Taking into account the data accuracy and using three diagnostic graphs for slug tests in aquifers

Robert P. Chapuis, François Duhaime

In the proceedings of: GeoRegina 2014: 67th Canadian Geotechnical Conference

Session: Laboratory and Field Testing

ABSTRACT: Several methods can be used to interpret slug tests in aquifers. Usually, the data plot does not take into account the data accuracy. However, all data contain a random error and a systematic error. The paper documents first the random error. A slug test uses the difference Z(t) between the present and at-rest positions of the water level. As a result, the random error on Z(t) is twice that on a single water level. In a data plot the assumed errors can be shown as fierrorfl bars, which help to interpret the data. The graphs with fierrorfl bars have a special look because all Z data have the same fierrorfl, but the smaller Z data have a higher relative uncertainty. Afterwards the paper documents the systematic error. It is proposed to plot all data and theories in two semi-log graphs and a third derivative graph: the three diagnostic graphs. Each semi-log graph yields user-dependent results when used alone, and each graph assumes that the piezometric level (PL) is known and does not need to be checked. The third graph does not depend on the assumed PL and can check its exactness. Most often, it shows that the assumed PL was slightly wrong, for at least five reasons creating a systematic error for the Z(t) data. The five sources of systematic error are briefly docuth

RÉSUMÉ: Plusieurs méthodes peuvent servir à interpréter les essais de perméabilité à niveau variable dans les aquifères. Le graphe en général ne tient pas compte de la précison des données. Cependant, toutes les données incluent une erreur aléatoire et une erreur systématique. L™article examine d™abord l™erreur aléatoire. L™essai utilise la différence Z(t) entre les positions, actuelle et au repos, du niveau d™eau. L™erreur aléatoire sur Z(t) vaut alors deux fois celle sur un simple niveau d™eau. Dans un graphe d™essai, on peut montrer les erreurs supposées par des barres d™erreur, qui aident à interpréter les données. Les graphes avec des barres d™erreur ont une allure spéciale car tous les Z ont la même erreur, mais les plus petits Z ont une plus grande incertitude relative. L™article examine ensuite l™erreur systématique. On propose de porter toutes les données et les théories dans deux graphes semi-log et dans un troisième graphe de dérivée : les trois graphes du diagnostic. Chaque graphe semi-log donne des résultats subjectifs quand il est utilisé seul, et chacun suppose que le niveau piézométrique (PL) est connu et n™a pas besoin d™être vérifié. Le troisième graphe, la dérivée, ne dépend pas du PL supposé et peut vérifier son exactitude. La plupart du temps, il montre que le PL supposé était légèrement erroné, pour au moins cinq raisons qui sont brièvement expliquées. Les trois graphes du dto 1 Slug tests are routinely performed in monitoring wells, driven flush-joint casings, driven field permeameters, and between packers in boreholes. They give the local hydraulic properties of the tested material. The water level is rapidly changed in a well-riser casing and the ensuing water level position is recorded over time t: it gives the difference in hydraulic head Z(t), which can be analyzed using different methods. The water level slowly returns to equilibrium (overdamped test) or oscillates back to equilibrium (underdamped test). Most users do not justify their choice of a method. They simply show some similarity between the data plot and a theory. For overdamped tests, they present a single graph, log Z vs. t, or Z vs. log t. For underdamped tests, they present a graph of Z vs. t, and sometimes they add a graph t, if the response is close to critically damped. Traditionally, the plotting does not take into account the data accuracy. However, all measured data contain a random error and a systematic error. The paper examines first the random error. The water level measurements can be taken manually (measuring tape and stopwatch), with a float recorder, or with a pressure transducer (PT) and an atmospheric pressure transducer (APT). The random error ranges between 3 mm and 30 mm for a water level, depending on the measurement method. For a slug test, Z(t) is the difference between the present water level and the water level at rest (or local piezometric level, PL). As a result, the random error on Z(t) is twice the error on a sole water level, thus between 6 and 60 mm. When the test data are plotted to be compared with a theory, the assumed error can be shown as an fierrorfl bar, or more correctly an fiuncertaintyfl bar, which conveys the presence and degree of uncertainty to users and readers. If the fierrorfl bars are missing, there is a risk to misinterpret the data and reach incorrect conclusions. For slug tests, the graphs with fierrorfl bars have a special look because all Z data have the same fierrorfl, but the smallest

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