scholarly journals Slurry flow, gravitational settling and a proppant transport model for hydraulic fractures

2014 ◽  
Vol 760 ◽  
pp. 567-590 ◽  
Author(s):  
E. V. Dontsov ◽  
A. P. Peirce
Keyword(s):  
Boundary Layer ◽  
Approximate Solution ◽  
Hydraulic Fracturing ◽  
Transport Model ◽  
Fluid Velocity ◽  
Spherical Particles ◽  
Hydraulic Fractures ◽  
Gravitational Settling ◽  
Proppant Transport ◽  
Two Dimensional Flow

AbstractThe goal of this study is to analyse the steady flow of a Newtonian fluid mixed with spherical particles in a channel for the purpose of modelling proppant transport with gravitational settling in hydraulic fractures. The developments are based on a continuum constitutive model for a slurry, which is approximated by an empirical formula. It is shown that the problem under consideration features a two-dimensional flow and a boundary layer, which effectively introduces slip at the boundary and allows us to describe a transition from Poiseuille flow to Darcy’s law for high proppant concentrations. The expressions for both the outer (i.e. outside the boundary layer) and inner (i.e. within the boundary layer) solutions are obtained in terms of the particle concentration, particle velocity and fluid velocity. Unfortunately, these solutions require the numerical solution of an integral equation, and, as a result, the development of a proppant transport model for hydraulic fracturing based on these results is not practicable. To reduce the complexity of the problem, an approximate solution is introduced. To validate the use of this approximation, the error is estimated for different regimes of flow. The approximate solution is then used to calculate the expressions for the slurry flux and the proppant flux, which are the basis for a model that can be used to account for proppant transport with gravitational settling in a fully coupled hydraulic fracturing simulator.

Numerical Simulation Study of Proppant Transport in Cross Fractures

2022 ◽  
Author(s):  
Cong Lu ◽  
Li Ma ◽  
Jianchun Guo
Keyword(s):  
Hydraulic Fracturing ◽  
Transport Model ◽  
Injection Rate ◽  
Natural Fracture ◽  
Hydraulic Fractures ◽  
Fluid Viscosity ◽  
Natural Fractures ◽  
Fracturing Fluid ◽  
Proppant Transport ◽  
Approach Angle

Abstract Hydraulic fracturing technology is an important means to stimulate unconventional reservoirs, and the placement morphology of proppant in cross fractures is a key factor affecting the effect of hydraulic fracturing. It is very important to study the proppant transport law in cross fractures. In order to study the proppant transportation law in cross fractures, based on the CFD-DEM method, a proppant transport model in cross fractures was established. From the two aspects of the flow field in the fractures and the morphology of the proppant dune, the influence of the natural fracture approach angle, the fracturing fluid viscosity and injection rate on the proppant transport is studied. Based on the principle of hydropower similarity, the conductivity of proppant dune under different conditions is quantitatively studied. The results show that the natural fracture approach angle affects the distribution of proppant and fracturing fluid in natural fractures, and further affects the proppant placement morphology in hydraulic fractures and natural fractures. When the fracturing fluid viscosity is low and the displacement is small, the proppant forms a "high and narrow" dune at the entrance of the fracture. With the increase of the fracturing fluid viscosity and injection rate, the proppant settles to form a "short and wide" placement morphology. Compared with the natural fracture approach angle, the fracturing fluid viscosity and injection rate have a more significant impact on the conductivity of proppant dune. This paper investigated the proppant transportation in cross fractures, and quantitatively analyzes the conductivity of proppant dunes with different placement morphology. The results of this study can provide theoretical guidance for the design of hydraulic fracturing.

Non-isothermal flow of Maxwell fluids above fixed flat plates under the influence of a transverse magnetic field

2011 ◽  
Vol 225 (4) ◽  
pp. 909-916 ◽  
Author(s):  
M M Heyhat ◽  
N Khabazi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Fluid Velocity ◽  
Maxwell Fluid ◽  
Transverse Magnetic ◽  
Deborah Number ◽  
Flat Plates ◽  
Two Dimensional Flow ◽  
Energy Equations

In this article, the magnetohydrodynamic flow and heat transfer of an upper-convected Maxwell fluid is studied theoretically above a flat rigid surface with constant temperature. It is assumed that the Reynolds number of the flow is high enough for boundary layer approximation to be valid. Assuming a laminar, two-dimensional flow above the plate, the concept of stream function coupled with the concept of similarity solution is utilized to reduce the governing equations, which are continuity, momentum, and energy equations, into two ordinary differential equations. The spectral method is used for solving the equations numerically. The effects of magnetic field, and Deborah, Prandtl, and Eckert numbers on the fluid velocity field and heat transfer behaviour are shown in several plots. Obtained results show that fluid velocity can be decreased by increasing the magnetic number while it increases by increasing the Deborah number. Moreover, the thickness of the thermal boundary layer is decreased by increasing the Deborah and Prandtl numbers. It is increased by an increase in the Eckert number.

On the advection of spherical and non-spherical particles in a non-uniform flow

1990 ◽  
Vol 333 (1631) ◽  
pp. 289-307 ◽  
Keyword(s):  
Settling Velocity ◽  
Fluid Velocity ◽  
Added Mass ◽  
Laminar Flows ◽  
Chaotic Advection ◽  
Spherical Particles ◽  
Inertial Effects ◽  
Gravitational Settling ◽  
Regular Motion ◽  
Velocity Gradients

Small spherical particles when introduced into a non-uniform or unsteady flow are usually subject to inertial effects, either of the particle mass or of the fluid added-mass, and the gravitational settling. Small non-spherical particles, even when inertial effects are negligible, turn in response to the local fluid velocity gradients and the settling velocity of a particle varies with its orientation. These features are distinct from the response of lagrangian elements which simply move with the local fluid velocity. In this paper these different responses for small, stokesian particles are considered for some example non-uniform laminar flows. It is noted that this added feature may lead to chaotic particle motion where the motion of lagrangian elements is regular, and conversely regular motion where there is chaotic advection of lagrangian elements.

The coupling of an enhanced pseudo-3D model for hydraulic fracturing with a proppant transport model

2020 ◽  
Vol 236 ◽  
pp. 107177
Author(s):  
A.M. Skopintsev ◽  
E.V. Dontsov ◽  
P.V. Kovtunenko ◽  
A.N. Baykin ◽  
S.V. Golovin
Keyword(s):  
Hydraulic Fracturing ◽  
3D Model ◽  
Transport Model ◽  
Proppant Transport

Modeling of Proppant Distribution During Fracturing of Multiple Perforation Clusters in Horizontal Wells

2021 ◽  
Author(s):  
Konstantin Sinkov ◽  
Xiaowei Weng ◽  
Olga Kresse
Keyword(s):  
Transport Model ◽  
Dynamic Pressure ◽  
Formation Rate ◽  
Network Models ◽  
Fracture Network ◽  
Low Flow ◽  
Hydraulic Fractures ◽  
Fluid Viscosity ◽  
Pumping Rate ◽  
Proppant Transport

Abstract Uniformity of proppant distribution among multiple perforation clusters affects treatment efficiency in multistage fractured wells stimulated using the plug-and-perf technique. Multiple physical phenomena taking place in the well and perforation tunnels can cause uneven proppant distribution among multiple clusters. The problem has been studied in the recent years with experimental and computational fluid dynamics (CFD) methods, which provide useful insights but are impractical for routine designs. Simplified models that incorporated the proppant transport efficiency (PTE) correlation derived from the CFD results in a hydraulic fracture model have been also presented in literature. In this paper, we present a numerical model that simulates the transient proppant slurry flow in the wellbore, considering proppant transport and settling including bed formation, rate- and concentration-dependent pressure drop, PTE, and dynamic pressure coupling with the hydraulic fractures. The model is efficient and is designed to be an independent wellbore transport model so it can be integrated with any fracture models, including fully 3D and/or complex fracture network models, for practical design optimization. The model predictions are compared and found to agree with previously published studies. Parametric studies demonstrate sensitivity of proppant distribution to grain size, fluid viscosity, and pumping rate for fixed perforation designs. Analysis of the simulation results shows that the dominant cause of uneven proppant distribution is proppant inertia. Possible slurry stratification is less important, except for the cases with relatively low flow rates and near toe clusters. Accordingly, proppant distribution is less sensitive to perforation phasing than to the number of perforations in clusters. Alterations of the number of perforations per cluster within a stage enable achieving more even proppant distribution.

Numerical Study on Proppant Transport in Hydraulic Fractures Using a Pseudo-3D Model for Multilayered Reservoirs

SPE Journal ◽  
2021 ◽  
pp. 1-16
Author(s):  
Xi Zhang ◽  
Lifeng Yang ◽  
Dingwei Weng ◽  
Zhen Wang ◽  
Robert G. Jeffrey
Keyword(s):  
Hydraulic Fracture ◽  
Transport Model ◽  
Numerical Study ◽  
Soft Rock ◽  
Injection Pressure ◽  
Field Measurements ◽  
Fracture Plane ◽  
Hydraulic Fractures ◽  
Fracture Aperture ◽  
Proppant Transport

Summary In this paper, we incorporated a kinematic proppant transport model for spherical suspensions in hydraulic fractures developed by Dontsov and Peirce (2014) in a pseudo-3D hydraulic-fracture simulator for multilayered rocks to capture a different proppant transport speed than fluid flow and abridged fracture channel by highly concentrated suspensions. For pressure-driven proppant transport, the bridges made of compact proppant particles can lead to both proppant distribution discontinuity and increased fracture aperture and height because of the higher pressure. The model is applied to growth of a fracture from a vertical well, which can contain thin-bedded intervals and more than one opened hydraulic-fracture interval, because the fracture plane extends in height through layers with contrasts in stress and material properties. Three numerical examples demonstrate that a loss of vertical connectivity can occur among multiple fracture sections, and proppant particles are transported along the more compliant layers. The proppant migration within a narrow fracture in a thin soft rock layer can result in bridging and formation of a proppant plug that strongly limits fluid speed. This generates an increase of injection pressure associated with fracture screenout, and these screenout events can emerge at different places along the fracture. Next, because of the lack of pretreatment geomechanical data, the values of layer stress and leakoff coefficient are adjusted for a field case so that the varying bottomhole pressure and fracture length are in line with the field measurements. This paper provides a useful illustration for hydraulic-fracturing treatments with proppant transport affected by and interacting with reservoir lithological complexities.

Numerical Investigation of Proppant Transport and Placement Along Opened Bedding Interfaces

2021 ◽  
Author(s):  
Jun Xie ◽  
Jizhou Tang ◽  
Sijie Sun ◽  
Yuwei Li ◽  
Yi Song ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Volume Fraction ◽  
Transport Model ◽  
Fluid Velocity ◽  
Fracture Propagation ◽  
Propagation Model ◽  
Fluid Viscosity ◽  
Fracture Width ◽  
Proppant Transport ◽  
Penny Shaped Crack

Abstract Slurry, as a proppant-laden fluid for hydraulic fracturing, is pumped into initial perforated cracks to generate a conductive pathway for hydrocarbon movement. Recently, numerous studies have been done to investigate mechanisms of proppant transport within vertical fractures. However, the distribution of proppant during stimulation becomes much more complicated if bedding planes (BPs), natural fractures (NFs) or other discontinuities pervasively distributed throughout the formation. Thus, how to capture the transport and placement mechanisms of proppant particles in the opened BPs becomes a significant issue. In this paper, we propose a closed-form continuous proppant transport model based on the conservation of total proppant volume and sedimentation of proppant particles. This model enables to integrate with the fluid flow section of a 3-D hydro-mechanical coupled fracture propagation model and then predict the distribution of proppant velocity and slurry volume fraction within a dynamic fracture network. Stokes’ law is applied to determine the sedimentation velocity. In the fracture propagation model, rock deformation is governed by the analytical solution of penny-shaped crack to determine fracture width. Fluid flow is characterized by finite differentiation scheme and then the fluid velocity is obtained. These two parameters above are inputs for the proppant transport model and both slurry viscosity and density are updated in this step. Afterwards, both fracture width and fluid velocity would be altered in the fracture model. Analysis of the proppant distribution within crossing-shaped fracture is conducted to study mechanisms of proppant transport along opened BPs. From our numerical analysis, we find that the distribution of proppant concentration is independent with the fluid viscosity, but highly dependent on the volume fraction of pumping slurry, under a given pumping pressure. Due to the difference of viscosity and proppant volume fraction at locations of upper and lower BPs, we observe that two symmetric BPs are unevenly opened, with different channel length along BP. Moreover, the width of opened upper BP is much smaller than that of opened lower BP as a result of discrepancy of proppant sedimentation. Last but not the least, a criterion of flow bed mobilization is established for dynamically tracking the sedimentation along the BP. Then the effect of different parameters (such as proppant size, proppant density, fluid viscosity, injection rate) on proppant distribution along opened BPs is also studied. Our model fully considers the proppant transport and settlement, proppant bed formation and interaction between fracture and proppant, which helps to predict the influence of proppant during fracturing treatment. Additionally, our model is also capable of dynamically tracking the settlement of proppant along opened BPs.

New Wellbore Proppant Transport Model Improves Prediction of Multiple Fracture Propagation in Horizontal Wells

2021 ◽  
Author(s):  
Konstantin Sinkov ◽  
Kaustubh Shrivastava ◽  
Olga Kresse ◽  
Safdar Abbas ◽  
Egor Knyazev ◽  
...  
Keyword(s):  
Transport Model ◽  
Mutual Influence ◽  
Coupled Model ◽  
Injection Rate ◽  
Diagnostic Methods ◽  
Analytical Models ◽  
Hydraulic Fractures ◽  
Transient Pressure ◽  
Multiple Fractures ◽  
Proppant Transport

Abstract Completion optimization in hydraulic fracturing operations requires understanding the interaction between simultaneously propagating multiple fractures and the distribution of fluid and proppant among the fractures during the treatment. Diagnostic methods often reveal that propagation of fractures within single stage is quite uneven. Nonuniform growth is caused by a complex interplay between fracture mechanics and hydrodynamics of proppant transport in wellbore and perforations. A recently developed numerical model simulates the transient proppant slurry flow in the wellbore, considering proppant transport and settling, including bed formation, fluid rheology, perforation erosion, rate- and concentration-dependent pressure drop, and variable efficiency of proppant transport through perforations. The model is numerically coupled to an advanced fracture simulator that models fracture growth, fluid flow, proppant transport inside complex hydraulic fracture networks, and mechanical interaction between adjacent hydraulic fractures. The coupled model enables comprehensive simulations and captures the mutual influence of the transport of proppant in the wellbore and the propagation of fractures. Integration of the model into the proprietary stimulation-to-production workflow allows leveraging available data and applying the model to optimization of completion strategy and design. The coupled model is shown to agree with the results of analytical models in special limiting cases. It also qualitatively reproduces patterns of proppant distribution observed in the field with the help of various fracturing monitoring techniques. Parametric studies demonstrate that the combined influence of proppant inertia causing higher concentration of proppant in toe clusters, erosion of perforations, and transient pressure response of fractures leads to the nonuniform and transient distribution of the injection rate among fractures. Simulation results show that the nonuniform proppant transport efficiency induced by proppant inertia and broad proppant size distribution can be superposed on the stress shadow effect and lead to the uneven growth of fractures within a stage. The integrated model is efficient and allows routine optimization of fracturing treatment designs. An example of the design optimization illustrating wellbore proppant transport effects on treatment dynamics and showing the value of the coupled wellbore-fractures simulations is also provided.

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