Boundary Control of the Gas Coning Problem
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This thesis was set to tackle the gas coning problem in oil-rim reservoirs with horizontal wells. The focus was short term production planning in the sub-critical phase only. Different controllers were developed and assessed based on the objective of net-present-value (NPV) of oil produced in the sub-critical phase. The reservoir model is a 1-D partial differential equation describing the dynamics of the gas-oil contact (GOC), for a homogeneous reservoir. Gas coning is considered to be the deformation of the GOC towards the well. Several controllers were developed and assessed alongside control laws from previous research: (i) the Backstepping method was used to develop a state-feedback controller, along with an observer. Coupled they make the Backstepping output-feedback controller. (ii) an output-feedback controller based on the structure proposed by previous research. (iii) linear-quadratic optimal control. An extended Kalman filter was also considered as a state observer, alongside the Backstepping observer. The backstepping controller did not deliver an increase of sub-critical payout which warrants the complicated structure of an observer-controller pair. It was even outperformed by simpler, output-feedback control laws. The optimal linear-quadratic controller achieved the best NPV of sub-critical production by far. This makes it the most attractive control strategy presented, even when considering that a real-world implementation will need to be paired with a state observer.