Abstract
A model coupling fluid hydraulics in a borehole with fluid flow in an aquifer is developed in this paper. Conservation of momentum is used to create a one-dimensional steady-state model of vertical flow in an open borehole combined with radially symmetric flow in an aquifer and with inflow to the well through the wellbore screen. Both laminar and turbulent wellbore conditions are treated. The influence of inflow through the wellbore screen on vertical flow in the wellbore is included, using a relation developed by Siwoń (1987). The influence of inflow reduces the predicted vertical variation in head up to 15% compared to a calculation of head losses due to fluid acceleration and the conventional Colebrook-White formulation of friction losses in a circular pipe. The wellbore flow model is embedded into the MODFLOW-2000 ground water flow code. The nonlinear conservation of momentum equations are iteratively linearized to calculate the conductance terms for vertical flow in the wellbore. The resulting simulations agree favorably with previously published results when the model is adjusted to meet the assumptions of the previous coupled models.
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