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.

The Capacitance Resistance Model (CRM) is a fast way for modeling and simulating gas and waterflooding recovery processes, making it a useful tool for improving flood management in real-time. CRM is an input-output and material balance-based model, and requires only injection and production history, which are the most readily available data gathered throughout the production life of a reservoir. In this work, the CRM input-output relationship is explored by representing the CRM with state-space (SS) equations. The linear system SS equations define the relationship between inputs, outputs and states to completely describe system dynamics. The SS-CRM is a multi-input/multi-output (matrix) representation, which provides more insight into reservoir behavior than analyzing performance on a well-by-well basis. Thus, it is computationally faster and easier to apply in fields with large numbers of wells. The CRM parameters are estimated using a grey-box system identification algorithm. The matrix form of the CRM history matching and a sensitivity analysis to the CRM parameters estimates are presented. Minimal realizations and reduced order models are easily obtained with the SS-CRM approach. The performance of three CRM representations are analyzed: integrated (ICRM), producer based (CRMP) and injectorproducer based (CRMIP). The methodology developed here is tested in two reservoir systems, homogeneous with flow barriers and channelized. We find that the ICRM does not reproduce the rate fluctuations as well as the CRMP and CRMIP. The CRMP works well for wells in low heterogeneity regions but not as well as the CRMIP in more heterogeneous areas, e.g. near the flanks of channel deposits. This new approach facilitates closed-loop reservoir management by enabling CRM's use for linear control algorithms, which can improve tracking performance and predictability, and is amenable to real-time optimization.

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Analytical single-well models have been particularly useful in forecasting production rates and estimated ultimate recovery (EUR) for the massive number of wells in unconventional reservoirs. In this work, a physics-based decline-curve model accounting for linear flow and material balance in horizontal multistage-hydraulically-fractured wells is introduced. The main characteristics of pressure diffusion in the porous media and the fact that the reservoir is a limited resource are embedded in the functional form, such that there is a transition from transient to boundary-dominated flow and the EUR is always finite. Analogously to the frequently used Arps (1945) hyperbolic model, the new model has only three parameters, where two of them define the decline profile and the third one is a multiplier. This model is applied to a large data set in a work flow that incorporates heuristic knowledge into the history matching and uncertainty quantification by assigning weights to rate measurements. The heuristic rules aim to lessen the effects of nonreservoir-related variations in the production data (e.g., temporary shut-in caused by fracturing in a neighboring well) and emphasize the reservoir dynamics to perform reliable predictions. However, there are additional degrees of freedom in the way these rules define the values of the weights; therefore, a criterion is established that "calibrates" the uncertainty in the probabilistic models by adjusting the parameters in the heuristic rules. Uncertainty quantification and calibration are performed using a Bayesian approach with hindcasts. This methodology is implemented in an automated framework and applied to 992 gas wells from the Barnett Shale. A comparison with the Arps (1945) hyperbolic model, the Duong (2011) model, and stretched exponential model for this data set shows that the new model is the most conservative in terms of estimated reserves.