The critical oil (or gas) rate to avoid coning of unwanted fluids into production wells is an important design parameter. Simulation methods are useful to predict critical rates in reservoirs with complex heterogeneities and boundaries, but they are manpower intensive and prone to errors when large grid blocks are used. Current analytical methods are quick and easy to use, but their assumptions are too restrictive. Thus, there is a need for improved analytical methods that can account for well patterns and more complex boundaries, and also serve as further benchmarks for simulation.

This paper makes analytical solutions more realistic by extending existing single-well analytical solutions to account for multiple wells and common no-flow and constant pressure boundary conditions. A potential function is derived to superimpose existing single well coning solutions for single-or simultaneous two-phase flow. Capillary pressure and relative permeability effects on coning are included. The only limiting assumptions are vertical equilibrium (VE) and steady-state flow.

Comparisons with simulation show good agreement in predicted critical oil rates when steady state and VE are approached. VE and steady-state are approximately achieved when aspect ratios are greater than about 10. Even when aspect ratios are less than 10, the predicted critical rates are useful in that they are always conservative. The proposed analytical solutions are quick and easy to use compared to reservoir simulation and can be used in the development of downhole water-sink technology (DWS).

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