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Engineering simulators used for steady-state multiphase flows in oil and gas wells and pipelines are commonly utilized to predict pressure drop and phase velocities. Such simulators are typically based on either empirical correlations (e.g., Beggs and Brill, Mukherjee and Brill, Duns and Ros) or first-principles mechanistic models (e.g., Ansari, Xiao, TUFFP Unified, Leda Flow Point model, OLGAS). The simulators allow one to evaluate the pressure drop in a multiphase pipe flow with acceptable accuracy. However, the only shortcoming of these correlations and mechanistic models is their applicability (besides steady-state versions of transient simulators such as Leda Flow and OLGA). Empirical correlations are commonly applicable in their respective ranges of data fitting; and mechanistic models are limited by the applicability of the empirically based closure relations that are a part of such models. 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 (ML) 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 application of the above-mentioned ML algorithms and the larger database used for their training will allow extending the proposed methodology to a wider applicability range of input parameters as compared to standard accessible techniques. The method for pressure drop prediction based on ML algorithms trained on lab data 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). Hence, the method for calculating the pressure distribution could give comparable or even higher scores on field data by contrast to correlations and mechanistic models. This fact is an indicator that the model can be scalable from the lab to the field conditions without any additional retraining of ML algorithms.

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This paper is concerned with an analysis of the near tip region of a propagating fluid-driven fracture in a saturated permeable rock. The study attempts to accurately resolve the coupling between the physical processes - rock breakage, fluid pressure drop in the viscous fluid flow in the fracture, and fluid exchange between fracture and the rock - that exert influence on the hydraulic fracture propagation, yet occur over length scales often too small to be efficiently captured in existing coarse grid numerical models. We consider three fluid balance mechanisms: storage in the fracture, pore fluid leak-in from the rock into the fracture as the result of dynamic suction at the dilating crack tip, and fluid leak-off from the fracture into the rock as the fluid pressure in the fracture recovers with distance away from the tip. This process leads to the formation of a pore fluid circulation cell adjacent to the propagating fracture tip. We obtain the general numerical solution for the fracture opening and fluid pressure in the semi-infinite steadily propagating fracture model and fully characterize the solution within the problem parametric space. This allows to identify the parametric regimes of fracture propagation, assess the impact of pore fluid leak-in and the associated near-tip circulation cavity on the solution, and explore limitations of the widely-used, pressure-independent Carter’s leak-off model. The obtained solution can be further used as a tip element in a numerical realization of a solution for a transient growth of a finite fracture (e.g., within the Planar3D approach).

This paper investigates the problem of a radial (or penny-shaped) hydraulic fracture propagating in a permeable reservoir. In particular, we consider the fluid exchange between the crack and ambient porous media as a pressure-dependent process. In most of the existing models, the fluid exchange process is represented as one-dimensional pressure-independent leak-off described by Carter's law. We modify this mechanism by including the dependence of the fluid-exchange rate on the fluid pressure inside the fracture. The proposed approach allows the liquid not only to flow out of the fracture but also to leak-in along the region adjacent to the fracture front. The complete model for hydraulic fracturing involves several physical processes that determine the crack propagation, namely, brittle rock failure, elastic equilibrium of rock, viscous fluid flow inside the fracture channel, and fluid exchange. In order to resolve these phenomena near the fracture front in the numerical scheme, we utilise a special asymptotic multi-scale model for the near-tip region, which is used as a propagation condition for the finite fracture. The main aspect of the analysis is a comparison of fracture characteristics such as aperture profile, radius and others calculated via the proposed model with the results of the radial fracture model that assumes standard pressure-independent fluid exchange mechanism governed by Carter's law. Based on the comparison, we determine parameter ranges, for which the effect of the pressure-dependent fluid exchange mechanism is essential, and, on the other hand, outline zones for which Carter's leak-off model provides accurate results. Finally, by using an approximate solution for the radial fracture with Carter's leak-off, we perform estimates of the effect for the entire parametric space, which allows one to evaluate the influence of the pressure-dependent leak-off for any problem parameters.