Type Curves for Two‐Regime Well Flow

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Abstract
Nonequilibrium analytical solutions are presented for fully penetrating wells by incorporating the concept of the existence of a non‐Darcy flow regime around the pumping well and a Darcian flow regime away from the well. For this purpose, an approximate procedure is proposed to find the distance to which the non‐Darcy flow extends. This distance is referred to as the critical well radius, which divides the whole flow domain into nonlinear and linear flow zones with distinctive hydraulic characteristics. The nonlinear flow law is characterized by the Forchheimer equation. Detailed expressions are derived separately for the specific discharge calculations for each zone. Depending on the observation well locations, drawdown distributions and subsequently relevant type curves are developed mathematically for each zone. Various limiting cases are discussed and their physical implications in the practical applications are exposed. In general, linear regime zone type curves converge asymptotically, for large times as well as distances, to the Theis type curve, whereas such a convergence is valid for the nonlinear flow regime, but for small times only.