Hierarchical Approach to Identifying Fluid Flow Models in a Heterogeneous Porous Medium

Abstract

A three-dimensional numerical hydrodynamic model fairly accurately describes the processes of developing oil and gas fields, and has good predictive properties only if there are high-quality input data and comprehensive information about the reservoir. However, under conditions of high uncertainty of the input data, measurement errors, significant time and resource costs for processing and analyzing large amounts of data, the use of such models may be unreasonable and can lead to ill-posed problems: either the uniqueness of the solution or its stability is violated. A well-known method for dealing with these problems is regularization or the method of adding some additional a priori information. In contrast to full-scale modeling, currently there is active development of reduced-physics models, which are used, first of all, in conditions when it is required to make an operational decision, and computational resources are limited. One of the most popular simplified models is the material balance model, which makes it possible to directly capture the relationship between reservoir pressure, flow rates and the integral reservoir characteristics. In this paper, it is proposed to consider a hierarchical approach when solving the problem of oil field waterflooding control using material balance models in successive approximations: first for the field as a whole, then for hydrodynamically connected blocks of the field, then for wells. When moving from one level of model detailing to the next, the modeling results from the previous levels of the hierarchy are used in the form of additional regularizing information, which ultimately makes it possible to correctly solve the history matching problem (identification of the filtration model) in conditions of incomplete input information.

Keywords

• filtration
• heterogeneous porous medium
• mathematical model
• material balance equation
• identification
• hierarchical approach