Optimal Stimulation of Oil Production

A single thin oil-bearing stratum has constant thickness and is surrounded by a circular impermeable boundary. This circle C contains a domain D_o which is filled with oil, the rest is filled with water. The permeabilities for oil and for water are taken to be the same.This stratum is pierced by several (vertical) wells one of which is a producer and intersects the oil domain D_o, the others intersect C outside D_o and are used for water injection.We consider several problems concerning the control and optimization of the production by controlling the flow rates into and out of the various wells with a view to optimizing the net present value of oil produced or certain other relevant objective functions.Following these deterministic optimization problems we allow for the considerable uncertainty in reservoir description by considering a stochastic scenario. The results are represented as probability distribution curves for the NPV and for total production. We also compute an efficient frontier analogous to the efficient frontier in portfolio management.