Abstract
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.
Highlights
This paper stems from our concern about the use of empirical formulas to assess the impact of groundwater extractions
This study focuses on the formula of Sichardt as it is frequently applied by groundwater consultants in Flanders and the Netherlands to estimate the radius of influence in case of pumping or dewatering [2,3,4,5,6,7]
As drawdown s is a function of radial distance r (m) to the center of the well, we explicitly indicate that drawdown at the well face is meant in the Sichardt formula [36]:
Summary
This paper stems from our concern about the use of empirical formulas to assess the impact of groundwater extractions. This study focuses on the formula of Sichardt as it is frequently applied by groundwater consultants in Flanders and the Netherlands to estimate the radius of influence in case of pumping or dewatering [2,3,4,5,6,7]. According to Narasimhan [38], Weber [39] made the first successful attempt to analyze non-steady flow towards a well It is not clear if Sichardt was inspired by this work, as the Sichardt equation holds for steady state conditions [36]. The Sichardt formula [36] is applied without citation, which may indicate it has become a standard tool in dewatering studies
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