Capacitance resistance models (CRMs) comprise a family of material balance reservoir models that have been applied to primary, secondary and tertiary recovery processes. CRMs predict well flow rates based solely on previously observed production and injection rates, and producers’ bottomhole pressures (BHPs); i.e., a geological model and rock/fluid properties are not required. CRMs can accelerate the learning curve of the geological analysis by providing interwell connectivity maps to corroborate features such as sealing faults and channels, as well as diagnostic plots to determine sweep efficiency and reservoir compartmentalization. Additionally, it is possible to compute oil and water rates by coupling a fractional flow model to CRMs which enables, for example, optimization of injected fluids allocation in mature fields. This literature review covers the spectrum of the CRM theory and conventional reservoir field applications, critically discussing their advantages and limitations, and recommending potential improvements. This review is timely because over the last decade there has been a significant increase in the number of publications in this subject; however, a paper dedicated to summarize them has not yet been presented.

We propose an online adaptive local-global POD-DEIM model reduction method for flows in heterogeneous porous media. The main idea of the proposed method is to use local online indicators to decide on the global update, which is performed via reduced cost local multiscale basis functions. This unique local-global online combination allows (1) developing local indicators that are used for both local and global updates (2) computing global online modes via local multiscale basis functions. The multiscale basis functions consist of offline and some online local basis functions. The approach used for constructing a global reduced system is based on Proper Orthogonal Decomposition (POD) Galerkin projection. The nonlinearities are approximated by the Discrete Empirical Interpolation Method (DEIM). The online adaption is performed by incorporating new data, which become available at the online stage. Once the criterion for updates is satisfied, we adapt the reduced system online by changing the POD subspace and the DEIM approximation of the nonlinear functions. The main contribution of the paper is that the criterion for adaption and the construction of the global online modes are based on local error indicators and local multiscale basis function which can be cheaply computed. Since the adaption is performed infrequently, the new methodology does not add significant computational overhead associated with when and how to adapt the reduced basis. Our approach is particularly useful for situations where it is desired to solve the reduced system for inputs or controls that result in a solution outside the span of the snapshots generated in the offline stage. Our method also offers an alternative of constructing a robust reduced system even if a potential initial poor choice of snapshots is used. Applications to single-phase and two-phase flow problems demonstrate the efficiency of our method.