Controls of wellbore flow regimes on pump effluent composition

Where well water and formation water are compositionally different or heterogeneous, pump effluent composition will vary due to partial mixing and transport induced by pumping. Investigating influences of purging and sampling methodology on composition variability requires quantification of wellbore flow regimes and mixing. As a basis for this quantification, analytical models simulating Poiseuille flow were developed to calculate flow paths and travel times. Finite element modeling was used to incorporate influences of mixing. Parabolic velocity distributions within the screened interval accelerate with cumulative inflow approaching the pump intake while an annulus of inflowing formation water contracts uniformly to displace an axial cylinder of pre-pumping well water as pumping proceeds. Increased dispersive mixing forms a more diffuse formation water annulus and the contribution of formation water to pump effluent increases more rapidly. Models incorporating viscous flow and diffusion scale mixing show that initially pump effluent is predominantly pre-pumping well water and compositions vary most rapidly. After two screen volumes of pumping, 94% of pump effluent is inflowing formation water. Where the composition of formation water and pre-pumping well water are likely to be similar, pump effluent compositions will not vary significantly and may be collected during early purging or with passive sampling. However, where these compositions are expected to be considerably different or heterogeneous, compositions would be most variable during early pumping, that is, when samples are collected during low-flow sampling. Purging of two screen volumes would be required to stabilize the content and collect a sample consisting of 94% formation water.