Unsteady flow to a partially penetrating pumping well with wellbore storage in a dual-permeability confined aquifer

Abstract

In this article, a new model is presented for imparting unsteady flow to a partially penetrating pumping well with wellbore storage placed in double-permeability confined aquifers to investigate the wellbore drawdown transient behavior. In this model, both the fracture and matrix systems are connected directly with the wellbore as flow pathways, while comprehensively considering the crossflow between the matrix and the fractures. The top and bottom boundaries are assumed to be impermeable, and the outer side boundaries could be infinite. Subsequently, Laplace transformation and finite Fourier cosine transformation are employed to obtain analytical solutions of the dual-permeability flow model in the Laplace domain. The derived analytical solution is general and can be reduced to several other previous results. The numerical inversion algorithm of Stehfest is used to solve the wellbore drawdown in the real time domain. Subsequently, the model is validated by comparing it with previous results. Groundwater flow characteristics are analyzed in detail and divided into five flow stages: wellbore storage flow, early-radial flow, quasi-spherical flow, crossflow between the matrix and the fractures, and quasi-radial flow. The different flow stages show some special values on the drawdown and its derivative log-log plots. There is a hump/dip feature in the semi-logarithmic curve of the drawdown derivative, which are inherent characteristic for dual-permeability flow behavior. The effects of some important parameters of the aquifer or pumping wells on drawdown and its derivative, such as wellbore storage coefficient, penetration ratio, crossflow coefficient, storativity ratio, transmissivity ratio, dimensionless aquifer thickness of anisotropy and skin factor, are analyzed and discussed in detail.