Study On Optimal Control Of Water Injection And Production For Oil Reservoir Using Reduced-order Model

Optimal control of water injection and production for oil reservoir is one of the ways to efficiently and reasonably exploit oil resources.Optimal control of water injection and production for oil reservoir is performed to calculate the optimal set of well controls to maximize economic profitability through solving the optimal control mathematical model which describes the production process,which can be attributed to solving extremum problems of functional and there is no analytical solution at present.Adjoint-gradient method combined with reservoir numerical simulation technology is the most efficient method by far.However,the calculation process requires major computational resources,which is also a challenge to computer performance.This dissertation proposes a new numerical algorithm for solving the optimal control problem water injection and production for oil reservoir using POD(Proper Orthogonal Decomposition).A reduced-order optimal control methodology for water injection and production for oil reservoir is obtained with the combination of POD based reduced-order model and optimal control model,only a small amount of POD coefficients are considered as optimization variables,which considerably reduces the difficulty and the demand for computational resources.The accuracy of POD basis functions are the key to determine the accuracy of the reduced-order optimal control model,while enough samples are guarantees of sufficient accurate POD basis functions.In order to not only overcome the enormous workload of sample selection due to large amount of injection and production parameters,but also comprehensively capture the dynamic characteristics of the reservoir model,as an alternative,the orthogonal design is used to design the samples selection schemes.For the fact that new POD base functions need to be recalculated due to the new production wells are switched on,an approach with the combination of reduced-order model and reduced-order optimal control methodology is designed to update the original POD base functions.The reduced-order optimal control methodology is improved according to the characteristics of multilayer reservoir.The test results on application examples show that the reduced-order optimal control methodology succeeds in directly solving the optimal control problem of water flooding reservoir,the optimized well controls greatly improves the NPV,and the NPV result approaches closely the result obtained by the adjoint-based gradient methodology,which keeps a difference of no more than 0.25%,this proves the feasibility of the methodology.Besides,increasing the number of grid blocks does not affect the implementation of reduced-order optimal control methodology,which fully reveals the great advantage of the methodology in computational resources.