The ensemble smoother with multiple data assimilation (ES-MDA) has proved to be a powerful assisted history-matching method. The main drawback of ES-MDA is that the inflation factors for damping the changes in model parameters have to be determined before starting the historymatch. Although various authors have provided suggestions for determining the inflation factors adaptively as the history-match proceeds, these methods often result in a large number of data assimilation steps which can make ES-MDA too computationally inefficient for practical application to largescale field problems. Here, we provide a theoretical procedure to determine exactly the minimum inflation factor at each data assimilation step that ensures the discrepancy principle is satisfied. Like previous adaptive ES-MDA methods, this method does not allow one to specify a priori the number of data assimilation steps to be done. Thus, using the exact theoretical procedure as a guide, we provide a practical efficient method for determining the inflation factors which allows one to specify a priori the number of data assimilation steps to be done with ES-MDA which still ensures that the initial inflation factor is chosen so that the discrepancy principle is approximately satisfied.

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Allocation of injection and production by layer is required for several production and reservoir engineering workflows including reserves estimation, water injection conformance, identification of workover and infill drilling candidates, etc. In cases of commingled production, allocation to layers is unknown; running production logging tools is expensive and not always possible. The current industry practice utilizes simplified approaches such as K*H based allocation which provides a static and inaccurate approximation of the allocation factors; this manual approach requires trial and error and can take several weeks in complex fields. This paper presents a novel technique to solve this problem using a combination of reservoir physics and machine learning. The methodology is made up of four stages: Data Entry: includes production at well level (commingled), injection at layer level and injection patterns or a connectivity map (optional) Gross Match: in order to match gross production for each well, the tool solves for time-varying layer-level injection allocation factors using a total material balance equation across all wells. Phase Match: having the allocation factors from the previous step, the tool automatically tunes various petrophysical parameters (i.e. porosity, relative permeability, etc.) in the physics model for each injector-producer pair across all the connected layers to match the oil and water production in each producer. An ensemble of several models can be run simultaneously to account for the probabilistic nature of the problem. Output: The steps 2 and 3 can be performed at pattern level for all connected patterns or for the whole field. The application of the technology in a complex field with 80+ layers in Southern Argentina is demonstrated as a case study of the benefits of the adoption of the technology.