Numerical methods for hydraulic fracture propagation: a review of recent trends

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Digital Design And Computer Architecture

Fluid Mechanics of Hydraulic Fracturing: a Review

Simulation of proppant transport with gravitational settling and fracture closure in a three-dimensional hydraulic fracturing simulator

https://open.library.ubc.ca/media/download/pdf/52383/1.0079344/2

Proppant transport in hydraulic fracturing : crack tip screen-out in KGD and P3D models

Integrated Approach To Simulation Of Near-Wellbore and Wellbore Cleanup

In the framework of a three-fluid approach, a new model of suspension filtration in a porous medium is constructed with account for the formation of a dense packing of trapped particles with finite permeability and porosity. The following three continua are considered: the carrier fluid, the suspended particles, and the deposited particles. For a one-dimensional transient flow of suspension, a system of equations for the concentrations of the suspended and deposited particles, the suspension velocity, and the pressure is constructed. Two cases of the flow in a porous medium are considered: plane and radial. Numerical solution is found using a finite-difference method. Numerical calculations are shown to be in agreement with an analytical solution for the simplest case of filtration with a constant velocity and constant porosity and permeability. A comparison is performed with the classic filtration models for five sets of experimental data on the contamination of a porous sample. It is shown that near the inlet boundary, where an intense deposition of particles takes place, the new model describes the concentration profile of the deposited particles more accurately than the classical model.

Multi-fluid model of suspension filtration in a porous medium

We developed a model for suspension flow in a hydraulic fracture, taking into account frictional rheology to capture the effects of shear-induced particle migration, jamming and transition to close...

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2019.0039

Lubrication model of suspension flow in a hydraulic fracture with frictional rheology for shear-induced migration and jamming.

In this paper we consider the near-tip region of a fluid-driven fracture propagating in permeable rock. We attempt 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 the 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, while assuming that the hydraulic fracturing and pore fluids have the same properties. We fully characterise the solution within the problem parametric space and identify different regimes of the fracture propagation. We assess the impact of the 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 could be potentially used as a tip element in the finite crack models (penny-shaped, Planar3D), provided that a fast numerical implementation is further elaborated.

/pdf/the-near-tip-region-of-a-hydraulic-fracture-with-pressure-1kmztf688n.pdf

The near-tip region of a hydraulic fracture with pressure-dependent leak-off and leak-in

This paper investigates the problem of a radial (or a 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 A 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, we outline the 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 obtain estimates of the effect in the entire parametric space, which allows one to evaluate the influence of the pressure-dependent leak-off for any problem parameters

https://eartharxiv.org/repository/object/274/download/543/

Andrei Osiptsov

Papers

Integrated Approach To Simulation Of Near-Wellbore and Wellbore Cleanup

Multi-fluid model of suspension filtration in a porous medium

Lubrication model of suspension flow in a hydraulic fracture with frictional rheology for shear-induced migration and jamming.

The near-tip region of a hydraulic fracture with pressure-dependent leak-off and leak-in

A radial hydraulic fracture with pressure-dependent leak-off