The Radius of Influence Myth
Empirical formulas to estimate the radius of influence, such as the Sichardt formula, occasionally appear in studies assessing the environmental impact of groundwater extractions. As they are inconsistent with fundamental hydrogeological principles, the term “radius of influence myth” is used by ana...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Water |
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| Online Access: | https://www.mdpi.com/2073-4441/14/2/149 |
| _version_ | 1797489660444803072 |
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| author | Andy Louwyck Alexander Vandenbohede Dirk Libbrecht Marc Van Camp Kristine Walraevens |
| author_facet | Andy Louwyck Alexander Vandenbohede Dirk Libbrecht Marc Van Camp Kristine Walraevens |
| author_sort | Andy Louwyck |
| collection | DOAJ |
| description | Empirical formulas to estimate the radius of influence, such as the Sichardt formula, occasionally appear in studies assessing the environmental impact of groundwater extractions. As they are inconsistent with fundamental hydrogeological principles, the term “radius of influence myth” is used by analogy with the water budget myth. Alternative formulations based on the well-known de Glee and Theis equations are presented, and the contested formula that estimates the radius of influence by balancing pumping and infiltration rate is derived from an asymptotic solution of an analytical model developed by Ernst in 1971. The transient state solution of this model is developed applying the Laplace transform, and it is verified against the finite-difference solution. Examining drawdown and total storage change reveals the relations between the presented one-dimensional radial flow solutions. The assumptions underlying these solutions are discussed in detail to show their limitations and to refute misunderstandings about their applicability. The discussed analytical models and the formulas derived from it to estimate the radius of influence cannot be regarded as substitutes for advanced modeling, although they offer valuable insights on relevant parameter combinations. |
| first_indexed | 2024-03-10T00:20:47Z |
| format | Article |
| id | doaj.art-5da19f327ef94e8198c1038e52e48373 |
| institution | Directory Open Access Journal |
| issn | 2073-4441 |
| language | English |
| last_indexed | 2024-03-10T00:20:47Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Water |
| spelling | doaj.art-5da19f327ef94e8198c1038e52e483732023-11-23T15:43:37ZengMDPI AGWater2073-44412022-01-0114214910.3390/w14020149The Radius of Influence MythAndy Louwyck0Alexander Vandenbohede1Dirk Libbrecht2Marc Van Camp3Kristine Walraevens4Laboratory for Applied Geology and Hydrogeology, Department of Geology, Ghent University, Krijgslaan 281-S8, 9000 Ghent, BelgiumDe Watergroep, Water Resources and Environment, Vooruitgangstraat 189, 1030 Brussels, BelgiumArcadis Belgium nv/sa, Gaston Crommenlaan 8, Bus 101, 9050 Ghent, BelgiumLaboratory for Applied Geology and Hydrogeology, Department of Geology, Ghent University, Krijgslaan 281-S8, 9000 Ghent, BelgiumLaboratory for Applied Geology and Hydrogeology, Department of Geology, Ghent University, Krijgslaan 281-S8, 9000 Ghent, BelgiumEmpirical formulas to estimate the radius of influence, such as the Sichardt formula, occasionally appear in studies assessing the environmental impact of groundwater extractions. As they are inconsistent with fundamental hydrogeological principles, the term “radius of influence myth” is used by analogy with the water budget myth. Alternative formulations based on the well-known de Glee and Theis equations are presented, and the contested formula that estimates the radius of influence by balancing pumping and infiltration rate is derived from an asymptotic solution of an analytical model developed by Ernst in 1971. The transient state solution of this model is developed applying the Laplace transform, and it is verified against the finite-difference solution. Examining drawdown and total storage change reveals the relations between the presented one-dimensional radial flow solutions. The assumptions underlying these solutions are discussed in detail to show their limitations and to refute misunderstandings about their applicability. The discussed analytical models and the formulas derived from it to estimate the radius of influence cannot be regarded as substitutes for advanced modeling, although they offer valuable insights on relevant parameter combinations.https://www.mdpi.com/2073-4441/14/2/149radius of influenceSichardt formulaDupuit equationThiem equationTheis equationde Glee equation |
| spellingShingle | Andy Louwyck Alexander Vandenbohede Dirk Libbrecht Marc Van Camp Kristine Walraevens The Radius of Influence Myth Water radius of influence Sichardt formula Dupuit equation Thiem equation Theis equation de Glee equation |
| title | The Radius of Influence Myth |
| title_full | The Radius of Influence Myth |
| title_fullStr | The Radius of Influence Myth |
| title_full_unstemmed | The Radius of Influence Myth |
| title_short | The Radius of Influence Myth |
| title_sort | radius of influence myth |
| topic | radius of influence Sichardt formula Dupuit equation Thiem equation Theis equation de Glee equation |
| url | https://www.mdpi.com/2073-4441/14/2/149 |
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