Vertical Growth of Hydraulic Fractures in Layered Formations

2021 ◽  
Author(s):  
Vibhas J. Pandey ◽  
Vamegh Rasouli
Keyword(s):  
Pressure Distribution ◽  
Solid Mechanics ◽  
High Rate ◽  
Design Parameters ◽  
Hydraulic Fractures ◽  
Vertical Wells ◽  
Wide Range ◽  
Net Pressure ◽  
Fracture Height ◽  
Injection Rates

AbstractFracture growth in layered formations with depth-dependent properties has been a topic of interest amongst researchers because of its critical influence on well performance. This paper revisits some of the existing height-growth models and discusses the evaluation process of a new and modified model developed after incorporating additional constraints.The net-pressure is the primary driver behind fracture propagation and the pressure distribution in the fracture plays an important role in vertical propagation, as it supplies the necessary energy for fracture advancement in the presence of opposing forces. The workflow adopted for this study included developing a preliminary model that solves a system of non-linear equations iteratively to arrive at fracture height versus net pressure mapping. The theoretical results were then compared to those available in the literature. The solution set was then extended to a 100-layer model after incorporating additional constraints using superposition techniques.The predicted outcomes were finally compared to the fracture height observations made in the field on several treatments.A reasonable agreement between model-predicted and observed height was observed when a comparison between the two was made, for most cases.The majority of these treatments were pumped in vertical wells, at low injection rates of up to 8.0 bbl/min (0.021 m3/s) where net pressures were intentionally restricted to 250 psi (1.72 MPa) in order to prevent fracture rotation to the horizontal plane.The leak-off was minimal given the low permeability formations. In some cases, however, the pumping parameters and fluid imparted pressure distribution appeared to dominate. Overall, it was apparent that for a slowly advancing fracture front, which is the case in low injection rate treatments, the fracture height could be predicted with reasonable accuracy. This condition could also be met in high rate treatments pumped down multiple perforation clusters such as in horizontal wells, though fracture-height measurement may not be as straightforward as in vertical wells.The model developed under the current study is suitable for vertical wells where fracture treatments are pumped at low injection rates. The solid-mechanics solution that is presented here is independent of pumping parameters and can be readily implemented to assist in selection of critical design parameters prior to the job, with a wide range of applicability worldwide.

scholarly journals A New Method and Application of Full 3D Numerical Simulation for Hydraulic Fracturing Horizontal Fracture

Energies ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 48 ◽  
Author(s):  
Bing Xu ◽  
Yikun Liu ◽  
Yumei Wang ◽  
Guang Yang ◽  
Qiannan Yu ◽  
...  
Keyword(s):  
Hydraulic Fracturing ◽  
Pressure Distribution ◽  
Three Dimensional ◽  
Initial Pressure ◽  
Fluid Viscosity ◽  
Fracturing Fluid ◽  
Horizontal Fracture ◽  
Initial Fracture ◽  
Net Pressure ◽  
Fracture Height

The numerical simulation of hydraulic fracturing fracture propagation is the core content of hydraulic fracturing design and construction. Its simulation results directly affect the effect of fracturing, and can effectively guide the fracturing construction plan and reduce the construction risk. At present, two-dimensional or quasi-three-dimensional models are mainly used, but most of them are used to simulate the vertical fracture of hydraulic fracturing. There are errors in the application process. In this paper, a three-dimensional mathematical model, including an elastic rock mechanics equation and a material flow continuity equation, is established to simulate horizontal fracture propagation in shallow reservoirs. The emphasis of this paper is to propose a new method for solving equations. The basic idea of the iteration method has been proposed by previous scholars: Firstly, assuming that the initial pressure of each point in the fracture is uniform, the fracture height of each initial point can be obtained by using Equation (20). Using the initial height values, the pressure values at each point of continuous variation are calculated by Equation (16), and then the new fracture height values are obtained by Equation (20). Because of the equal initial pressure, this method leads to too many iterations in the later stages, which makes the calculation more complicated. In this paper, a new Picca iteration method is proposed. The iteration parameters are changed sequentially. Firstly, the distribution value of fracture height is assumed. Then, the pressure distribution value is calculated according to Equation (16). Then, the new distribution value of fracture height is obtained by bringing the obtained pressure distribution value into Equation (20). Then, the new distribution value of the fracture height is calculated according to Equation (16). The pressure distribution value completes an iteration process until the iteration satisfies the convergence condition. In addition, Sneddon’s model is introduced into the hypothesis of fracture height to obtain the maximum fracture height and assume that the initial fracture profile is a parabola. Finally, the proposed method can rapidly improve the convergence rate. Next, on the basis of investigating the solutions of previous equations, the Galerkin finite element method is used to solve the above equations. The new Picard iteration sequence method is applied to solve the height and pressure at different points in the fracture. By calculating the stress intensity factor, we can judge whether the fracture continues to extend or not, and then simulate the full three-dimensional horizontal fracture of the hydraulic fracturing expansion process. The infiltration process of three types of oil reservoirs in Daqing Changyuan oilfield is simulated. The results show that during the initial fracture stage, the radius and height of fractures increase rapidly, and the rate of increase slows down with the increase of construction time. The height and net pressure of each point in the fracture are unequal. The height and net pressure of the fracture in the wellbore reach the maximum, and gradually decrease to the front of the fracture. Compared with conventional fracturing, the fracturing-flooding percolation process has the characteristics of short fracture-making and large vertical percolation distance, which can greatly increase the swept volume of flooding fluid and thus enhance oil recovery. With the increase in the rock modulus of elasticity, the radius of fractures decreases and the height of fractures increases. With the increase in construction displacement, the radius of fractures hardly changes, the height of fractures increases, and the vertical infiltration distance of the fractures increases. It is suggested that the construction displacement should be 4.0 m3/min. In the range of fracturing fluid viscosity in the studied block, with the change of fracturing fluid viscosity, the change of fracture radius and height is not obvious. In order to further increase sweep volume, the fracturing fluid viscosity should be further reduced.

Role of Turbulent Flow in Generating Short Hydraulic Fractures with High Net Pressure in Slickwater Treatments

2015 ◽  
Author(s):  
Brandon C. Ames ◽  
Andrew P. Bunger
Keyword(s):  
Fluid Flow ◽  
Turbulent Flow ◽  
Flow Regime ◽  
Flow Model ◽  
High Rate ◽  
Hydraulic Fractures ◽  
Fracture Length ◽  
Wellbore Pressure ◽  
Net Pressure ◽  
Shale Reservoirs

Abstract This paper provides an argument for considering turbulent flow for hydraulic fracturing using slickwater in shale reservoirs. It shows that the tendency of models that assume laminar fluid flow to over-predict fracture length and under-predict net pressure can be corrected by instead recognizing that the flow regime is turbulent for high rate, water-driven hydraulic fractures. Firstly, we provide a rationale supporting the appropriateness of assuming turbulent flow. Then, using a Perkins-Kern-Nordgren (PKN) fracture model and parameters similar to slickwater treatments in shale reservoirs, we show that the laminar flow model overpredicts fracture length and underpredicts fracture width and net pressure, compared to the turbulent flow model. The result, if indeed a hydraulic fracture grows in the turbulent fluid flow regime, is that matching the length with the laminar model requires input of an unreasonably large leak-off coefficient, resulting in an exacerbation of the underprediction of the wellbore pressure. On the other hand, the turbulent model is shown to be able, in principle, to account for short, high pressure hydraulic fractures without resorting to inflating the leak-off coefficient or compromising the calibration of the model to the wellbore pressure.

A Different Perspective on the Forchheimer and Ergun Equations

SPE Journal ◽  
2016 ◽  
Vol 21 (05) ◽  
pp. 1501-1507 ◽  
Author(s):  
Deming Mao ◽  
John M. Karanikas ◽  
Phillip S. Fair ◽  
Ionut D. Prodan ◽  
George K. Wong
Keyword(s):  
Shale Gas ◽  
Reynolds Numbers ◽  
High Rate ◽  
Hydraulic Fractures ◽  
Focused Attention ◽  
Inertia Effect ◽  
Forchheimer Equation ◽  
Wide Range ◽  
Converging Flow ◽  
Fixed Beds

Summary The need to better estimate the performance of hydraulically fractured wells in shale-gas formations has focused attention on the description of the non-Darcy flow in the region of the hydraulic fracture near the borehole where the converging flow may be increasingly dominated by the inertia effect. The analogy between high-rate flow in proppant-filled hydraulic fractures—best described by the Forchheimer equation—and the flow of reactants in fixed beds or granular beds in catalysis—widely described by the Ergun equation—may offer insights on how to estimate the value of the coefficient β across the complete range of velocities (or, equivalently, Reynolds numbers). In this paper, we show that, although the value of β varies over a wide range depending on the porosity (ϕ) and permeability (K) of the porous medium, the value of the product βK is confined in the range of 10−5 to 10−4 m, and a correlation is obtained with narrower uncertainty compared with published ones.

Sustaining Research-Based Practices in Reading

1999 ◽  
Vol 20 (5) ◽  
pp. 263-287 ◽  
Author(s):  
Janette K. Klingner ◽  
Sharon Vaughn ◽  
Marie Tejero Hughes ◽  
Maria Elena Arguelles
Keyword(s):  
Instructional Practices ◽  
High Rate ◽  
Strategic Reading ◽  
School Year ◽  
Wide Range ◽  
Sustained Use ◽  
Development Experience ◽  
Collaborative Strategic Reading ◽  
Research Based Practices ◽  
Over Time

This study examined the extent to which the reading instructional practices learned by a cohort of teachers who participated in an intensive, yearlong professional development experience during the 1994-1995 school year have been sustained and modified over time. Teachers learned three multileveled practices—partner reading, collaborative strategic reading, and making words—that promote gains in reading for students from a wide range of achievement levels. Teachers were observed and interviewed 3 years later to determine the extent to which they continued to implement the practices, the ways in which they modified them, and factors that influenced their sustained use of the practices. With the exception of one teacher, all the teachers sustained one or more of the three practices at a high rate.

scholarly journals Multi-stable composite twisting structure for morphing applications

2012 ◽  
Vol 468 (2141) ◽  
pp. 1230-1251 ◽  
Author(s):  
X. Lachenal ◽  
P. M. Weaver ◽  
S. Daynes
Keyword(s):  
Analytical Model ◽  
Material Properties ◽  
Degrees Of Freedom ◽  
Design Parameters ◽  
Engineering Structures ◽  
The Past ◽  
Wide Range ◽  
Morphing Structure ◽  
Low Mass ◽  
Unstable States

Conventional shape-changing engineering structures use discrete parts articulated around a number of linkages. Each part carries the loads, and the articulations provide the degrees of freedom of the system, leading to heavy and complex mechanisms. Consequently, there has been increased interest in morphing structures over the past decade owing to their potential to combine the conflicting requirements of strength, flexibility and low mass. This article presents a novel type of morphing structure capable of large deformations, simply consisting of two pre-stressed flanges joined to introduce two stable configurations. The bistability is analysed through a simple analytical model, predicting the positions of the stable and unstable states for different design parameters and material properties. Good correlation is found between experimental results, finite-element modelling and predictions from the analytical model for one particular example. A wide range of design parameters and material properties is also analytically investigated, yielding a remarkable structure with zero stiffness along the twisting axis.

scholarly journals Influence of Thermodynamic Effect on Blade Load in a Cavitating Inducer

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Kengo Kikuta ◽  
Noriyuki Shimiya ◽  
Tomoyuki Hashimoto ◽  
Mitsuru Shimagaki ◽  
Hideaki Nanri ◽  
...  
Keyword(s):  
Pressure Distribution ◽  
Liquid Nitrogen ◽  
Cavity Length ◽  
Cold Water ◽  
Pressure Rise ◽  
Cavitation Number ◽  
Design Parameters ◽  
Trailing Edge ◽  
Thermodynamic Effect ◽  
Blade Tip

Distribution of the blade load is one of the design parameters for a cavitating inducer. For experimental investigation of the thermodynamic effect on the blade load, we conducted experiments in both cold water and liquid nitrogen. The thermodynamic effect on cavitation notably appears in this cryogenic fluid although it can be disregarded in cold water. In these experiments, the pressure rise along the blade tip was measured. In water, the pressure increased almost linearly from the leading edge to the trailing edge at higher cavitation number. After that, with a decrease of cavitation number, pressure rise occurred only near the trailing edge. On the other hand, in liquid nitrogen, the pressure distribution was similar to that in water at a higher cavitation number, even if the cavitation number as a cavitation parameter decreased. Because the cavitation growth is suppressed by the thermodynamic effect, the distribution of the blade load does not change even at lower cavitation number. By contrast, the pressure distribution in liquid nitrogen has the same tendency as that in water if the cavity length at the blade tip is taken as a cavitation indication. From these results, it was found that the shift of the blade load to the trailing edge depended on the increase of cavity length, and that the distribution of blade load was indicated only by the cavity length independent of the thermodynamic effect.

Closed-Form Correlation of Buildings Energy Use With Key Design Parameters Calibrated Using a Genetic Algorithm

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Raed I. Bourisli ◽  
Adnan A. AlAnzi
Keyword(s):  
Genetic Algorithm ◽  
Closed Form ◽  
Energy Use ◽  
Building Design ◽  
Office Buildings ◽  
Design Parameters ◽  
Wide Range ◽  
Variable Function ◽  
Real Coded Genetic Algorithm ◽  
The Difference

This work aims at developing a closed-form correlation between key building design variables and its energy use. The results can be utilized during the initial design stages to assess the different building shapes and designs according to their expected energy use. Prototypical, 20-floor office buildings were used. The relative compactness, footprint area, projection factor, and window-to-wall ratio were changed and the resulting buildings performances were simulated. In total, 729 different office buildings were developed and simulated in order to provide the training cases for optimizing the correlation’s coefficients. Simulations were done using the VisualDOE TM software with a Typical Meteorological Year data file, Kuwait City, Kuwait. A real-coded genetic algorithm (GA) was used to optimize the coefficients of a proposed function that relates the energy use of a building to its four key parameters. The figure of merit was the difference in the ratio of the annual energy use of a building normalized by that of a reference building. The objective was to minimize the difference between the simulated results and the four-variable function trying to predict them. Results show that the real-coded GA was able to come up with a function that estimates the thermal performance of a proposed design with an accuracy of around 96%, based on the number of buildings tested. The goodness of fit, roughly represented by R2, ranged from 0.950 to 0.994. In terms of the effects of the various parameters, the area was found to have the smallest role among the design parameters. It was also found that the accuracy of the function suffers the most when high window-to-wall ratios are combined with low projection factors. In such cases, the energy use develops a potential optimum compactness. The proposed function (and methodology) will be a great tool for designers to inexpensively explore a wide range of alternatives and assess them in terms of their energy use efficiency. It will also be of great use to municipality officials and building codes authors.

Application areas of the angle reflector

2021 ◽  
pp. 54-59
Author(s):  
L. R. Yurenkova ◽  
O. A. Yakovuk ◽  
I. V. Morozov
Keyword(s):  
Radio Wave ◽  
Outer Space ◽  
Road Transport ◽  
Optical Systems ◽  
Design Parameters ◽  
Design Activity ◽  
Primary Role ◽  
Beam Laser ◽  
Wide Range ◽  
Graphical Calculation

The article provides examples of how the device known as the «angle reflector» a few decades ago has been increasingly used in various fields of science and technology in recent years. Angle reflectors are designed to change (reflect) optical and radar rays in the direction, opposite to the original direction. At present, angle reflectors are widely used to ensure the safety of road transport on dangerous road sections. Radio wave reflectors have the same design as optical ones; therefore, in radio detection and location, angle reflectors are used to send warning signals to ship radars on bridge supports, beacons and buoys. Modern angle reflectors attached to meteorological probes allow determining the direction and speed of the wind at high altitude, which is especially important in the study of the outer space. In recent years, devices have been developed to improve the accuracy of radar stations calibration. The examples of graphical calculation of angle reflectors presented in the article clearly demonstrate the primary role of geometry in the design activity of an engineer. The graphical calculation is based on the theoretical positions of projective geometry. The design and calculation of optical systems is carried out by the graphoanalytic method, since only with a combination of graphical and analytical methods it is possible to accurately calculate the course of a light beam, laser, or radio wave and thereby determine the design parameters of the devices. The article focuses on a graphical method for calculating two types of angle reflectors using orthogonal projection, due to which modern engineers will be able to create more up-to-date designs of optical systems with a wide range of applications.

Airbag Inflators

1999 ◽  
Author(s):  
William G. Broadhead ◽  
D. Theodore Zinke
Keyword(s):  
High Speed ◽  
Motor Vehicle ◽  
Seat Belt ◽  
Design Parameters ◽  
Steering Wheel ◽  
Instrument Panel ◽  
Highway Traffic ◽  
National Highway Traffic Safety ◽  
Column Collapse ◽  
Wide Range

Abstract The design of an airbag restraint system presents a classic engineering challenge. There are numerous design parameters that need to be optimized to cover the wide range of occupant sizes, occupant positions and vehicle collision modes. Some of the major parameters that affect airbag performance include, the airbag inflator characteristics, airbag size and shape, airbag vent size, steering column collapse characteristics, airbag cover characteristics, airbag fold pattern, knee bolsters, seat, seat belt characteristics, and vehicle crush characteristics. Optimization of these parameters can involve extremely costly programs of sled tests and full scale vehicle crash tests. Federal Motor Vehicle Safety Standards (FMVSS) with regard to airbag design are not specific and allow flexibility in component characteristics. One design strategy, which is simplistic and inexpensive, is to utilize a very fast, high output gas generator (inflator). This ensures that the bag will begin restraining the occupant soon after deployment and can make up for deficiencies in other components such as inadequate steering column collapse or an unusually stiff vehicle crush characteristic. The use of such inflators generally works well for properly positioned occupants in moderate to high-speed frontal collisions by taking advantage of the principle of ridedown. When an airbag quickly fills the gap between the occupant and the instrument panel or steering wheel it links him to the vehicle such that he utilizes the vehicle’s front-end crush to help dissipate his energy, thus reducing the restraint forces. Unfortunately, powerful airbag systems can be injurious to anyone in the path of the deploying airbag. This hazard is present for short statured individuals, out of position children or any occupant in a collision that results in extra ordinary crash sensing time. Currently, the National Highway Traffic Safety Administration (NHTSA) is proposing to rewrite FMVSS 208 to help reduce such hazards.

Development of a Methodology for Model Testing of Utor Welded Joints of a Vertical Cylindrical Tank

2021 ◽  
pp. 21-27
Author(s):  
D.A. Neganov ◽  
◽  
A.E. Zorin ◽  
O.I. Kolesnikov ◽  
G.V. Nesterov ◽  
...  
Keyword(s):  
Welded Joints ◽  
Strain State ◽  
Welded Joint ◽  
Design Parameters ◽  
Cylindrical Tank ◽  
Stress Strain ◽  
The Real ◽  
Stress Strain State ◽  
Hydraulic Machines ◽  
Wide Range

The methodology of laboratory modeling of the loading of utor welded joint of the tank is presented. The methodology is based on testing of the special design sample. It allows under uniaxial tension on the typical servo-hydraulic machines to reproduce in the zone of a utor welded joint the combined action of bending and shear forces, similar to that which occurs during the operation of a vertical cylindrical tank. To assess the distribution of the stress-strain state in the proposed design of the sample under its loading, the finite element modeling was performed in the ANSYS software package. It showed the fundamental correspondence of the stress distribution in the zone of the utor node in the sample and in the real tank. The experimental studies consisted in carrying out tests for the durability of a series of 16 samples loaded with the maximum force in the cycle, causing the calculated stresses in the zone of the welded utor node in the range of 100–200 % from the maximum permissible ones. The obtained results showed that the maximum loaded zone, where the destruction of the samples occurred, is the near-seam zone of the utor welded joint on the inside of the tank. This corresponds to the statistics of the real tank failures. It is established that the developed methodology ensures the possibility of carrying out correct resource tests of the tank utor welded joints. It is also possible to vary the stress-strain state scheme within a wide range in the area of the utor welded joint by changing the design parameters of the test sample. In compliance with the regulated welding technologies and the absence of unacceptable defects in the welded joint, the utor node has a high resource, which significantly exceeding 50 years of the tank operation.

Sign in / Sign up

Export Citation Format

Share Document