A Simple Analytical Formula for the Leakage Flux Through a Perforated Aquitard. Issue 4 (12th July 2014)

• Record Type: Journal Article
• Authors: Bonte, Matthijs; Zaadnoordijk, Willem Jan; Maas, Kees
• Is Part Of: Ground water. Volume 53:Issue 4(2015:Jul./Aug.)
• Page Start: 638
• Page End: 644
• Publication Date: 2014-07-12
• Subjects: Groundwater -- Periodicals; Wells -- Periodicals; Eau souterraine -- Périodiques; Puits -- Périodiques; Grondwater; Eau souterraine; Puits; Electronic journals; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 551.49
• DOI: 10.1111/gwat.12239
• Languages: English
• ISSNs: 0017-467X

Abstract

<abstract abstract-type="main" id="gwat12239-abs-0001"> <title>Abstract</title> <p id="gwat12239-para-0001">In this methods note, we present a simple analytical formula to quantify the steady‐state leakage flux (<italic>Q</italic>) over a perforated aquitard. The flux depends on the aquitard thickness (<italic>D</italic>), the radius of the perforation (<italic>R</italic>), the hydraulic conductivity of the material inside the perforation (<italic>k</italic><sub>fill</sub>), the conductivities of the overlying and underlying aquifers (<italic>k</italic><sub>1</sub> and <italic>k</italic><sub>2</sub>, respectively), and the head difference between the two aquifers (Δ<italic>H</italic>): <disp-formula content-type="mathematics" id="gwat12239-disp-8500"><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj1d0rq259" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" overflow="scroll" altimg="urn:x-wiley:0017467X:media:gwat12239:gwat12239-math-0001" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Q</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>R</mml:mi><mml:mi>Δ</mml:mi><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mfrac><mml:mi>D</mml:mi><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>fill</mml:mtext></mml:msub><mml:mi mathvariant="normal">π</mml:mi><mml:mi>R</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>4</mml:mn></mml:mfrac><mml:mfenced open="(" close=")"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mfrac></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></disp-formula> This equation assumes an aquitard separating two homogeneous and infinite aquifers (<italic>R</italic> ≪ aquifer thickness) in which radial flow to and from the perforation occurs, with no other recharge or discharge boundaries near the perforation. The flux through a perforation in a hypothetical case study with <italic>D</italic> = 10 m, <italic>k</italic><sub>1</sub> = 10 m/d, <italic>k</italic><sub>2</sub> = 20 m/d, <italic>R</italic> = 0.072 m, and Δ<italic>H</italic> = 1 m ranges between less than 1 mL/d if the hole is backfilled with bentonite (<italic>k</italic><sub>fill</sub> = 10<sup>−4</sup> m/d), to several liters per day if the perforation is backfilled with sand from the overlying aquifer (<italic>k</italic><sub>fill</sub> = 10 m/d), to several m<sup>3</sup>/d if the perforation forms an open conduit (<italic>k</italic><sub>fill</sub> = 10<sup>5</sup> m/d). The leakage fluxes calculated with this model agree well with those calculated using a numerical model (MODFLOW).</p> </abstract>