A. L. Vainshtein

E. A. Kanin, A. A. Garipova, S. A. Boronin et al.

We propose a new method for construction of the absolute permeability map consistent with the interpreted results of well logging and well test measurements in oil reservoirs. Nadaraya-Watson kernel regression is used to approximate two-dimensional spatial distribution of the rock permeability. Parameters of the kernel regression are tuned by solving the optimization problem in which, for each well placed in an oil reservoir, we minimize the difference between the actual and predicted values of (i) absolute permeability at the well location (from well logging); (ii) absolute integral permeability of the domain around the well and (iii) skin factor (from well tests). Inverse problem is solved via multiple solutions to forward problems, in which we estimate the integral permeability of reservoir surrounding a well and the skin factor by the surrogate model. The last one is developed using an artificial neural network trained on the physics-based synthetic dataset generated using the procedure comprising the numerical simulation of bottomhole pressure decline curve in reservoir simulator followed by its interpretation using a semi-analytical reservoir model. The developed method for reservoir permeability map construction is applied to the available reservoir model (Egg Model) with highly heterogeneous permeability distribution due to the presence of highly-permeable channels. We showed that the constructed permeability map is hydrodynamically similar to the original one. Numerical simulations of production in the reservoir with constructed and original permeability maps are quantitatively similar in terms of the pore pressure and fluid saturations distribution at the end of the simulation period. Moreover, we obtained an good match between the obtained results of numerical simulations in terms of the flow rates and total volumes of produced oil, water and injected water.

A. D. Morozov, D. O. Popkov, V. M. Duplyakov et al.

Growing amount of hydraulic fracturing (HF) jobs in the recent two decades resulted in a significant amount of measured data available for development of predictive models via machine learning (ML). In multistage fractured completions, post-fracturing production analysis reveals that different stages produce very non-uniformly due to a combination of geomechanics and fracturing design factors. Hence, there is a significant room for improvement of current design practices. The workflow is essentially split into two stages. As a result of the first stage, the present paper summarizes the efforts into the creation of a digital database of field data from several thousands of multistage HF jobs on wells from circa 20 different oilfields in Western Siberia, Russia. In terms of the number of points (fracturing jobs), the present database is a rare case of a representative dataset of about 5000 data points. Each point in the data base contains the vector of 92 input variables (the reservoir, well and the frac design parameters) and the vector of production data, which is characterized by 16 parameters, including the target, cumulative oil production. Data preparation has been done using various ML techniques: the problem of missing values in the database is solved with collaborative filtering for data imputation; outliers are removed using visualisation of cluster data structure by t-SNE algorithm. The production forecast problem is solved via CatBoost algorithm. Prediction capability of the model is measured with the coefficient of determination (R^2) and reached 0.815. The inverse problem (selecting an optimum set of fracturing design parameters to maximize production) will be considered in the second part of the study to be published in another paper, along with a recommendation system for advising DESC and production stimulation engineers on an optimized fracturing design.