Masters Thesis: Oil-Reservoir Flooding Optimization using the Simultaneous Method

Today, oil recovery is often based on reactive control using water flooding. Water is injected to push the oil towards the producing wells until water is being produced, which requires a shutdown of the producing well. This form of production may not yield more than 35% of the oil initially present. A better strategy exists which is based on closed-loop reservoir management (CLRM). CLRM uses a reservoir model which is successively updated and optimized, resulting in a theoretical maximization of the net present value (NPV). The optimization is called flooding optimization. A flooding optimization problem is an optimal control problem based on a non-linear deterministic reservoir model and solved using the sequential method. This method performs a sequential procedure of integration of every ordinary differential equation (ODE) and optimization using a discrete set of control inputs. The main issue of the sequential method is that it cannot deal with state-constraints directly, resulting in solutions which are in practice infeasible. Furthermore, the optimized control input may suffer from chattering1. However, a variance minimization is difficult when using the sequential method. Besides these two issues, the sequential method is a computationally expensive optimization as it performs 30 to 100 ODE integrations. Moreover, implementation of the sequential method may be a laboriously procedure because gradient information has to be pre-programmed manually in the ODE solver. To overcome the issues of the sequential method, a literature study has been conducted which concluded that the simultaneous method should provide a solution. The simultaneous method is used in the chemical industry to solve the issue of handling state-constraints. Besides, the method can be implemented using algebraic modeling, providing automatic discretization support and symbolic differentiation. Although the simultaneous method may provide a solution to the issues of the sequential method, it is known to have several limitations as well. The first limitation is the large non-linear programming (NLP) problem which is obtained due to full discretization in both space and time of all variables and states. The second limitation is that it may be difficult to obtain an initial guess (IG) for all discrete variables, because the IG has to satisfy all constraints. Chattering refers to the optimized non-unique solution to the control input, which causes the input-profile to behave irregularly. Master of Science Thesis L.M.C.F. Alblas