF MODELS USING MATHCAD™ .................................................................... 165
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:31:28Z |
| institution | BVB |
| isbn | 1566704146 |
| language | English |
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| physical | 183 S. graph. Darst. |
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| publisher | Lewis |
| record_format | marc |
| spelling | Choy, Bruce Verfasser aut Diffusion models of environmental transport Bruce Choy ; Danny D. Reible Boca Raton [u.a.] Lewis 2000 183 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chimie de l'environnement - Modèles mathématiques Diffusion (Physique) - Modèles mathématiques Transport, Théorie du - Modèles mathématiques Mathematisches Modell Diffusion Mathematical models Environmental chemistry Mathematical models Transport theory Mathematical models Diffusion (DE-588)4012277-3 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Transporttheorie (DE-588)4185936-4 gnd rswk-swf Ökologische Chemie (DE-588)4135167-8 gnd rswk-swf Ökologische Chemie (DE-588)4135167-8 s Transporttheorie (DE-588)4185936-4 s Diffusion (DE-588)4012277-3 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Reible, Danny D. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008603281&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Choy, Bruce Diffusion models of environmental transport Chimie de l'environnement - Modèles mathématiques Diffusion (Physique) - Modèles mathématiques Transport, Théorie du - Modèles mathématiques Mathematisches Modell Diffusion Mathematical models Environmental chemistry Mathematical models Transport theory Mathematical models Diffusion (DE-588)4012277-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Transporttheorie (DE-588)4185936-4 gnd Ökologische Chemie (DE-588)4135167-8 gnd |
| subject_GND | (DE-588)4012277-3 (DE-588)4114528-8 (DE-588)4185936-4 (DE-588)4135167-8 |
| title | Diffusion models of environmental transport |
| title_auth | Diffusion models of environmental transport |
| title_exact_search | Diffusion models of environmental transport |
| title_full | Diffusion models of environmental transport Bruce Choy ; Danny D. Reible |
| title_fullStr | Diffusion models of environmental transport Bruce Choy ; Danny D. Reible |
| title_full_unstemmed | Diffusion models of environmental transport Bruce Choy ; Danny D. Reible |
| title_short | Diffusion models of environmental transport |
| title_sort | diffusion models of environmental transport |
| topic | Chimie de l'environnement - Modèles mathématiques Diffusion (Physique) - Modèles mathématiques Transport, Théorie du - Modèles mathématiques Mathematisches Modell Diffusion Mathematical models Environmental chemistry Mathematical models Transport theory Mathematical models Diffusion (DE-588)4012277-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Transporttheorie (DE-588)4185936-4 gnd Ökologische Chemie (DE-588)4135167-8 gnd |
| topic_facet | Chimie de l'environnement - Modèles mathématiques Diffusion (Physique) - Modèles mathématiques Transport, Théorie du - Modèles mathématiques Mathematisches Modell Diffusion Mathematical models Environmental chemistry Mathematical models Transport theory Mathematical models Diffusion Transporttheorie Ökologische Chemie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008603281&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT choybruce diffusionmodelsofenvironmentaltransport AT reibledannyd diffusionmodelsofenvironmentaltransport |