Step-drawdown tests and the Forchheimer equation

Step‐drawdown tests (SDTs) typically involve pumping a well at a constant rate until a quasi‐steady state (QSS) is observed in the drawdown response. The well is then pumped at a higher constant rate until a new QSS is achieved. The process is repeated for additional flow rates. Analysis involves plotting the QSS drawdowns against their corresponding ion rates and fitting a nonlinear empirical expression. A commonly used expression, the so‐called Jacob method, contains a linear “formation loss” coefficient, A, and a nonlinear “well loss” coefficient, B. In this paper, an analytical formula is derived relating B to the Forchheimer parameter. The efficiency of the Forchheimer equation for simulating SDTs is demonstrated through four case studies. Quantitative guidance is given as to when the Jacob method can be used as an accurate alternative to numerical simulation of the Forchheimer equation. Finally, the four corresponding estimates of field‐scale Forchheimer parameter are implicitly compared to those obtained from smaller scale laboratory experiments. Unfortunately, the comparison remains implicit due to uncertainty associated with quantifying effective well radius and aquifer formation thickness for the SDTs.