Optimization of displacement efficiency of oil recovery in porous media using optimal control theory.

摘要

An important issue in reservoir management is the optimization of displacement efficiency in processes where a displacing agent is injected at various wells to displace oil in place. Given a well configuration, the optimization of displacement efficiency should be done by controlling the injection rates. At present, this problem has not been systematically addressed. The objective of this thesis is to investigate the optimization of displacement efficiency by controlling injection rates in a system with a non-symmetric well configuration, due to geometry and/or heterogeneity.;An optimal control methodology is developed for optimizing the displacement efficiency at breakthrough in displacements involving incompressible fluids in 2-D, areal reservoirs with multiple injectors and one producer, where effects of gravity, dispersion and capillarity are neglected. It is found that the optimal injection policy is of the bang-bang type, in which the injection rate takes either a maximum or a minimum value. Numerical and experimental results show that this policy gives better efficiency at breakthrough than a constant-rate injection policy, confirming the theoretical predictions. The results also show that the efficiency improvement depends on the well configuration (it increases as the well configuration becomes more asymmetric), the reservoir heterogeneity (it varies significantly from one realization of permeability field to another), and the mobility ratio (it increases with mobility ratio). We also studied the related "targeted delivery" problem, in which a fluid parcel is steered along a specified trajectory in a porous medium by controlling the flow rates at various wells. An algorithm for specifying flow rates to steer a fluid parcel along a specified trajectory was devised. Numerical results show, however, that the non-uniform flow field, caused by the limited number of wells and/or the reservoir heterogeneity, deforms the shape of the fluid parcel significantly. The reservoir variability leads to a deviation of the actual trajectory from the specified one, which grows with time according to a power-law.