Diagenetic models and their implementation: modelling transport and reactions in aquatic sediments ; with 19 tables
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Deutsch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1997
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007301872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVI, 414 S. graph. Darst. |
| ISBN: | 3540611258 0387611258 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV010914556 | ||
| 003 | DE-604 | ||
| 005 | 20220518 | ||
| 007 | t| | ||
| 008 | 960819s1997 gw d||| |||| 00||| ger d | ||
| 016 | 7 | |a 947821112 |2 DE-101 | |
| 020 | |a 3540611258 |9 3-540-61125-8 | ||
| 020 | |a 0387611258 |9 0-387-61125-8 | ||
| 035 | |a (OCoLC)247259355 | ||
| 035 | |a (DE-599)BVBBV010914556 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-703 |a DE-12 |a DE-29 |a DE-634 |a DE-83 |a DE-188 | ||
| 082 | 0 | |a 552/.03/015118 | |
| 084 | |a RB 10259 |0 (DE-625)142220:12677 |2 rvk | ||
| 084 | |a TG 4500 |0 (DE-625)162523: |2 rvk | ||
| 100 | 1 | |a Boudreau, Bernard P. |d 1953- |e Verfasser |0 (DE-588)1055797831 |4 aut | |
| 245 | 1 | 0 | |a Diagenetic models and their implementation |b modelling transport and reactions in aquatic sediments ; with 19 tables |c Bernard P. Boudreau |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
| 300 | |a XVI, 414 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Aquatisches Sediment - Frühdiagenese - Mathematisches Modell | |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Aquatisches Sediment |0 (DE-588)4129652-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Frühdiagenese |0 (DE-588)4334614-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Aquatisches Sediment |0 (DE-588)4129652-7 |D s |
| 689 | 0 | 1 | |a Frühdiagenese |0 (DE-588)4334614-5 |D s |
| 689 | 0 | 2 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
| 689 | 0 | |5 DE-188 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007301872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007301872 | |
Datensatz im Suchindex
| _version_ | 1825049514188210176 |
|---|---|
| adam_text |
TABLE OF CONTENTS
Chapter Page
PREFACE vii
1 IJWl'HJLLUSUi'HY Ut UlAliUJNUm; MODELLING 1.1 Introduction 1 1
1.2 Problem Identification 3
1.3 Model Formulation 4
1.4 Solution 4
2 MATHEMATICAL BACKGROUND 6
2.1 Introduction 6
2.2 Variables and Parameters 6
2.3 Types of Equations 7
2.3.1 Algebraic Equations 7
2.3.2 Differential Equations 7
2.3.3 Integrals and Integral Equations 13
2.3.4 Integro-Differential Equations 15
2.4 Series Approximation and Expansion 15
2.4.1 Power Series 15
2.4.2 Taylor Series 15
2.4.3 Binomial Expansion 16
2.4.4 Fourier Series 17
2.5 The Mean Value Theorems 18
2.6 Leibnitz's Rule and Gauss' Theorem 18
2.7 Reynolds Decomposition and Averaging 19
2.8 The Dirac Delta Function 21
3 MODEL CONSTRUCTION 23
3.1 The Standard Approach 23
3.2 Total Derivatives and Diagenesis 26
3.3 Conservation (Balance) Equations in 1-D 30
3.4 Types of Fluxes in 1-D 32
3.4.1 Advection 33
Burial and Compaction 34
Externally Impressed Flow 34
Biological Advection 36
3.4.2 Diffusive Fluxes 37
Molecular and Ionic Diffusion 37
Hydrodynamic Dispersion 39
Bioturbation 41
3.4.3 The Standard (Local) Diagenetic Equations 47
3.5 Special Equations for Total Solids and Total Fluid 48
No Compaction 49
Steady-State Compaction 50
3.6 Static Conservation of Volume 50
3.7 Integral Conservation Balances in 1-D 52
3.8 Well-Mixed Zones in 1 -D 54
3.9 Multi-Dimensional Conservation Equations 55
3.9.1 Derivation 55
3.9.2 The Cartesian Coordinate System 57
3.9.3 The Cylindrical Coordinate System 59
3.9.4 The Spherical Coordinate System 63
3.10 Nonlocal Transport Processes 66
3.10.1 Nonlocal Mixing within Sediments 67
3.10.2 Conveyor-Belt Mixing (Head-Down Deposit-Feeding) 70
3.10.3 Burrow-and-Fill Mixing 71
3.10.4 Resuspension-Redeposition 73
3.10.5 Porewater Irrigation as a 1-D Nonlocal Source/Sink 75
3.11 Reaction Processes and Differential-Algebraic Equations 77
3.11.1 Homogeneous and Heterogeneous Reactions 77
3.11.2 Reversible and Irreversible Reactions 78
3.12 Conservation Equations via Volume Averaging 82
3.13 Modelling Continua 88
3.13.1 Age-Dependent Processes 88
3.13.2 Reactive Continua 89
CONSTITUTIVE EQUATIONS 91
4.1 Introduction 91
4.2 Fickian Transport Processes 92
4.2.1 Fluid Viscosity 92
4.2.2 Electrical Conductivity 94
4.2.3 Molecular/Ionic Diffusion Coefficients 96
Molecular/Statistical Basis 99
Irreversible Thermodynamic Basis 103
Infinite Dilution Diffusion Coefficients 105
Uncharged Particles 105
Ions and Ion Pairs 114
4.2.4 Diffusion in Multicomponent Porewaters 118
4.2.5 Diffusion in Pores and Tortuosity 125
Numerical Estimation 127
4.2.6 Permeability and Dispersion Coefficients 132
4.2.7 Biodiffusion Coefficients and Mixing Depths 138
Dg versus w 138
Dß versus Water Depth 140
Mixing-Depth versus w 140
4.3 Burial Velocity 141
4.4 Source/Sink-Type Parameters 142
4.4.1 Irrigation Parameters 142
4.4.2 Reaction Kinetics 144
General Forms 144
Inhibition 149
4.4.3 Rate Constants for Organic Matter Decomposition 152
4.4.4 Rate Constants for Other Geochemically Significant Reactions 154
4.4.5 Distribution Functions for Reactive Continua 155
4.5 Thermodynamic Constants 159
4.6 Other Environmental Parameters 163
5 BOUNDARY CONDITIONS 165
5.1 Introduction 165
Example 5-1 167
Example 5-2 167
Example 5-3 167
Example 5-4 167
5.2 Origin and Types of Diagenetic Boundary Conditions 168
5.2.1 Concentration or Dirichlet Conditions 168
5.2.2 Fluxes at External Boundaries 169
5.2.3 Conditions at Internal Boundaries 172
5.2.4 Boundary Conditions for Unknown Points 176
5.2.5 At a Well-Stirred Reservoir of Limited Size 177
5.2.6 Coupled Boundary Conditions 177
5.2.7 Nonlocal Boundary Conditions 178
5.3 Boundary Condition Parameters 178
5.3.1 Mass-Transfer Coefficients for Solutes 178
Classical Boundary Layer Theory 179
Periodic Boundary Layer Models 183
Slip at the Sediment-Water Interface 186
Interfacial Roughness 188
5.3.2 Sediment-Water Flux of Organic Carbon 189
5.3.3 Flux of Oxidants at the Sediment-Water Interface 189
6 ANALYTICAL SOLUTION OF STEADY STATE 1-DIMENSIONAL
DIAGENETIC EQUATIONS 191
6.1 Steady State and Uni-Dimensionality 191
6.2 Dimensional Analysis: Scaling and Simplification 192
6.2.1 Scaling 192
6.2.2 Regular Perturbation Method 196
6.3 Solution of First Order ODEs 198
6.3.1 Linear Equations 199
Example 6-1 199
Example 6-2 200
Example 6-3 201
Example 6-4 201
Example 6-5 203
6.3.2 Nonlinear Equations 204
Example 6-6 204
6.4 Solution of Second Order ODEs 205
6.4.1 Directly Integratible Equations 205
Example 6-7 205
Example 6-8 205
Example 6-9 206
XIV
6.4.2 Linear Equations with Constant Coefficients 206
Homogeneous Equations, g(x) = 0 206
Example 6-10 208
Example 6-11 208
Example 6-12 209
Special Cases 211
Inhomogeneous Equations g(x) * 0 212
Example 6-13 212
Example 6-14 213
6.4.3 Linear Equations with Variable Coefficients 215
6.4.4 Series Solution about an Ordinary Point 215
Example 6-15 215
Example 6-16 218
6.4.5 Series Solution about a Regular Singularity 220
6.4.6 Solution by Variable Transformation and the "Look-Up"
Technique 222
Example 6-17 223
Example 6-18 226
Example 6-19 229
Example 6-20 230
6.4.7 Calculation of Special Functions 234
6.5 Nonlinear Second-Order ODEs 235
Example 6-21 235
Example 6-22 238
Example 6-23 239
Example 6-24 241
6.6 Solution of Steady-State DAEs 243
Example 6-25 244
7 ANALYTICAL SOULTIONS FOR TIME-DEPENDENT AND/OR
MULTI-DIMENSIONAL DIAGENETIC MODELS 246
7.1 Introduction 246
7.2 Transformations and Simplifications 247
7.3 Similarity Variables 250
Example 7-1 (The Error Function) 251
7.4 Separation of Variables (SoV) 254
Example 7-2 254
7.4.1 SoV for 1-D Diffusion in a Finite Sediment Layer 256
Example 7-3 256
General 1-D Problems 261
Example 7-4 Spatially Variable Coefficients 262
7.4.2 SoV for 1-D Diffusion in a Semi-Infinite Sediment 268
Example 7-5 270
7.4.3 SoV for Multi-Dimensional Steady-State Problems 271
Example 7-6 (Aller's Tube Model) 272
Example 7-7 276
7.5 Duhamel's Theorem 282
7.6 The Convolution Integral and Delta Function Inputs 283
7.7 Laplace Transforms 284
Example 7-8 285
Example 7-9 285
Example 7-10 288
Example 7-11 290
7.8 The Advection-Reaction Equation 293
Example 7-12 294
Example 7-13 295
NUMERICAL METHODS 297
8.1 Introduction 297
8.2 Accuracy and Stability 297
8.3 Finding Roots 298
Bisection 299
Newton-Raphson 299
8.4 Basic Numerical Integration 301
8.5 Finite Differences and Diagenetic Equations 302
Finite Difference Method 302
8.5.1 Lessons from Initial Value Problems 302
8.5.2 Dealing with Second-Order Derivatives 310
8.5.3 Finite Differences in 3-D Coordinate Systems 317
The Cartesian System 317
The Cylindrical System 318
The Spherical System 320
8.5.4 Depth-Dependent Diffiisivity 321
8.6 Boundary Conditions 322
8.6.1 Dirichlet (Concentration) Conditions 322
8.6.2 Neumann (No Flux) Boundary Conditions 322
8.6.3 Robin's (Prescribed Flux) Boundary Conditions 324
8.6.4 Unknown Points 325
8.7 Uneven Grids 325
8.8 Solution by the Method of Lines (MoL) 328
8.8.1 Diffusion Present 328
Example 8-1 328
Example 8-2 329
Example 8-3 331
Example 8-4 333
Example 8-5 333
8.8.2 Pure Advective Transport 335
8.9 Full Differencing 338
8.9.1 Diffusive Transport Present 338
Explicit Differencing (8=0) 339
Fully Implicit Differencing (£=1) 341
Crank-Nicolson Finite Differencing (e=l/2) 343
8.9.2 Diffusive Transport Absent 344
8.10 Diagenesis in 2 and 3 Dimensions 349
8.10.1 Explicit Method 349
8.10.2 Operator Splitting - Locally 1-D Method 350
Example 8-6 350
8.10.3 Alternating-Direction-Implicit Method 353
XVI
Example 8-7 353
8.10.4 Boundary Conditions 354
8.11 Canned Codes for ODEs and PDEs 354
8.12 Differential-Algebraic Equations 355
Example 8-8 356
8.13 Calculating Diffusive Fluxes 359
9 EPILOGUE 361
10 APPENDIX: HOW TO OBTAIN FORTRAN CODES 362
11 REFERENCES 364
12 COMMON AND IMPORTANT SYMBOLS 394
13 INDEX 398 |
| any_adam_object | 1 |
| author | Boudreau, Bernard P. 1953- |
| author_GND | (DE-588)1055797831 |
| author_facet | Boudreau, Bernard P. 1953- |
| author_role | aut |
| author_sort | Boudreau, Bernard P. 1953- |
| author_variant | b p b bp bpb |
| building | Verbundindex |
| bvnumber | BV010914556 |
| classification_rvk | RB 10259 TG 4500 |
| ctrlnum | (OCoLC)247259355 (DE-599)BVBBV010914556 |
| dewey-full | 552/.03/015118 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 552 - Petrology |
| dewey-raw | 552/.03/015118 |
| dewey-search | 552/.03/015118 |
| dewey-sort | 3552 13 515118 |
| dewey-tens | 550 - Earth sciences |
| discipline | Geologie / Paläontologie Geographie |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV010914556</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20220518</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">960819s1997 gw d||| |||| 00||| ger d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">947821112</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540611258</subfield><subfield code="9">3-540-61125-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387611258</subfield><subfield code="9">0-387-61125-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)247259355</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010914556</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-29</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">552/.03/015118</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">RB 10259</subfield><subfield code="0">(DE-625)142220:12677</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">TG 4500</subfield><subfield code="0">(DE-625)162523:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Boudreau, Bernard P.</subfield><subfield code="d">1953-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1055797831</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Diagenetic models and their implementation</subfield><subfield code="b">modelling transport and reactions in aquatic sediments ; with 19 tables</subfield><subfield code="c">Bernard P. Boudreau</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 414 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Aquatisches Sediment - Frühdiagenese - Mathematisches Modell</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematisches Modell</subfield><subfield code="0">(DE-588)4114528-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Aquatisches Sediment</subfield><subfield code="0">(DE-588)4129652-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Frühdiagenese</subfield><subfield code="0">(DE-588)4334614-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Aquatisches Sediment</subfield><subfield code="0">(DE-588)4129652-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Frühdiagenese</subfield><subfield code="0">(DE-588)4334614-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Mathematisches Modell</subfield><subfield code="0">(DE-588)4114528-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-188</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007301872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007301872</subfield></datafield></record></collection> |
| id | DE-604.BV010914556 |
| illustrated | Illustrated |
| indexdate | 2025-02-25T17:00:47Z |
| institution | BVB |
| isbn | 3540611258 0387611258 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007301872 |
| oclc_num | 247259355 |
| open_access_boolean | |
| owner | DE-703 DE-12 DE-29 DE-634 DE-83 DE-188 |
| owner_facet | DE-703 DE-12 DE-29 DE-634 DE-83 DE-188 |
| physical | XVI, 414 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| spelling | Boudreau, Bernard P. 1953- Verfasser (DE-588)1055797831 aut Diagenetic models and their implementation modelling transport and reactions in aquatic sediments ; with 19 tables Bernard P. Boudreau Berlin [u.a.] Springer 1997 XVI, 414 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aquatisches Sediment - Frühdiagenese - Mathematisches Modell Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Aquatisches Sediment (DE-588)4129652-7 gnd rswk-swf Frühdiagenese (DE-588)4334614-5 gnd rswk-swf Aquatisches Sediment (DE-588)4129652-7 s Frühdiagenese (DE-588)4334614-5 s Mathematisches Modell (DE-588)4114528-8 s DE-188 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007301872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boudreau, Bernard P. 1953- Diagenetic models and their implementation modelling transport and reactions in aquatic sediments ; with 19 tables Aquatisches Sediment - Frühdiagenese - Mathematisches Modell Mathematisches Modell (DE-588)4114528-8 gnd Aquatisches Sediment (DE-588)4129652-7 gnd Frühdiagenese (DE-588)4334614-5 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4129652-7 (DE-588)4334614-5 |
| title | Diagenetic models and their implementation modelling transport and reactions in aquatic sediments ; with 19 tables |
| title_auth | Diagenetic models and their implementation modelling transport and reactions in aquatic sediments ; with 19 tables |
| title_exact_search | Diagenetic models and their implementation modelling transport and reactions in aquatic sediments ; with 19 tables |
| title_full | Diagenetic models and their implementation modelling transport and reactions in aquatic sediments ; with 19 tables Bernard P. Boudreau |
| title_fullStr | Diagenetic models and their implementation modelling transport and reactions in aquatic sediments ; with 19 tables Bernard P. Boudreau |
| title_full_unstemmed | Diagenetic models and their implementation modelling transport and reactions in aquatic sediments ; with 19 tables Bernard P. Boudreau |
| title_short | Diagenetic models and their implementation |
| title_sort | diagenetic models and their implementation modelling transport and reactions in aquatic sediments with 19 tables |
| title_sub | modelling transport and reactions in aquatic sediments ; with 19 tables |
| topic | Aquatisches Sediment - Frühdiagenese - Mathematisches Modell Mathematisches Modell (DE-588)4114528-8 gnd Aquatisches Sediment (DE-588)4129652-7 gnd Frühdiagenese (DE-588)4334614-5 gnd |
| topic_facet | Aquatisches Sediment - Frühdiagenese - Mathematisches Modell Mathematisches Modell Aquatisches Sediment Frühdiagenese |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007301872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT boudreaubernardp diageneticmodelsandtheirimplementationmodellingtransportandreactionsinaquaticsedimentswith19tables |