Analytic evaluations of pressure in oil reservoirs with radial multilateral wells

An approximate model is derived for the flow of oil in a reservoir resulting from specified pressure at a horizontal cylindrical well with circular cross-section. This model applies in a limit as the ratios of well radius and reservoir thickness to well length approach zero. Long-time solutions to the resulting model can be found both for a single well and for some symmetric arrangements of multilateral wells, and for both fixed pressure and fixed flow rates, using complex-variable methods.