The coupling of an enhanced pseudo-3D model for hydraulic fracturing with a proppant transport model
Arthur M. Skopintsev, Egor V. Dontsov, Pavel V. Kovtunenko, Alexey N. Baykin, Sergey V. Golovin
备注：
Although the EP3D model was used in this study, the Planar3D model is a benchmark for engineering simulators that are currently being developed. Authors have understood how to represent the better agreement between results by both models, how to explain results in coupled model in more general sense, so we need to withdraw the manuscript and re-submit it in significantly updated form
This paper presents the coupled model of a hydraulic fracturing and proppant transport. The former is described in terms of enhanced pseudo-3D model that considers height growth across two symmetric stress barriers, while the latter is given by two-dimensional transport model, stemming from the solution of an elliptical equation for fluid pressure and advection equation for the proppant transport. These two sub-modules are solved numerically using implicit time integration in hydraulic part and explicit time stepping in the transport part. In addition to that, interpolation is used to couple the two models with different grids. Results of several numerical simulations are presented for different configurations to demonstrate the interplay between these two modules. In particular, the developed coupled scheme allows us to study phenomena associated with complex fluid flow within the fracture, such as for the case of Saffman-Taylor instability.
The paper presents results of numerical experiments performed to evaluate the effective viscosity of a fluid-proppant mixture, used in hydraulic fracturing. The results, obtained by two complimenting methods (the particle dynamics and the smoothed particle hydrodynamics), coincide to the accuracy of standard deviation. They provide an analytical equation for the dependence of effective viscosity on the proppant concentration, needed for numerical simulation of the hydraulic fracture propagation.
This paper investigates proppant flow and transport in intersected fractures at angles typical for intersections of pre-existing and new hydraulic fractures. Proppant is small granular material, which is placed into hydraulic fractures during geothermal and hydrocarbon reservoir stimulation and props the fluid paths open during reservoir exploitation. This study uses plexiglas laboratory slot experiments enhanced with an advanced image analysis for identifying particle trajectories and quantifying slurry velocities. Although proppant flow and transport has been broadly studied, the effects of …
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 …
Peking University（北京大学）；Peng Cheng Laboratory（鹏城实验室）；Southern University of Science and Technology（南方科技大学）；China University of Geosciences（中国地质大学）
Particle settling in inclined channels is an important phenomenon that occurs during hydraulic fracturing of shale gas production. Generally, in order to accurately simulate the large-scale (field-scale) proppant transport process, constructing a fast and accurate sub-scale proppant settling model, or surrogate model, becomes a critical issue, since mapping between physical parameters and proppant settling velocity is complex. Previously, particle settling has usually been investigated via high-fidelity experiments and meso-scale numerical simulations, both of which are time-consuming. In this…
We present a model of the hydraulic fracturing of heterogeneous poroelastic media. The formalism is an effective continuum model that captures the coupled dynamics of the fluid pressure and the fractured rock matrix and models both the tensile and shear failure of the rock. As an application of the formalism, we study the geomechanical stress interaction between two injection points during hydraulic fracturing (hydrofracking) and how this interaction influences the fracturing process. For injection points that are separated by less than a critical correlation length, we find that the fracturin…
The paper aims to answer the question: if and how non-Newtonian fluids may be compared in their mechanical action when used for hydraulic fracturing? By employing the modified formulation of the PKN problem we obtain its simple analytical solutions in the cases of perfectly plastic and Newtonian fluids. Since the results for shear thinning fluids are intermediate between those for these cases, the obtained equation for the fracture length suggests a criterion of the equivalence of various shear thinning fluids for the problem of hydraulic fractures. We assume fluids equivalent in their hydrofr…
It is usually assumed that hydraulic fracture has two symmetrical wings with respect to the fluid injection point. Hence, authors limit themselves to modelling of one half of the fracture. In our work we demonstrate that the case of a symmetrical fracture occurs only in a homogeneous reservoir with constant physical parameters and confining {\it in situ} stress. Otherwise, inhomogeneity in the stress or the rock permeability can significantly change the dynamics of the fracture propagation. The mathematical model of the hydraulic fracturing used in the paper is adopted from our earlier work \c…
In subterranean coal seam gas CSG reservoirs, massive amounts of small-sized coal fines are released during the production and development stages, especially during hydraulic fracturing stimulation. These coal fines inevitably cause mechanical pump failure and permeability damage due to aggregation and subsequent pore throat blockage. This aggregation behavior is thus of key importance in CSG production and needs to be minimized. Consequently, such coal fines dispersions need to be stabilized, which can be achieved by the formulation of improved fracturing fluids. Here, we thus systematically …
Detailed understanding of the coupling between fluid flow and solid deformation in porous media is crucial for the development biomedical devices and novel energy technologies relating to a wide range of geological and biological processes. Well established models based on poroelasticity theory exist for describing coupled fluid-solid mechanics. However, these models are not adapted to describe systems with multiple fluid phases or 'hybrid-scale' systems containing both solid-free regions and porous matrices. To address this problem, we present a novel computational fluid dynamics approach bas…
Pressurized fluid injection into underground rocks occurs in applications like carbon sequestration, hydraulic fracturing, and wastewater disposal, and may lead to human-induced earthquakes and surface uplift. The fluid injection raises the pore pressure within the porous rocks, while deforming them, yet this coupling is not well understood as experimental studies of rocks are usually limited to postmortem inspection and cannot capture the complete deformation process in time and space. We investigate injection-induced deformation of a unique rock-like transparent medium mimicking the deformat…
Suspension flows are ubiquitous in nature (hemodynamics, subsurface fluid mechanics, etc.) and industrial applications (hydraulic fracturing, CO$_2$ storage, etc.). However, such flows are notoriously difficult to model due to the variety of fluid-particle and particle-particle interactions that can occur. In this work, we focus on non-Brownian shear-dominated suspensions, where kinetic collisions are negligible and frictional effects play a dominant role. Under these circumstances, irreversible phenomena such as particle diffusion and migration arise, requiring anisotropic stress models to de…
