An Aquifer-Well Coupled Model: a Refined Implementation of Wellbore Boundary Conditions in Three-Dimensional, Heterogeneous Formations

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Cyr, D. Matthew
Horizontal Well , Pipe Flow , Reynolds Number , Finite Difference , Finite Element , Remediation , Coupled Model , HydroGeoSphere , MODFLOW
This paper presents modifications to two widely used numerical groundwater flow models in an effort to improve upon the interaction between a well of finite length and conductivity with the surrounding formation. The first objective is to discard the common assumptions about flux- or head-based boundary conditions along the well screen by coupling pipe flow hydraulics and groundwater flow. The second objective is to avoid restricting the wellbore hydraulics to a single flow regime. Five flow regimes (laminar through rough-turbulent), based on Reynolds number and pipe roughness, are considered. The modifications are integrated into the highly versatile, well-documented and well-tested models HydroGeoSphere (finite-element/finite-difference) and USGS MODFLOW (finite-difference). Verification of the algorithm and code and is performed by comparing results to: 1) the idealized, analytical Theis solution; 2) the original, unmodified code; and 3) the results of a third party numerical solution that also accounts for variable frictional wellbore losses. Results highlight the inadequacy of either a uniform flux or a uniform head assumption along the wellbore. The solution also tends to produce much steeper hydraulic gradients in those portions of the aquifer nearest the pump intake than have previously been predicted. Systems most affected by in-well hydraulic losses include those for which well screen is long, pumping rate is large, pipe diameter is small, pipe roughness is large (either through design or aging) and aquifer conductivity is high. Improved modeling of the non-linear hydraulic conditions within the well screen can particularly influence the interpretation of wellbore flowmeter and tracer tests, leading to more precise knowledge of the variation of local aquifer hydraulic conductivity along well screens. Aquifer drawdown curves, solute transport and inflow velocities will also be influenced, which can impact capture zones and remediation costs. Given that the solution is incorporated within the HydroGeoSphere and MODFLOW models, it presents the additional advantage over existing approaches of offering a wide range of modeling capabilities, such as three-dimensional flow, arbitrary well inclination and surface-subsurface flow integration.
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