Optimal feedback control for reservoir waterflooding

Waterflooding is a process where water is injected into an oil reservoir to supplement its natural pressure for increment in productivity. The reservoir properties are highly heterogeneous; its states change as production progresses which require varying injection and production settings for economic recovery. As water is injected into the reservoir, more oil is expected to be produced. There is also likelihood that water is produced in association with the oil. The worst case is when the injected water meanders through the reservoir; it bypasses pools of oil and gets produced. Therefore, any effort geared toward finding the optimal settings to maximize the value of this venture can never be over emphasized. Traditional optimal control is an open-loop solution, hence cannot cope with various uncertainties inevitably existing in any practical systems. Reservoir models are highly uncertain. Its properties are known with some degrees of certainty near the well-bore region only. In this work, a novel data-driven approach for control variable (CV) selection was developed and applied to reservoir waterflooding process for a feedback strategy resulting in optimal or near optimal control. The results indicated that the feedback control method was close to optimal in the absence of uncertainty. The loss recorded in the value of performance index, net present value (NPV) was only 0.26%. Furthermore, the new strategy performs better than the open-loop optimal control solution when system/model mismatch was considered. The performance depends on the scale of the uncertainty introduced. A gain in NPV as high as 30.04% was obtained.