Calculation method of proppant embedment depth in hydraulic fracturing

Proppant is one of the key materials used for hydraulic fracturing, directly determining the production of oil and gas wells, which greatly affects the economic benefits. The main function of the proppant is to prop fracture, and create channels with high fracture conductivity for oil and gas to flow through. First, the microscopic arrangement structure of proppant was studied, and the proppant porosity was calculated in different arrangement structures. Second, a proppant embedment model was established based on the elastic-plastic deformation between the proppant partcles and the fracture surface. Third, a fracture conductivity model was established based on various parameters, such as, diameter, concentration, strength, crushing rate, embedment, etc. Finally, the proppant embedment depth was calculated on the basis of the new model, from which predicted values match with the experimental values within an average error of less than 7%. The fracture conductivity was calculated. From a comparison with the experimental values, the average error was less than 6.8%. The calculated proppant embedment depth and fracture conductivity were consistent with the experimental results, which verified the accuracy of the new model. This study is of significance for guiding hydraulic fracturing design.

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Discrete-Element-Method/Computational-Fluid-Dynamics Coupling Simulation of Proppant Embedment and Fracture Conductivity After Hydraulic Fracturing

SPE Journal ◽

10.2118/185172-pa ◽

2017 ◽

Vol 22 (02) ◽

pp. 632-644 ◽

Cited By ~ 34

Author(s):

Fengshou Zhang ◽

Haiyan Zhu ◽

Hanguo Zhou ◽

Jianchun Guo ◽

Bo Huang

Keyword(s):

Fluid Dynamics ◽

Computational Fluid Dynamics ◽

Hydraulic Fracturing ◽

Discrete Element Method ◽

Discrete Element ◽

Particle Assembly ◽

Fracture Conductivity ◽

Shale Formation ◽

Proppant Embedment ◽

Element Method

Summary In this paper, an integrated discrete-element-method (DEM)/computational-fluid-dynamics (CFD) numerical-modeling work flow is developed to model proppant embedment and fracture conductivity after hydraulic fracturing. Proppant with diameter from 0.15 to 0.83 mm was modeled as a frictional particle assembly, whereas shale formation was modeled as a bonded particle assembly by using the bonded-particle model in PFC3D (Itasca Consulting Group 2010). The mechanical interaction between proppant pack and shale formation during the process of fracture closing was first modeled with DEM. Then, fracture conductivity after the fracture closing was evaluated by modeling fluid flow through the proppant pack by use of DEM coupled with CFD. The numerical model was verified by laboratory fracture-conductivity experiment results and the Kozeny-Carman equation. The simulation results show that the fracture conductivity increases with the increase of proppant concentration or proppant size, and decreases with the increase of fracture-closing stress or degree of shale hydration; shale-hydration effect was confirmed to be the main reason for the large amount of proppant embedment.

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Recent Advances in Proppant Embedment and Fracture Conductivity after Hydraulic Fracturing

Petroleum & Petrochemical Engineering Journal ◽

10.23880/ppej-16000135 ◽

2017 ◽

Vol 1 (4) ◽

Author(s):

Zhu HY

Keyword(s):

Hydraulic Fracturing ◽

Fracture Conductivity ◽

Recent Advances ◽

Proppant Embedment

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A Fast Calculation Method for Natural Fractures Activation Considering Stress Shadow and Study on the Law of Natural Fractures Activation State Changes

10.2118/207888-ms ◽

2021 ◽

Author(s):

Yan Qiao ◽

Yang Zhang ◽

Tianhong Jiang ◽

Guobin Zhang ◽

Qing Chen ◽

...

Keyword(s):

Hydraulic Fracturing ◽

Principal Stress ◽

Calculation Method ◽

Maximum Principal Stress ◽

Natural Fractures ◽

Fast Calculation ◽

Fracture Spacing ◽

Stress Shadow ◽

Minimum Principal Stress ◽

Net Pressure

Abstract During hydraulic fracturing process of the Permian Basin in North America, the cluster spacing has been shortened to 3m, and stress shadow can no longer be ignored. Many scholars have studied the influence of stress shadows to optimize cluster spacing. For reservoirs with natural fractures, how to activate more natural fractures through hydraulic fracturing has become the purpose. However, few scholars have studied changes in the activation law of natural fractures under stress shadow conditions. This paper establishes stress change value around single fracture according to Sneddon formula, and calculates the maximum and minimum principal stress according to plane principal stress calculation formula. Considering attenuation of net pressure, stress field of multiple fractures is established, and influence of various factors on stress re-orientation is studied. Finally, considering attenuation of net pressure with distance, according to discriminant formulas of tension & shear activation, the proportion of natural fractures that are easily activated is calculated. By designing orthogonal experiments, the influence of different factors on the proportion of activated natural fractures was studied. The stress increase in the direction of the minimum principal stress is much greater than the increase in the direction of the maximum principal stress. The stress increases in the direction of the maximum principal stress at the tip of the hydraulic fracture. The tip position between hydraulic fractures is "neutralized" due to the superposition of shear stress. Stress-fracture angle and the in-situ stress difference are the common main influencing factors for both tensile and shear activation, but the net pressure has little effect on the tensile activation of natural fracture. The fracture spacing has little effect on the activation of natural fractures. When formulating the fracturing scheme, we should pay more attention to the net pressure rather than the fracture spacing. This article provides a fast calculation method for the activation state of natural fractures considering the stress shadow, which provides a reference index for activating more natural fractures and increasing the production of a single well.

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Shear stiffness of inclined screws in timber–concrete composite beam with timber board interlayer

Advances in Structural Engineering ◽

10.1177/1369433220940814 ◽

2020 ◽

Vol 23 (16) ◽

pp. 3555-3565

Author(s):

Hao Du ◽

Xiamin Hu ◽

Zhixiang Sun ◽

Weijie Fu

Keyword(s):

Calculation Method ◽

Composite Structures ◽

Concrete Slab ◽

Concrete Strength ◽

Shear Stiffness ◽

Composite Beams ◽

Embedment Depth ◽

Practical Applications ◽

Screw Diameter ◽

Timber Board

The timber board interlayer is applied as the formwork for the pouring of concrete slab in various practical applications of timber–concrete composite structures, with the rehabilitation of timber buildings, in particular. At present, there are few studies performed to study the shear stiffness of inclined screws in timber–concrete composite beams with timber board interlayer. In this article, eight groups of shear tests were carried out to study the shear stiffness of inclined screws in timber–concrete composite beams with timber board interlayer. The key parameters included the embedment depth of the screw connector into timber, screw diameter, the thickness of concrete slab, and concrete strength. As indicated by the test results, the shear stiffness of the inclined screws was improved as the embedment depth of screw into timber and screw diameter increased. When the embedded depth of screw into concrete remained unchanged, the thickness of concrete slab and concrete strength exhibited no significant impact on the shear stiffness of inclined crossing screws. On the basis of the theory of a beam on a two-dimensional elastic foundation, the calculation method for predicting the shear stiffness of inclined screw in timber–concrete composite beams with interlayer was proposed. The comparisons demonstrated that the shear stiffness of inclined screw can be well predicted using the calculation method.

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Computation model of proppant embedment depth based on dimensional analysis

Journal of Coal Science and Engineering (China) ◽

10.1007/s12404-013-0407-x ◽

2013 ◽

Vol 19 (4) ◽

pp. 483-487

Author(s):

Cong Lu ◽

Jian-Chun Guo

Keyword(s):

Dimensional Analysis ◽

Embedment Depth ◽

Computation Model ◽

Proppant Embedment

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Study on the evaluation method and influencing factors of fracture conductivity of hydraulic fracturing support in shale reservoir

E3S Web of Conferences ◽

10.1051/e3sconf/202125203049 ◽

2021 ◽

Vol 252 ◽

pp. 03049

Author(s):

Yin Shun-li ◽

Zhuang Tian-lin ◽

Yang Li-yong ◽

Jia Yun-peng ◽

Liu Xue-wei ◽

...

Keyword(s):

Hydraulic Fracturing ◽

Evaluation Method ◽

Guar Gum ◽

Great Influence ◽

Clay Content ◽

Fracturing Fluid ◽

Fracture Conductivity ◽

Shale Reservoir ◽

Shale Reservoirs ◽

Proppant Embedment

The conductivity of supporting fractures is an important parameter to evaluate the hydraulic fracturing effect of shale reservoirs, and its size is affected by many factors. In this paper, the proppant is optimized and evaluated on the basis of real rock slab simulation and actual construction proppant test. The laboratory experimental study on the influence of proppant type, sand concentration, proppant embedding and fracturing fluid residue on propping fracture conductivity is carried out, the results show that the average conductivity of 40 / 70 mesh proppant is about 7.15d · cm at 5kg / m2 sand concentration under the condition of reservoir closure pressure of about 50MPa, which can basically meet the requirements of main fracture conductivity of Kong 2 shale reservoir in Dagang Oilfield; the damage of guar gum fracturing fluid and proppant embedment are two important factors that cause the great decline of conductivity of rock slab, and the damage of guar gum fracturing fluid has a great influence on the conductivity, reaching about 50%; the stronger the mud is (the higher the clay content is), the greater the embedment degree of proppant is, and the greater the loss of conductivity is; for the same lithology, the proppant particle size has little damage to the conductivity, and the sand concentration has a greater impact on the conductivity. The larger the sand concentration is, the smaller the loss of the conductivity is.

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