Evaluation of Fracture Asymmetry of Finite-Conductivity Fractured Wells

Nearly all commercial hydraulic fracture design models are based on the assumption that a single fracture is initiated and propagated identically and symmetrically about the wellbore, i.e., the fracture growth and proppant transport occurs symmetrically with respect to the well. However, asymmetrical fractures have been observed in hundreds of hydraulic fracturing treatments and reported to be a more realistic outcome of hydraulic fracturing. The asymmetry ratio (length of short fracture wing divided by length of long wing) influenced the production rate adversely. In the worst case, the production rate could be reduced to that of an unfractured well. Several authors observed asymmetrically propagated hydraulic fractures in which one wing could be ten times longer than the other. Most pressure transient analysis techniques of hydraulically fractured wells assume the fracture is symmetric about the well axis for the sake of simplicity in developing mathematical solution. This study extends the work by Rodriguez to evaluate fracture asymmetry of finite-conductivity fracture wells producing at a constant-rate. The analysis presented by Rodriguez only involves the slopes of the straight lines that characterize the bilinear, linear and radial flow from the conventional Cartesian and semilog plots of pressure drop versus time. This study also uses the Tiab’s direct synthesis (TDS) technique to analyze the linear and bilinear flow regimes in order to find the asymmetry factor of the fractured well. With the fracture conductivity estimated from the bilinear flow region, dimensionless fracture conductivity and the asymmetry ratio are calculated. A technique for estimating the fracture asymmetry ratio from a graph is presented. An equation relating the asymmetry ratio and dimensionless fracture conductivity is also presented. This equation assumes that the linear and/or bilinear flow regime is observed. However, using the TDS technique, the asymmetry ratio can be estimated even in the absence of bilinear or linear flow period. It is concluded that the relative position of the well in the fracture, i.e., the asymmetry condition, is an important consideration for the fracture characterization. A log-log plot of pressure derivative can be used to estimate the fracture asymmetry in a well intersected with a finite-conductivity asymmetric fracture. The analysis using pressure derivative plot does not necessarily require the radial flow period data to calculate the asymmetric factor.

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New Analytical Approach to Operational Assessment of Fractured Well Productivity with Variable Permeability

10.2118/206652-ms ◽

2021 ◽

Author(s):

Evgeniy Viktorovich Yudin ◽

George Aleksandrovich Piotrovskiy ◽

Maria Vladimirovna Petrova ◽

Alexey Petrovich Roshchektaev ◽

Nikita Vladislavovich Shtrobel

Keyword(s):

Hydraulic Fracturing ◽

Hydraulic Fracture ◽

Free Parameter ◽

Numerical Solutions ◽

Analytical Models ◽

Productivity Index ◽

Finite Conductivity ◽

Well Productivity ◽

Fracture Conductivity ◽

Variable Permeability

Abstract Requirements of targeted optimization are imposed on the hydraulic fracturing operations carried out in the conditions of borderline economic efficiency of fields taking into account geological and technological features. Consequently, the development of new analytical tools foranalyzing and planning the productivity of fractured wells, taking into account the structuralfeatures of the productive reservoir and inhomogeneous distribution of the fracture conductivity, is becoming highly relevant. The paper proposes a new approach of assessing the vertical hydraulic fracture productivityin a rectangular reservoir in a pseudo-steady state, based on reservoir resistivity concept described in the papers of Meyer et al. However, there is a free parameter in the case of modeling the productivity of a hydraulic fracture by the concept. The parameter describes the distribution of the inflow along the plane of the fracture. This paper presents a systematic approach to determining of the parameter. The resulting model allows to conduct an assessment of the influence of various complications in the fracture on the productivity index. During the research a method of determining the free parameter was developed,it was based on the obtained dependence of the inflow distribution on the coordinate along the fracture of finite conductivity. The methodology allowed to refine existent analytical solution of the Meyer et al. model, which, in turn, allowed to assess the influence of different fracture damages in the hydraulic fracture on the productivity index of the well. The work includes the cases of the presence of fracture damages at the beginning and at the end of the fracture. A hydraulic fracture model was built for each of the types of damages, it was based on the developed method, and also the solution of dimensionless productivity ratio was received. The results of the obtained solution were confirmed by comparison with the numerical solutions of commercial simulators and analytical models available in the literature. The advantage of the methodology is the resulting formulas for well productivity are relatively simple, even for exotic cases ofvariable conductivity fractures. The approaches and algorithms described in the paper assume the calculation of the productivity of a hydraulic fracture with variable conductivity and the presence of other complicatingfactors.The methodology of the paper can be used for analysis and diagnosis problems with formation hydraulic fracturing. The efficiency of the calculations allows using the presented methodology to solve inverse problems of determining the efficiency of the hydraulic fracturing operation.

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Pressure Transient Performance for a Horizontal Well Intercepted by Multiple Reorientation Fractures in a Tight Reservoir

Energies ◽

10.3390/en12224232 ◽

2019 ◽

Vol 12 (22) ◽

pp. 4232 ◽

Cited By ~ 1

Author(s):

Guoqiang Xing ◽

Shuhong Wu ◽

Jiahang Wang ◽

Mingxian Wang ◽

Baohua Wang ◽

...

Keyword(s):

Horizontal Well ◽

Flow Behavior ◽

Flow Equation ◽

Finite Conductivity ◽

Transient Pressure ◽

Pressure Derivative ◽

Fracture Conductivity ◽

Fracture Spacing ◽

Economic Production ◽

Tight Reservoir

A fractured horizontal well is an effective technology to obtain hydrocarbons from tight reservoirs. In this study, a new semi-analytical model for a horizontal well intercepted by multiple finite-conductivity reorientation fractures was developed in an anisotropic rectangular tight reservoir. Firstly, to establish the flow equation of the reorientation fracture, all reorientation fractures were discretized by combining the nodal analysis technique and the fracture-wing method. Secondly, through coupling the reservoir solution and reorientation fracture solution, a semi-analytical solution for multiple reorientation fractures along a horizontal well was derived in the Laplace domain, and its accuracy was also verified. Thirdly, typical flow regimes were identified on the transient-pressure curves. Finally, dimensionless pressure and pressure derivative curves were obtained to analyze the effect of key parameters on the flow behavior, including fracture angle, permeability anisotropy, fracture conductivity, fracture spacing, fracture number, and fracture configuration. Results show that, for an anisotropic rectangular tight reservoir, horizontal wells should be deployed parallel to the direction of principal permeability and fracture reorientation should be controlled to extend along the direction of minimum permeability. Meanwhile, the optimal fracture number should be considered for economic production and the fracture spacing should be optimized to reduce the flow interferences between reorientation fractures.

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Experimental Investigation of Seepage Mechanism on Oil-Water Two-Phase Displacement in Fractured Tight Reservoir

Geofluids ◽

10.1155/2022/6792154 ◽

2022 ◽

Vol 2022 ◽

pp. 1-13

Author(s):

Xuyang Zhang ◽

Jianming Zhang ◽

Cong Xiao

Keyword(s):

Hydraulic Fracturing ◽

Water Content ◽

Production Rate ◽

Oil Recovery ◽

Hydraulic Fractures ◽

Fracture System ◽

Two Phase ◽

Phase Displacement ◽

Before And After ◽

Oil Water

As a type of unconventional oil and gas resources, tight sandstone reservoir has low permeability and porosity properties and thus is commonly necessary to develop through hydraulic fracturing treatment. Due to the coexistence of natural fractures and induced hydraulic fractures, the heterogeneity of reservoir permeability becomes severe and therefore results in complicated fluid seepage mechanism. It is of significance to investigate the oil-water two-phase seepage mechanics before and after the hydraulic fracturing stimulation with the aim of supporting the actual production and development of oilfield. This paper experimentally investigated the influences of fracture system on seepage characteristics of two-phase displacement in sample cores of fractured tight sandstones. In details, the changes of injection rate, cumulative production rate, recovery ratio, and water content were analyzed before and after the hydraulic fracturing treatments. To further analyze the displacement characteristics of the sample core, the displacement indices of four rock samples in different displacement stages were investigated. The sensitivity of sample core displacement indices to many key factors, including injection time, oil production rate, oil recovery factor and injection multiple factor, and moisture (i.e., water content was 95%, 98%, and 99.5%, respectively), before and after the hydraulic fracturing treatments were obtained synthetically. Besides, the relationship between recovery difference and contribution of fracture to permeability was explored at different water contents. The experimental results reveal that the fracture system shortens the water-free production period and hence reduces the recovery rate. The greater the contribution of fractures to permeability, the lower the recovery of water during this period.

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Influence of Finite Hydraulic-Fracture Conductivity on Unconventional Hydrocarbon Recovery With Horizontal Wells

SPE Journal ◽

10.2118/187947-pa ◽

2017 ◽

Vol 22 (06) ◽

pp. 1790-1807 ◽

Cited By ~ 1

Author(s):

Deming Mao ◽

David S. Miller ◽

John M. Karanikas ◽

Ed A. Lake ◽

Phillip S. Fair ◽

...

Keyword(s):

Hydraulic Fracturing ◽

Horizontal Wells ◽

Normal Derivative ◽

Unconventional Reservoirs ◽

Analytical Models ◽

Hydraulic Fractures ◽

Multiple Fractures ◽

Hydraulic Stimulation ◽

Fracture Conductivity ◽

Hydrocarbon Recovery

Summary The classic plots of dimensionless fracture conductivity (CfD) vs. equivalent wellbore radius or equivalent negative skin are useful for evaluating the performance of hydraulic fractures (HFs) in vertical wells targeting conventional reservoirs (Prats 1961; Cinco-Ley and Samaniego-V. 1981). The increase in well productivity after hydraulic stimulation can be estimated from the “after fracturing” effective wellbore radius or from the “after fracturing” equivalent negative skin. However, this earlier work does not apply to the case of horizontal wells with multiple fractures. A revision of the diagnostic plots is needed to account for the combination of the resulting radial-flow regime and the transient effect in unconventional reservoirs with ultralow permeability. This paper reviews and extends this earlier work with the objective of making it applicable in the case of horizontal wells with multiple fractures. It also demonstrates practical application of this new technique for fracture-design optimization for horizontal wells. The influence of finite fracture conductivity (FC) on the HF flow efficiency is evaluated through analytical models, and it is confirmed by a 3D transient numerical-reservoir simulation. This work demonstrates that a redefined dimensionless fracture conductivity for horizontal wells CfD,h = 4 is found to be optimal by use of the maximum of log-normal derivative (subject to economics) for HFs in horizontal wells, and this value of CfD,h can provide 50% of the fracture-flow efficiency and 90% of the estimated ultimate recovery (EUR) that would have been obtained from an infinitely conductive fracture for the same production period. This new master plot can provide guidance for hydraulic-fracturing design and its optimization for hydrocarbon recovery in unconventional reservoirs through hydraulic fracturing in horizontal wells.

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Non-Darcy Flow in Wells With Finite-Conductivity Vertical Fractures

Society of Petroleum Engineers Journal ◽

10.2118/8281-pa ◽

1982 ◽

Vol 22 (05) ◽

pp. 681-698 ◽

Cited By ~ 42

Author(s):

K.H. Guppy ◽

H. Cinco-Ley ◽

H.J. Ramey ◽

F. Samaniego-V.

Keyword(s):

Hydraulic Fracturing ◽

Turbulent Flow ◽

High Flow ◽

Darcy Flow ◽

Finite Conductivity ◽

Gas Wells ◽

Fracture Conductivity ◽

Flow Rates ◽

Vertical Fracture ◽

Constant Rate

Abstract Several methods have been proposed in the literature for analyzing drawdown data for the determination of fracture conductivity of vertically fractured wells. These techniques have paved accurate, but in some cases the fracture conductivity calculated is much smaller than anticipated. This study shows that producing fractured wells at high flow rates will cause nondarcy effects in the fracture, resulting in a pessimistic fracture conductivity.Numerical and semianalytical models were developed to analyze the unsteady flow behavior of finite conductivity fractures producing at high flow rates. Two methods are presented for determining the true fracture conductivity when drawdown data are available at two different flow rates. The amount of turbulent effects also is quantified by the techniques. Examples are presented to illustrate the solution methods. Introduction The increasing use of hydraulic fracturing as a means of improving the productivity of oil and gas wells in low-permeability formations has resulted in many research efforts aimed at increasing fracturing capabilities as well as evaluating the characteristics of the fracture in the postfracturing period. With the advent of the massive postfracturing period. With the advent of the massive hydraulic fracturing (MHF) treatment in recent years, the need for new solutions for evaluating these systems has increased. The problem with the older solutions was the need for many assumptions to arrive at a simple solution. One of the more common assumptions made in these systems was the use of linear flow to describe the flow within the fracture. In gas wells with finite-conductivity fractures producing at high flow rates, the non-Darcy effect is created within the fracture. Hence, new solutions must be developed for these systems. The objective of this paper is to present a new semianalytical solution to this problem that can be applied both to the linear and to the nondarcy flow regimes within the fracture.Over the years. several methods have been developed to analyze postfracture data. Gringarien et al. first solved the fracture system analytically for three special cases: infinite-conductivity vertical fracture, uniform flux vertical fracture, and horizontal fracture. At that time, its application became quite useful. But since not all systems behaved in this manner, the need for further solutions was warranted. Cinco-L. et al. investigated the general case of finite-conductivity vertical fractures, which included the above solution. as well as fracture conductivities as low as 0.1. This research also led to the need to analyze short-time data to obtain unique solutions. Similar results were obtained by Agarwat et al., who presented a finite-difference solution to this problem, considering both the constant rate as well as the problem, considering both the constant rate as well as the constant pressure cases.One of the first papers written on the effects of non-Darcy flow in fractured systems was by Wattenbarger and Ramey. They investigated the effects of non-Darcy flow in the formation and concluded that these effects cannot be felt if the fracture is long or intermediate in size. They further concluded that the effects of turbulent flow within the fracture were more significant.Holditch and Morse investigated the effect of turbulent flow in a fracture and analyzed the transient behavior of specific conductivities (low, medium, and high), giving a qualitative approach to the solution. They stressed the need for greater detail on these solutions and showed that there was indeed a large reduction in the fracture conductivity when non-Darcy flow was included. Although Holditch and Morse gave a detailed descriptive insight into the flow regime problem, they did not develop any general methods for determining the actual conductivity of the fracture. SPEJ P. 681

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Laboratory Testing of Fracture Conductivity Damage by Foam-Based Fracturing Fluids in Low Permeability Tight Gas Formations

Energies ◽

10.3390/en14061783 ◽

2021 ◽

Vol 14 (6) ◽

pp. 1783

Author(s):

Klaudia Wilk-Zajdel ◽

Piotr Kasza ◽

Mateusz Masłowski

Keyword(s):

Hydraulic Fracturing ◽

Guar Gum ◽

Polymer Concentration ◽

Laboratory Research ◽

Damage Effect ◽

Tight Gas ◽

Fracturing Fluid ◽

Fracture Conductivity ◽

Fracturing Fluids ◽

Sandstone Rock

In the case of fracturing of the reservoirs using fracturing fluids, the size of damage to the proppant conductivity caused by treatment fluids is significant, which greatly influence the effective execution of hydraulic fracturing operations. The fracturing fluid should be characterized by the minimum damage to the conductivity of a fracture filled with proppant. A laboratory research procedure has been developed to study the damage effect caused by foamed and non-foamed fracturing fluids in the fractures filled with proppant material. The paper discusses the results for high quality foamed guar-based linear gels, which is an innovative aspect of the work compared to the non-foamed frac described in most of the studies and simulations. The tests were performed for the fracturing fluid based on a linear polymer (HPG—hydroxypropyl guar, in liquid and powder form). The rheology of nitrogen foamed-based fracturing fluids (FF) with a quality of 70% was investigated. The quartz sand and ceramic light proppant LCP proppant was placed between two Ohio sandstone rock slabs and subjected to a given compressive stress of 4000–6000 psi, at a temperature of 60 °C for 5 h. A significant reduction in damage to the quartz proppant was observed for the foamed fluid compared to that damaged by the 7.5 L/m3 natural polymer-based non-foamed linear fluid. The damage was 72.3% for the non-foamed fluid and 31.5% for the 70% foamed fluid, which are superior to the guar gum non-foamed fracturing fluid system. For tests based on a polymer concentration of 4.88 g/L, the damage to the fracture conductivity by the non-foamed fluid was 64.8%, and 26.3% for the foamed fluid. These results lead to the conclusion that foamed fluids could damage the fracture filled with proppant much less during hydraulic fracturing treatment. At the same time, when using foamed fluids, the viscosity coefficient increases a few times compared to the use of non-foamed fluids, which is necessary for proppant carrying capacities and properly conducted stimulation treatment. The research results can be beneficial for optimizing the type and performance of fracturing fluid for hydraulic fracturing in tight gas formations.

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Numerical simulation of the laws of fracture propagation of multi-hole linear co-directional hydraulic fracturing

Energy Exploration & Exploitation ◽

10.1177/0144598721988993 ◽

2021 ◽

pp. 014459872198899

Author(s):

Weiyong Lu ◽

Changchun He

Keyword(s):

Hydraulic Fracturing ◽

Hydraulic Fracture ◽

Minimum Principle ◽

Fracture Propagation ◽

Axial Direction ◽

Rock Breaking ◽

Hydraulic Fractures ◽

Directional Hydraulic Fracturing ◽

Fracture Intersection ◽

Expansion Stage

Directional rupture is one of the most important and most common problems related to rock breaking. The goal of directional rock breaking can be effectively achieved via multi-hole linear co-directional hydraulic fracturing. In this paper, the XSite software was utilized to verify the experimental results of multi-hole linear co-directional hydraulic fracturing., and its basic law is studied. The results indicate that the process of multi-hole linear co-directional hydraulic fracturing can be divided into four stages: water injection boost, hydraulic fracture initiation, and the unstable and stable propagation of hydraulic fracture. The stable expansion stage lasts longer and produces more microcracks than the unstable expansion stage. Due to the existence of the borehole-sealing device, the three-dimensional hydraulic fracture first initiates and expands along the axial direction in the bare borehole section, then extends along the axial direction in the non-bare hole section and finally expands along the axial direction in the rock mass without the borehole. The network formed by hydraulic fracture in rock is not a pure plane, but rather a curved spatial surface. The curved spatial surface passes through both the centre of the borehole and the axial direction relative to the borehole. Due to the boundary effect, the curved spatial surface goes toward the plane in which the maximum principal stress occurs. The local ground stress field is changed due to the initiation and propagation of hydraulic fractures. The propagation direction of the fractures between the fracturing boreholes will be deflected. A fracture propagation pressure that is greater than the minimum principle stress and a tension field that is induced in the leading edge of the fracture end, will aid to fracture intersection; as a result, the possibility of connecting the boreholes will increase.

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Performance Evaluation of Enzyme Breaker for Fracturing Applications under Simulated Reservoir Conditions

Molecules ◽

10.3390/molecules26113133 ◽

2021 ◽

Vol 26 (11) ◽

pp. 3133

Author(s):

Yuling Meng ◽

Fei Zhao ◽

Xianwei Jin ◽

Yun Feng ◽

Gangzheng Sun ◽

...

Keyword(s):

Hydraulic Fracturing ◽

Shear Resistance ◽

Ammonium Persulfate ◽

Fracturing Fluid ◽

Medium Temperature ◽

Fracture Conductivity ◽

Wide Range ◽

Reservoir Conditions ◽

Alkaline Conditions ◽

Resistance Performance

Fracturing fluids are being increasingly used for viscosity development and proppant transport during hydraulic fracturing operations. Furthermore, the breaker is an important additive in fracturing fluid to extensively degrade the polymer mass after fracturing operations, thereby maximizing fracture conductivity and minimizing residual damaging materials. In this study, the efficacy of different enzyme breakers was examined in alkaline and medium-temperature reservoirs. The parameters considered were the effect of the breaker on shear resistance performance and sand-suspending performance of the fracturing fluid, its damage to the reservoir after gel breaking, and its gel-breaking efficiency. The experimental results verified that mannanase II is an enzyme breaker with excellent gel-breaking performance at medium temperatures and alkaline conditions. In addition, mannanase II did not adversely affect the shear resistance performance and sand-suspending performance of the fracturing fluid during hydraulic fracturing. For the same gel-breaking result, the concentration of mannanase II used was only one fifth of other enzyme breakers (e.g., mannanase I, galactosidase, and amylase). Moreover, the amount of residue and the particle size of the residues generated were also significantly lower than those of the ammonium persulfate breaker. Finally, we also examined the viscosity-reducing capability of mannanase II under a wide range of temperatures (104–158 °F) and pH values (7–8.5) to recommend its best-use concentrations under different fracturing conditions. The mannanase has potential for applications in low-permeability oilfield development and to maximize long-term productivity from unconventional oilwells.

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On the scattering behaviour of bullet-rosette and bullet-shaped ice crystals

Annales Geophysicae ◽

10.1007/s00585-996-0566-9 ◽

1996 ◽

Vol 14 (5) ◽

pp. 566-573

Author(s):

B. Strauss

Keyword(s):

Ray Tracing ◽

Ice Crystals ◽

Asymmetry Factor ◽

Model Calculations ◽

Geometrical Features ◽

The Asymmetry ◽

Particle Length ◽

Phase Functions ◽

Tracing Method ◽

Factor G

Abstract. The scattering behaviour of bullet-rosette and bullet-shaped ice particles is investigated using model calculations (ray tracing method) with special emphasis on the asymmetry factor g. Because the variability of the geometrical features of these particles is very large, some representative shapes are used in the calculations. The model is based on geometrical optics, and particles are assumed to be oriented randomly; a wavelength of 0.56 μm is considered; absorption is neglected. The scattering behaviour of bullet rosettes is compared to that of single branches out of the bullet rosette. It turns out that there are slight differences in the asymmetry factor values, depending on the lengths of the branches (∆g~0.02) and on the angles between the branches (∆g~0.01). Bullets show some special features in their phase functions due to the pyramid. The length of the particle influences the asymmetry factor (∆g~0.10), as does the shape of the pyramid (∆g~0.07). The influence of the pyramidal shape decreases with increasing particle length. Bullets were compared to hexagonally shaped columns. This was done for two columns, one as long as the columnar part of the bullet (length without pyramid), and one for a column as long as the bullet including the pyramid. Asymmetry factor values of bullets with a pyramidal angle of 28° deviate less than ∆g~0.01 from the range given by the two values of the columns.

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Comparison of Bone-Conducted Vibration for Eliciting Ocular Vestibular-Evoked Myogenic Potentials

Otolaryngology ◽

10.1177/0194599811425884 ◽

2011 ◽

Vol 146 (2) ◽

pp. 289-294 ◽

Cited By ~ 33

Author(s):

Chia-Chen Tseng ◽

Shou-Jen Wang ◽

Yi-Ho Young

Keyword(s):

Prospective Study ◽

Study Design ◽

Healthy Subjects ◽

University Hospital ◽

Vestibular Evoked Myogenic Potentials ◽

Ménière’S Disease ◽

Asymmetry Ratio ◽

Significant Difference ◽

The Asymmetry ◽

The Right

Objective. This study compared bone-conducted vibration (BCV) stimuli at forehead (Fz) and mastoid sites for eliciting ocular vestibular-evoked myogenic potentials (oVEMPs). Study Design. Prospective study. Setting. University hospital. Methods. Twenty healthy subjects underwent oVEMP testing via BCV stimuli at Fz and mastoid sites. Another 50 patients with unilateral Meniere’s disease also underwent oVEMP testing. Results. All healthy subjects showed clear oVEMPs via BCV stimulation regardless of the tapping sites. The right oVEMPs stimulated by tapping at the right mastoid had earlier nI and pI latencies and a larger nI-pI amplitude compared with those stimulated by tapping at the Fz and left mastoid. Similar trends were also observed in left oVEMPs. However, the asymmetry ratio did not differ significantly between the ipsilateral mastoid and Fz sites. Clinically, tapping at the Fz revealed absent oVEMPs in 28% of Meniere’s ears, which decreased to 16% when tapping at the ipsilesional (hydropic) mastoid site, exhibiting a significant difference. Conclusion. Tapping at the ipsilateral mastoid site elicits earlier oVEMP latencies and larger oVEMP amplitudes when compared with tapping at the Fz site. Thus, tapping at the Fz site is suggested to screen for the otolithic function, whereas tapping at the ipsilesional mastoid site is suitable for evaluating residual otolithic function.

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