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.

Investigation of Rupture and Slip Mechanisms of Hydraulic Fractures in Multiple-Layered Formations

SPE Journal ◽  
2019 ◽  
Vol 24 (05) ◽  
pp. 2292-2307 ◽  
Author(s):  
Jizhou Tang ◽  
Kan Wu ◽  
Lihua Zuo ◽  
Lizhi Xiao ◽  
Sijie Sun ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Hydraulic Fracture ◽  
Fracture Propagation ◽  
Propagation Model ◽  
Rock Deformation ◽  
Hydraulic Fractures ◽  
Fracture Geometry ◽  
Fracture Width ◽  
Hydraulic Fracture Propagation ◽  
Fracture Height

Summary Weak bedding planes (BPs) that exist in many tight oil formations and shale–gas formations might strongly affect fracture–height growth during hydraulic–fracturing treatment. Few of the hydraulic–fracture–propagation models developed for unconventional reservoirs are capable of quantitatively estimating the fracture–height containment or predicting the fracture geometry under the influence of multiple BPs. In this paper, we introduce a coupled 3D hydraulic–fracture–propagation model considering the effects of BPs. In this model, a fully 3D displacement–discontinuity method (3D DDM) is used to model the rock deformation. The advantage of this approach is that it addresses both the mechanical interaction between hydraulic fractures and weak BPs in 3D space and the physical mechanism of slippage along weak BPs. Fluid flow governed by a finite–difference methodology considers the flow in both vertical fractures and opening BPs. An iterative algorithm is used to couple fluid flow and rock deformation. Comparison between the developed model and the Perkins–Kern–Nordgren (PKN) model showed good agreement. I–shaped fracture geometry and crossing–shaped fracture geometry were analyzed in this paper. From numerical investigations, we found that BPs cannot be opened if the difference between overburden stress and minimum horizontal stress is large and only shear displacements exist along the BPs, which damage the planes and thus greatly amplify their hydraulic conductivity. Moreover, sensitivity studies investigate the impact on fracture propagation of parameters such as pumping rate (PR), fluid viscosity, and Young's modulus (YM). We investigated the fracture width near the junction between a vertical fracture and the BPs, the latter including the tensile opening of BPs and shear–displacement discontinuities (SDDs) along them. SDDs along BPs increase at the beginning and then decrease at a distance from the junction. The width near the junctions, the opening of BPs, and SDDs along the planes are directly proportional to PR. Because viscosity increases, the width at a junction increases as do the SDDs. YM greatly influences the opening of BPs at a junction and the SDDs along the BPs. This model estimates the fracture–width distribution and the SDDs along the BPs near junctions between the fracture tip and BPs and enables the assessment of the PR required to ensure that the fracture width at junctions and along intersected BPs is sufficient for proppant transport.

The Investigation of Proppant Particle-Fluid Flow in the Vertical Fracture with a Contracted Aperture

SPE Journal ◽  
2021 ◽  
pp. 1-18
Author(s):  
Hai Qu ◽  
Rui Wang ◽  
Xiang Ao ◽  
Ling Xue ◽  
Zhonghua Liu ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Volume Fraction ◽  
Particle Density ◽  
Particle Volume Fraction ◽  
Experimental Results ◽  
Fluid Viscosity ◽  
Flow Conditions ◽  
Particle Volume ◽  
Proppant Transport ◽  
Bed Height

Summary Proppant placement plays a crucial role in maintaining the conductivity of fractures after a hydraulic fracturing treatment. The process involves the transport of particles by fluid flow in complex fractures. Many studies have focused on proppant transport and distribution in the fracture with a constant aperture, but relatively few studies have investigated the proppant-fluid flow in a vertical fracture with a contracted aperture. In this work, we examine experimentally proppant transport in a fracture with a contracted aperture. The objective is to evaluate the distribution of particle beds in the contracted fracture at different flow conditions. In this paper, particle-fluid flow in the contracted fracture is studied experimentally by a laboratory size slot. A planar slot with a constant width is used to benchmark the experimental results, and a published correlation validates the bed equilibrium heights in the planar slot. Six types of particles are chosen to simulate the effects of particle density and size. The proppant distribution is evaluated by the bed height when the bed reaches the equilibrium states. The effects of fluid velocity, fluid viscosity, particle density, particle size, and particle volume fraction on particle distribution are investigated. The results confirm that the proppant particle-fluid flow in the contracted slot is more complicated than that in the planar slot. The phenomena of particle vortices and resuspension were observed at the contraction of the cross-section. The shape on the top of the bed is like a descending stair in which the height gradually decreases in the length direction. The bed height in the contracted slot is lower and more irregular than that in the planar slot at the same flow conditions. Smaller sands injected at a high flow rate and fluid viscosity can form a lower bed. The trend would be reversed by using denser particles and high particle volume fraction. A reliable model expressed by four dimensionless numbers is developed by the linear regression method for predicting the bed equilibrium height. The model and experimental results provide directions to quantitatively evaluate the particle transport and distribution in a fracture with a contracted aperture.

Efficient Modeling of Proppant Transport During Three-Dimensional Hydraulic Fracture Propagation

2021 ◽  
Author(s):  
Jiacheng Wang ◽  
Jon Olson
Keyword(s):  
Particle Size ◽  
Hydraulic Fracture ◽  
Three Dimensional ◽  
Fracture Propagation ◽  
Displacement Discontinuity ◽  
Fluid Viscosity ◽  
Fracture Geometry ◽  
Fracture Width ◽  
Proppant Transport ◽  
Hydraulic Fracture Propagation

Abstract We propose an adaptive Eulerian-Lagrangian (E-L) proppant module and couple it with our simplified three-dimensional displacement discontinuity method (S3D DDM) hydraulic fracture model. The integrated model efficiently calculates proppant transport during three-dimensional (3D) hydraulic fracture propagation in multi-layer formations. The results demonstrate that hydraulic fracture height growth mitigates the form of proppant bed, so the proppant placement is more uniform in the hydraulic fracture under a smaller stress contrast. A higher fracturing fluid viscosity improves the suspension of proppant particles and generates a fracture larger in height and width but shorter in length. Lower proppant density and particle size reduce the proppant settling and create more uniform proppant placements, while they do not affect the hydraulic fracture geometry. Moreover, a larger proppant particle size limits the accessibility of the hydraulic fracture to the proppant, so the larger proppant particles do not fill the fracture tip and edge where the fracture width is small.

Laboratory Experiments in Fracture Propagation

1984 ◽  
Vol 24 (03) ◽  
pp. 256-268 ◽  
Author(s):  
W.L. Medlin ◽  
L. Masse
Keyword(s):  
Hydraulic Fracturing ◽  
Fracture Propagation ◽  
Fluid Viscosity ◽  
Confining Stress ◽  
Fracture Width ◽  
Metal Plates ◽  
Fracture Closure ◽  
Crack Volume ◽  
Aluminum Plates ◽  
Fracturing Experiments

Abstract This paper describes fracturing experiments in dry blocks of various rock materials. The results have application to evaluation of hydraulic fracturing theories. The block dimensions were 3 in.×4 in.×12 in. [7.6 cm×10.2 cm×30.5 cm] with metal plates epoxied to the 3-in.×12-in. [7.6-cm×30.5-cm] faces. Remaining faces were coated with soft epoxy to provide an impermeable jacket. The blocks were loaded in a pressure cell with an upper movable piston bearing on the 3-in.×4-in. [7.6-cm×10.2-cm] faces. A servo-controlled press applied constant stress to these faces higher than a lateral confining stress applied by oil pressure. Fractures were initiated by injection of various fluids into a small notch located on a center plane parallel to the 4-in.×12-in. [10.2-cm×30.5-cm] faces. Fracture growth along the same plane was assured by the stress conditions. Use of these experiments to test theories of fracture propagation required measurement of three variables, fracture width bi, and propagation pressure pi at the notch entrance, and fracture length, L. bi was determined by a capacitance method, and pi was measured directly by a pressure transducer. L was measured by two methods - either ultrasonic signals or pressure pulses generated in miniature cavities. The ultrasonic method confirmed the existence of a Barenblatt liquid-free crack ahead of the liquid front whose relative length decreased with confining stress. The metal plates bonded to the 3-in.×4-in. [7.6-cm×10.2-cm] faces prevented slip at the top and bottom of the fracture, giving a three-dimensional (3D) crack of constant height. However, the bi, pi, and L data followed trends predicted by two-dimensional (2D) (plane strain) elastic theory reasonably well. Fracture closure measurements after shut-in showed an initial period of leakoff-controlled closure and a final period of creep-controlled closure. A pi slope change at the transition is identified with the instantaneous shut-in pressure (ISIP) in field records and is higher than the true confining stress. Introduction Methods of predicting crack dimensions during fracturing operations are essential to proper design of field treatments. Many fracture-propagation theories have been advanced. Contributions have been made by Barenblatt,1 Khristianovitch and Zheltov,4,5 Howard and Fast,6 Perkins and Kern,7 LeTirant and Dupuy,8 Nordgren,9 Geertsma and de Klerk,10 Daneshy,11 and Cleary12,13 among others. However, practical methods of evaluating the theoretical work have been few. Mostly they have been. limited to indirect and generally inconclusive field evaluations. The Sandia mineback experiments14–16 have provided more direct evaluations. However, even here important fracturing parameters are uncontrolled or unknown. This paper describes laboratory-scale hydraulic fracturing experiments that provide critical data for evaluating crack propagation theories. In these experiments we measured the fundamental variables of crack growth under controlled conditions with known fracturing parameters. Experimental Methods All fracturing experiments were carried out in dry blocks 3 in.×4 in.×12 in. [7.6 cm×10.2 cm×30.5 cm] in size. Mesa Verde sandstone and Carthage and Lueders limestone were used as sample materials. Scaling considerations were important. It was necessary to scale down injection rate and leakoff to be consistent with fracture dimensions. The scaling factor of importance was taken to be fluid efficiency, the ratio of crack volume to injected volume. This factor was controlled through appropriate combinations of sample permeability and fracturing fluid viscosity. As fracturing fluids we used thick grease, hydraulic oils of various viscosities, and gelled kerosene (Dowell's YFGO™). Fluid efficiencies ranged from 3 to 70%. Most experiments were conducted at efficiencies between 30 and 50 %, a range typical of most field treatments. Fig. 1 shows the experimental arrangement. Shaped aluminum plates were bonded with Hysol clear epoxy to the 3-in.×12-in. [7.6-cm×30.5-cm] faces of the sample block as shown. The remaining faces were coated with a thin layer of the same epoxy to provide an impermeable jacket for confining pressure. One of the aluminum plates contained an injection port communicating with a 1.4-in. [0.64-cm] borehole as illustrated. A pair of brass plates with faces 0.2 in.×0.5 in. [0.5 cm×1.3 cm] was epoxied into the borehole at its center. These plates, separated by a gap of 0.01 in. [0.025 cm] served as a parallel plate capacitor. They were connected to a capacitance bridge that detected changes in gap width through changes in capacitance. This provided a direct, continuous measurement of fracture width at the borehole.

Simultaneous Multifracture Treatments: Fully Coupled Fluid Flow and Fracture Mechanics for Horizontal Wells

SPE Journal ◽  
2014 ◽  
Vol 20 (02) ◽  
pp. 337-346 ◽  
Author(s):  
Kan Wu ◽  
Jon E. Olson
Keyword(s):  
Fluid Flow ◽  
Fracture Propagation ◽  
Horizontal Wells ◽  
Gas Production ◽  
Propagation Model ◽  
Displacement Discontinuity ◽  
Hydraulic Fractures ◽  
Multiple Fractures ◽  
Frictional Pressure Drop ◽  
Horizontal Wellbore

Summary Successfully creating multiple hydraulic fractures in horizontal wells is critical for unconventional gas production economically. Optimizing the stimulation of these wells will require models that can account for the simultaneous propagation of multiple, potentially nonplanar, fractures. In this paper, a novel fracture-propagation model (FPM) is described that can simulate multiple-hydraulic-fracture propagation from a horizontal wellbore. The model couples fracture deformation with fluid flow in the fractures and the horizontal wellbore. The displacement discontinuity method (DDM) is used to represent the mechanics of the fractures and their opening, including interaction effects between closely spaced fractures. Fluid flow in the fractures is determined by the lubrication theory. Frictional pressure drop in the wellbore and perforation zones is taken into account by applying Kirchoff's first and second laws. The fluid-flow rates and pressure compatibility are maintained between the wellbore and the multiple fractures with Newton's numerical method. The model generates physically realistic multiple-fracture geometries and nonplanar-fracture trajectories that are consistent with physical-laboratory results and inferences drawn from microseismic diagnostic interpretations. One can use the simulation results of the FPM for sensitivity analysis of in-situ and fracture treatment parameters for shale-gas stimulation design. They provide a physics-based complex fracture network that one can import into reservoir-simulation models for production analysis. Furthermore, the results from the model can highlight conditions under which restricted width occurs that could lead to proppant screenout.

scholarly journals Numerical Study of Simultaneous Multiple Fracture Propagation in Changning Shale Gas Field

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1335 ◽  
Author(s):  
Jun Xie ◽  
Haoyong Huang ◽  
Yu Sang ◽  
Yu Fan ◽  
Juan Chen ◽  
...  
Keyword(s):  
Shale Gas ◽  
Fracture Propagation ◽  
Injection Rate ◽  
Propagation Model ◽  
Fluid Viscosity ◽  
Multiple Fracture ◽  
Gas Field ◽  
Fracture Spacing ◽  
Stress Shadow ◽  
Engineering Parameters

Recently, the Changning shale gas field has been one of the most outstanding shale plays in China for unconventional gas exploitation. Based on the more practical experience of hydraulic fracturing, the economic gas production from this field can be optimized and gradually improved. However, further optimization of the fracture design requires a deeper understanding of the effects of engineering parameters on simultaneous multiple fracture propagation. It can increase the effective fracture number and the well performance. In this paper, based on the Changning field data, a complex fracture propagation model was established. A series of case studies were investigated to analyze the effects of engineering parameters on simultaneous multiple fracture propagation. The fracture spacing, perforating number, injection rate, fluid viscosity and number of fractures within one stage were considered. The simulation results show that smaller fracture spacing implies stronger stress shadow effects, which significantly reduces the perforating efficiency. The perforating number is a critical parameter that has a big impact on the cluster efficiency. In addition, one cluster with a smaller perforating number can more easily generate a uniform fracture geometry. A higher injection rate is better for promoting uniform fluid volume distribution, with each cluster growing more evenly. An increasing fluid viscosity increases the variation of fluid distribution between perforation clusters, resulting in the increasing gap between the interior fracture and outer fractures. An increasing number of fractures within the stage increases the stress shadow among fractures, resulting in a larger total fracture length and a smaller average fracture width. This work provides key guidelines for improving the effectiveness of hydraulic fracture treatments.

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.

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.

Propagation, proppant transport and the evolution of transport properties of hydraulic fractures

2018 ◽  
Vol 855 ◽  
pp. 503-534 ◽  
Author(s):  
Jiehao Wang ◽  
Derek Elsworth ◽  
Martin K. Denison
Keyword(s):  
Preferential Flow ◽  
Fluid Pressure ◽  
Fracture Propagation ◽  
Hydraulic Fractures ◽  
Fracture Aperture ◽  
Fluid Viscosity ◽  
Fracture Conductivity ◽  
Proppant Transport ◽  
Fracture Closure ◽  
Proppant Embedment

Hydraulic fracturing is a widely used method for well stimulation to enhance hydrocarbon recovery. Permeability, or fluid conductivity, of the hydraulic fracture is a key parameter to determine the fluid production rate, and is principally conditioned by fracture geometry and the distribution of the encased proppant. A numerical model is developed to describe proppant transport within a propagating blade-shaped fracture towards defining the fracture conductivity and reservoir production after fracture closure. Fracture propagation is formulated based on the PKN-formalism coupled with advective transport of an equivalent slurry representing a proppant-laden fluid. Empirical constitutive relations are incorporated to define rheology of the slurry, proppant transport with bulk slurry flow, proppant gravitational settling, and finally the transition from Poiseuille (fracture) flow to Darcy (proppant pack) flow. At the maximum extent of the fluid-driven fracture, as driving pressure is released, a fracture closure model is employed to follow the evolution of fracture conductivity with the decreasing fluid pressure. This model is capable of accommodating the mechanical response of the proppant pack, fracture closure of potentially contacting rough surfaces, proppant embedment into fracture walls, and most importantly flexural displacement of the unsupported spans of the fracture. Results show that reduced fluid viscosity increases the length of the resulting fracture, while rapid leak-off decreases it, with both characteristics minimizing fracture width over converse conditions. Proppant density and size do not significantly influence fracture propagation. Proppant settling ensues throughout fracture advance, and is accelerated by a lower viscosity fluid or greater proppant density or size, resulting in accumulation of a proppant bed at the fracture base. ‘Screen-out’ of proppant at the fracture tip can occur where the fracture aperture is only several times the diameter of the individual proppant particles. After fracture closure, proppant packs comprising larger particles exhibit higher conductivity. More importantly, high-conductivity flow channels are necessarily formed around proppant banks due to the flexural displacement of the fracture walls, which offer preferential flow pathways and significantly influence the distribution of fluid transport. Higher compacting stresses are observed around the edge of proppant banks, resulting in greater depths of proppant embedment into the fracture walls and/or an increased potential for proppant crushing.

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.

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