Non-Darcian radial flow toward a finite-diameter, fully penetrating well in a confined aquifer was analyzed on the basis of the Izbash equation with consideration of the wellbore storage effect. We derived semi-analyt...Non-Darcian radial flow toward a finite-diameter, fully penetrating well in a confined aquifer was analyzed on the basis of the Izbash equation with consideration of the wellbore storage effect. We derived semi-analytical solutions of drawdown by using the Boltzmann transform, and obtained approximate analytical solutions of the drawdown at early and late times. MATLAB programs were developed to facilitate computation of the semi-analytical solutions. The turbulence factor v which was directly related to the pumping rate appeared to have negligible influence upon the wellbore well function at early times, but imposed significant influence at intermediate and late times. However, the turbulence factor v imposed non-negligible influence upon the aquifer well function during the entire pumping period, provided that the observation point was not sufficiently close to the wellbore. Sensitivity analysis indicated that the power index n in the Izbash equation had less influence on the type curves at the face of the pumping wellbore, but had much greater influence upon the well function in the aquifer. As the n values increased, the drawdown in the aquifer decreased at early times and increased at late times. The Boltzmann transformation could only be used in an approximate sense for radial non-Darcian flow problems. This approximation would provide accurate solutions at early times, and introduce small but consistent discrepancies at intermediate and late times for the wellbore well function.展开更多
基金the National Natural Science Foundation of China (Nos.50428907 and 50479011)
文摘Non-Darcian radial flow toward a finite-diameter, fully penetrating well in a confined aquifer was analyzed on the basis of the Izbash equation with consideration of the wellbore storage effect. We derived semi-analytical solutions of drawdown by using the Boltzmann transform, and obtained approximate analytical solutions of the drawdown at early and late times. MATLAB programs were developed to facilitate computation of the semi-analytical solutions. The turbulence factor v which was directly related to the pumping rate appeared to have negligible influence upon the wellbore well function at early times, but imposed significant influence at intermediate and late times. However, the turbulence factor v imposed non-negligible influence upon the aquifer well function during the entire pumping period, provided that the observation point was not sufficiently close to the wellbore. Sensitivity analysis indicated that the power index n in the Izbash equation had less influence on the type curves at the face of the pumping wellbore, but had much greater influence upon the well function in the aquifer. As the n values increased, the drawdown in the aquifer decreased at early times and increased at late times. The Boltzmann transformation could only be used in an approximate sense for radial non-Darcian flow problems. This approximation would provide accurate solutions at early times, and introduce small but consistent discrepancies at intermediate and late times for the wellbore well function.
