Revised productivity index equation to improve transient history match for the Capacitance Resistance Model

Pan, Zhong
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The Capacitance Resistance Model (CRM) is a data-driven reservoir model developed for well surveillance and management. The model is gaining popularity in reservoir engineering community because of its simplicity and ability to provide insights on well-to-well connectivity during water/gas flooding project. Furthermore, the model can be used to optimize injection scheme or even plan for infill drilling. The model was built on the assumptions that during waterflooding the dominant flow regime is semi-steady state. However, to extend the functionality of this model to unconventional reservoirs, a productivity index model that works well in transient flow regime should be investigated. In this thesis, two different productivity models are proposed. The first is the combined productivity index model. This model originates from the analytical solution of single compartment model and the constant behavior of the productivity index in fracture-dominated flow. These two components are then linearly combined to form a new productivity index model. The second is the logistic productivity index model, which uses a well-studied logistic growth model to capture the S-shaped production profile starting from a transient linear flow regime to a late-time fracture-dominated regime. These two proposed productivity index models are incorporated into the fundamental CRM equation, respectively, to derive the logistic CRM and combined CRM. To validate the models, multiple reservoir simulations were conducted to generate synthetic cases capturing both transient linear flow and fracture-dominated regime, and then the proposed models were fitted to the simulation data using Microsoft Excel Solver. Case validation is also accomplished with field data. Very good history matches were obtained from these two models, and they demonstrate that with proper revision to semi-steady state model CRM is able to match production history sufficiently and quickly. In addition, the combined CRM is physics-based so it is shown that the model is able to provide insights on some important reservoir properties.