Quantification of non‐Darcian flow observed during packer testing in fractured sedimentary rock

Abstract

High‐precision straddle packer tests were conducted in boreholes in a fractured dolostone aquifer using constant rate injection (Q) step tests to identify the conditions of change from Darcian to non‐Darcian flow on the basis of Q versus the applied head above ambient (dH), where the ambient head represents static conditions. The linear portion, representing Darcian flow, passes through the origin, but after the onset of non‐Darcian flow, there is proportionally less Q per unit dH, and the transmissivity (T) calculated for the test interval using Darcy's law‐based models can be substantially underestimated. Onset of nonlinear flow depends on the test interval length and permeability, typically beginning at injection rates less than 0.5 L min−1 for a relatively transmissive (2 × 10−5 m2 s−1) 1.5 m test interval. In studies of nonlinear flow during pumping tests, the Forchheimer equation is commonly used to describe nonlinear flow near the well using a Q2 versus dH relationship. However, for packer tests in fractured rock, we propose the Darcy‐Missbach equation, which relates Qn to dH, as an alternative equation. While both equations accurately predict the observed dH within the range of flows used, the Darcy‐Missbach exponent (n) describes the degree of deviation from the linear regime; moreover, all calculated exponents were less than 2, implying that the flow is nonlinear but not quadratic in nature. This quantification of the linear to nonlinear flow relations provides for a more accurate identification of the Darcian range, resulting in better T estimates.