Analysis of slug tests in bypassed wells

In Berlin many wells are constructed with an additional small diameter bypass tube flanged on to the large diameter casing and running parallel to the later upward to the surface. The response to a slug test conducted in such a well is usually characterised by significant water level oscillations developing inside the branched pipe system. In the present paper, a general non-linear model is developed for the analysis of slug tests performed in bypassed wells. The model includes skin effects, non-linear head losses due to internal well bore fluid friction, minor losses originating at radius changes along the flow path inside the well, and inertial effects of the water columns contained within the primary casing and the bypass. Pipe flow inside the branched tubing system is described by the one-dimensional conservation law of the mechanical energy of the well bore fluid. Aquifer flow is quantified by a convolution-type approach. The coupled well-aquifer system is governed by an integro-differential equation representing the mean mechanical energy of the total well bore fluid and, coupled to it, by a non-linear ordinary differential equation which accounts for mechanical energy fluctuations between the water columns inside the main casing and the bypass. Both equations are solved by finite difference approximations coupled to point iterative numerical techniques. An application of the model to field data suggests that non-linear hydraulic head losses originating inside the well bore may cause the measured head responses to depend on the initial displacement. A packer used to initiate a slug test can induce these non-linear distortions through the combined effect of minor losses originating at the inlet and the outlet of a small diameter packer flow-through tube and internal fluid friction potentially developing inside that packer passage. As classical linear theories do not allow for the analysis of such phenomena, a model accounting for these non-linear processes should be used if field data show significant dependencies on the initial slug height.