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CO2 injection into a saline aquifer crossed by a tectonic fault is studied with coupled fluid mechanics - geomechanics modeling. The simulation approach is based on coupling of the MUFITS reservoir simulator and the FLAC3D mechanical simulator via an in-house API (i.e., an algorithm for data transfer between simulators). MUFITS simulates the non-isothermal multiphase flow of CO2 and brine in rock formation accounting for phase transitions and thermal effects. The modeling workflow is sequential, so that hydrodynamical simulations are carried out at a certain time interval, after which pressure, temperature, and density distributions are passed to FLAC3D, which calculates the equilibrium mechanical state. Computed deformations and stresses are utilized to update the porosity and permeability fields for the subsequent hydrodynamic modeling. In particular, we focus on the tectonic fault and its behavior during CO2 injection. We distinguish the damage zone and core inside the fault and derive the closure relations for their permeability alteration analytically. The coupled approach developed here is applied to simulate CO2 injection into synthetic and realistic reservoir models. For the former one, we study the effect of formation depth and presence of the tectonic stresses at the initial mechanical state, while for the latter, we consider different injection modes (bottomhole pressure). In each numerical experiment, we describe the evolution of the fault permeability due to the slip along its plane and the development of plastic deformations leading to the loss of reservoir integrity and CO2 leakage. Sensitivity analysis of the coupled model to realistic values of input parameters to assess the fault stability is carried out.

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.

We propose a novel approach to data-driven modeling of a transient production of oil wells. We apply the transformer-based neural networks trained on the multivariate time series composed of various parameters of oil wells measured during their exploitation. By tuning the machine learning models for a single well (ignoring the effect of neighboring wells) on the open-source field datasets, we demonstrate that transformer outperforms recurrent neural networks with LSTM/GRU cells in the forecasting of the bottomhole pressure dynamics. We apply the transfer learning procedure to the transformer-based surrogate model, which includes the initial training on the dataset from a certain well and additional tuning of the model's weights on the dataset from a target well. Transfer learning approach helps to improve the prediction capability of the model. Next, we generalize the single-well model based on the transformer architecture for multiple wells to simulate complex transient oilfield-level patterns. In other words, we create the global model which deals with the dataset, comprised of the production history from multiple wells, and allows for capturing the well interference resulting in more accurate prediction of the bottomhole pressure or flow rate evolutions for each well under consideration. The developed instruments for a single-well and oilfield-scale modelling can be used to optimize the production process by selecting the operating regime and submersible equipment to increase the hydrocarbon recovery. In addition, the models can be helpful to perform well-testing avoiding costly shut-in operations.

We describe a stacked model for predicting the cumulative fluid production for an oil well with a multistage-fracture completion based on a combination of Ridge Regression and CatBoost algorithms. The model is developed based on an extended digital field data base of reservoir, well and fracturing design parameters. The database now includes more than 5000 wells from 23 oilfields of Western Siberia (Russia), with 6687 fracturing operations in total. Starting with 387 parameters characterizing each well, including construction, reservoir properties, fracturing design features and production, we end up with 38 key parameters used as input features for each well in the model training process. The model demonstrates physically explainable dependencies plots of the target on the design parameters (number of stages, proppant mass, average and final proppant concentrations and fluid rate). We developed a set of methods including those based on the use of Euclidean distance and clustering techniques to perform similar (offset) wells search, which is useful for a field engineer to analyze earlier fracturing treatments on similar wells. These approaches are also adapted for obtaining the optimization parameters boundaries for the particular pilot well, as part of the field testing campaign of the methodology. An inverse problem (selecting an optimum set of fracturing design parameters to maximize production) is formulated as optimizing a high dimensional black box approximation function constrained by boundaries and solved with four different optimization methods: surrogate-based optimization, sequential least squares programming, particle swarm optimization and differential evolution. A recommendation system containing all the above methods is designed to advise a production stimulation engineer on an optimized fracturing design., Comment: 13 pages, 21 figures, 1 table, preprint submitted to Journal of Petroleum Science & Engineering

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.

Engineering simulators used for steady-state multiphase pipe flows are commonly utilized to predict pressure drop. Such simulators are typically based on either empirical correlations or first-principles mechanistic models. The simulators allow evaluating the pressure drop in multiphase pipe flow with acceptable accuracy. However, the only shortcoming of these correlations and mechanistic models is their applicability. In order to extend the applicability and the accuracy of the existing accessible methods, a method of pressure drop calculation in the pipeline is proposed. The method is based on well segmentation and calculation of the pressure gradient in each segment using three surrogate models based on Machine Learning algorithms trained on a representative lab data set from the open literature. The first model predicts the value of a liquid holdup in the segment, the second one determines the flow pattern, and the third one is used to estimate the pressure gradient. To build these models, several ML algorithms are trained such as Random Forest, Gradient Boosting Decision Trees, Support Vector Machine, and Artificial Neural Network, and their predictive abilities are cross-compared. The proposed method for pressure gradient calculation yields $R^2 = 0.95$ by using the Gradient Boosting algorithm as compared with $R^2 = 0.92$ in case of Mukherjee and Brill correlation and $R^2 = 0.91$ when a combination of Ansari and Xiao mechanistic models is utilized. The method for pressure drop prediction is also validated on three real field cases. Validation indicates that the proposed model yields the following coefficients of determination: $R^2 = 0.806, 0.815$ and 0.99 as compared with the highest values obtained by commonly used techniques: $R^2 = 0.82$ (Beggs and Brill correlation), $R^2 = 0.823$ (Mukherjee and Brill correlation) and $R^2 = 0.98$ (Beggs and Brill correlation).

This work is focused on the development of a dynamic criterion for the arching and bridging of spherical particles in a 3D suspension flow through a channel with plane walls. Elasticity of the particles and the channel walls are taken into account. The carrier fluid is viscous and incompressible. Bridging occurs under the balance of the hydrodynamic force exerted from the fluid on the particles and the friction force exerted from the walls on the particles. The 3D motion of particles in fluid is analyzed by means of direct numerical simulation. The bridging criterion is formulated as a domain on the plane in terms of the two nondimensional parameters: the particle size to channel width ratio and the flow velocity. For each scaled particle diameter there is a range of critical velocities, in which bridging occurs. Various geometrical configurations are considered: three and four particles across the slot. Stability of the bridge is studied. The dynamic bridging criterion is different from the earlier purely kinematic criteria, which were formulated in terms of the particle-to-channel width ratio only. The bridging criterion is implemented into the 2D width-averaged lubrication model of suspension flow through a plane channel, and illustrative simulations are conducted. Application is for proppant transport in hydraulic fractures.