Théorie du puits Application à la méthode de Porchet

Well theory and its application to Porchet's method

Ingénieur en chef du Génie rural.

Résumé

Porchet's well test method cannot be used to determine the steady flow from a well for a given amount of drawdown as he expected, but gives instead the rate of flow q (t) supplied by the water table to the well at time t, at which the considered level difference q (t) = Q X (MP/MN) is attained, Q being the discharge pumped from the well (cf. Fig. 2). One can attempt to deduce from the transient water table supply discharge thus obtained 1) the value of this discharge under steady conditions-Le. elements of the drawdown vs. discharge curse- and 2) characteristic coefficients for the aquifer concerned. I. - For this, the first requirement is to assume relationship between supply discharge and water table configuration; it is considered that, providing the water table is recharged, and especially if the amount of drawdown is small, conditions are as for an evenly distributed flow supplied at a rate proportional to the amount of drawdown. II - With the above assumption and the usual approximations required to linearise the problem, the motion of the free-surface of a water table featuring converging stream lines and resting on a horizontal bottom satisfies the general equation (1), which in the case of a point well subjected to pumping at constant discharge, is integrated with the aid of the Laplace transformation. The formula for transient conditions (5 or 5 'bis') and the one for steady conditions (6 or 6 'bis') are thus obtained, and this solution in turn yields the formula (8 or 8 'bis') whereby the transrnissivity and effective porosity of the medium can be determined very simply from Porchet's construction (Fig. 2) by a graphical method. III. - The point well is, however, only a reliable theoretical model where the effect of the water stored in the well can be neglected. Where this is not so, the general case of the non-punctuai well applies, which differs form the point well case by its discharge conditions (11), whereby a non-punctual well form which a constant discharge is being pumped can be considered as a point well from which a variable discharge is being pumped. With this assumption, an approximate solution can be round for the problem, which is based on the experimental observation expressed by relation (12). The results are listed in the table associated with formula (17). Practical application of this is similar to that for the point well; here again, the aquifer characteristics are found by a simple graphical method, and the drawdown vs. discharge curve is given by the same relationship (10). IV. - The theoretical results are applied to the concrete case of a large-diameter well. The final conclusion is that a single Porchet test carried out under particularly simple convenient conditions could supply all the information usually obtained by much lengthier and less straightforward methods.