Superposition of steady-state coning solutions for multiple wells with reservoir boundaries

The critical oil (or gas) rate to avoid coning of unwanted fluids into production wells is an important design parameter. Simulation methods are typically used 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 useful to provide benchmark solutions for simulation, but their assumptions are too restrictive for more general use. Thus, there is a need for improved analytical methods to account for well patterns and more complex boundaries that can serve as additional benchmarks for simulation, and in some cases to predict critical rates. aper 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 simultaneous two-phase flow. Capillary pressure and relative permeability effects on coning are included in the new potential function. Vertical equilibrium (VE) and steady-state flow are assumed. isons with finely-gridded 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. The predicted critical rates are conservative for aspect ratios less than 10. The new solutions demonstrate for several examples how the critical rates from one well are affected by reservoir boundaries, and the two-phase production rates of other wells.