Fluid residence times within a recirculation zone created by an extraction–injection well pair

We present several analytical and semi-analytical solutions to evaluate the fluid residence times within the recirculation zone created by an extraction–injection well pair for several types of flow fields. The flow fields include: a well doublet in the absence of regional flow; an ‘encaged recirculation cell’ where a well doublet is located within and parallel to a uniform regional flow; and a well doublet with arbitrarily oriented uniform regional flow. For a well doublet in the absence of regional flow, we present an analytical solution for all streamlines. For the encaged recirculation cell, the first breakthrough time is solved analytically. We also develop a semi-analytical scheme to evaluate the residence time for any ratio of recirculated flow in a well doublet with arbitrarily oriented uniform regional flow. Both streamlines and travel times in the recirculation zone are strictly symmetric with respect to the midpoint between the two wells. We determine the starting points of streamlines at the well screen for a specific cumulative discharge by an analytical method. Using these starting points in a particle-tracking scheme, one is led directly to the cumulative breakthrough curve at the extraction well. Furthermore, we provide a convenient semi-analytical solution for the average residence time in the recirculation zone. The presented schemes minimize the number of particles that need to be tracked in the construction of breakthrough curves and help to efficiently design recirculation schemes for remediation purposes and to analyze tracer test data obtained in such systems.