Methods and Algorithms for the Solution of Inverse Problems of Modelling and Control in Reservoir Engineering

Abstract

Statement and solution of the problems of modelling and control of hydrodynamic parameters in reservoir engineering are usually associated with insufficiency and/or inaccuracy of the original input data (initial and boundary conditions) and the parameters of filtration equations in porous medium of reservoirs. In such conditions it is necessary to solve the identification problem (machinery monitoring) of the rough specified initial data (initial and boundary conditions), as well as parameters (permeability coefficients) of hydrodynamic models of reservoirs by historical data. This means that the traditional hydrodinamic models, which are formulated as direct initial boundary value problems for the equations of fluid filtration are improperly posed, i.e. small changes in the input data can lead to an arbitrarily large changes in the output. Therefore the models for the control of the field development are formulated as inverse problems and the iterative regularization methods are offered for their solutions. Problem of high dimensionality naturally arises under these statements of the problems of modelling and control, to solve which the multilevel parallel computing technologies based on the hierarchical decomposition combined with the multigrid versions of the methods of splitting by physical processes, spatial and temporal coordinates are offered. Dimension of the problem is even greater increases under development of offshore fields and coastal areas (e.g. in the Arctic) in real-time when it is required to create the integrated simulation models of the complex technological system (reservoir - well - oil and gas collecting network) as a whole.To solve the problems of identification and adaptation of initial and boundary conditions and filtration parameters the iterative regularization methods for direct and inverse problems for the original model equations by historical data are offered. To create the integrated model of the complex technological system as a whole the innovative parallel computing technologies with optimal hierarchical (multilevel) embedding of parallel algorithms into the architecture of multiprocessor computer systems using MPI/OpenMP or OpenCL/CUDA are offered.