A Proxy Flow Modelling Workflow to Estimate Gridded Dynamic Properties and Well Production Rates by Deep Learning Algorithms
Authors: Chaki Soumi , Zagayevskiy Yevgeniy , Wong Terry 
Published: October 2021

Abstract
This paper proposes a deep learning-based framework for proxy flow modeling to predict gridded dynamic petroleum reservoir properties (like pressure and saturation) and production rates for wells in a single framework. It approximates the solution of a full physics-based numerical reservoir simulator, but runs much more rapidly, allowing users to generate results for a much wider range of scenarios in a given time than could be done with a full physics simulator. The proxy can be used for reservoir management tasks like history matching, uncertainty quantification, and field development optimization. A deep-learning based methodology for accurate proxy-flow modeling is presented which combines U-Net (a variant of convolutional neural network) to predict gridded dynamic properties and deep neural network (DNN) models to forecast well production rates.
First, gridded dynamic properties, such as reservoir pressure and phase saturations, are predicted from static properties like reservoir rock porosity and absolute permeability using a U-Net. Then, the static properties and the dynamic properties predicted by the U-Net are input to a DNN to predict production rates at the well perforations. The inclusion of U-net predicted pressure and saturations improves the quality of the well rate predictions.
The proposed methodology is presented with the synthetic Brugge reservoir discretized into grid blocks. The U-Net input consists of three properties: dynamic gridded reservoir properties (such as pressure or fluid saturation) at the current state, static gridded porosity, and static gridded permeability. The U-Net has only one output property, the target gridded property (such as pressure or saturation) at the next time step. Training and testing datasets are generated by running 13 full physics flow simulations and dividing them in a 12:1 ratio. Nine U-Net models are calibrated to predict pressures/saturations, one for each of the nine grid layers present in the Brugge model. These outputs are then concatenated to obtain the complete pressure/saturation model for all nine layers. The constructed U-Net models match the distributions of generated pressures/saturations of the numerical reservoir simulator with a correlation coefficient value of approximately 0.99 and above 95% accuracy. The DNN models approximate well production rates accurately from U-Net predicted pressures and saturations along with static properties like transmissibility and horizontal permeability. For each well and each well perforation, the production rate is predicted with the DNN model. The use of the constructed proxy flow model generates reservoir predictions within a few minutes compared to the hours or days typically taken by a full physics flow simulator.
The direct connection that is established between the gridded static and dynamic properties of the reservoir and well production rates using U-Net and DNN models has not been presented previously. Using only a small number of runs for its training, the workflow matches the numerical reservoir simulator results with reduced computational effort. This helps reservoir engineers make informed decisions more quickly, resulting in more efficient reservoir management.