Semi-analytical homogeneous anisotropic capture zone delineation

We present an algorithm for the quick delineation of capture zones using complex discharge potential. The flow is steady and two-dimensional in a homogeneous domain with anisotropic transmissivity. The procedure accommodates an arbitrary number of injection and extraction wells at any locations throughout the flowfield, as well as regional flow, in the form of a uniform flow component. Capture zones are delineated by finding stagnation points and using a particle tracking scheme to plot separation streamlines along trajectories upgradient or downgradient from the stagnation points as appropriate. Stagnation points are found exactly using a partial fractions expansion. Initial particle tracking directions are determined by evaluating the Hessian matrix of the potential at stagnation points. Streamline tracing is performed using a fourth-order Runge-Kutta particle tracking scheme.