P-wave attenuation anisotropy in TI media and its application in fracture parameters inversion

The existence of aligned fractures in fluid-saturated rocks leads to obvious attenuation anisotropy and velocity anisotropy. Attenuation anisotropy analysis can be applied to estimate fracture density and scale, which provide important information for reservoir identification. This paper derives P-wave attenuation anisotropy in the ATI media where the symmetry axis is in the arbitrary direction theoretically and modifies the spectral ratio method to measure attenuation anisotropy in the ATI media, thus avoiding a large measurement error when applied to wide azimuth or full azimuth data. Fracture dip and azimuth can be estimated through attenuation anisotropy analysis. For small-scale fractures, fracture scale and fracture density can be determined with enhanced convergence if velocity and attenuation information are both used. We also apply the modified spectralratio method to microseismic field data from an oilfield in East China and extract the fracture dip through attenuation anisotropy analysis. The result agrees with the microseismie monitoring.

Experimental study on tensile failure process of double-K fracture parameters in roller compacted concrete layer

Study on failure of soft stratum of roller compacted concrete (RCC) is an important aspect of stability of high RCC dam. Six kinds of specimens with different interfaces were investigated by wedge splitting method. Double-K fracture parameters (initial fracture parameter and unsteady fracture parameter) were calculated by the concrete double-K fracture theory. It is indicated that the approach of construction joint or old joint after RCC final set is the most efficient among the six cases, and its fracture parameter is the largest among them. Its propagation path is sinuous. Its failure surface is scraggly. Bedding plane crack fails at the underside of the concrete surface, bond course or the surface between them for each approach. So disturbance on the underside of the concrete surface should be avoided or decreased at best during RCC construction.

A Data-Oriented Method to Optimize Hydraulic Fracturing Parameters of Tight Sandstone Reservoirs

Based on the actual data collected from the tight sandstone development zone, correlation analysis using theSpearman method was conducted to determine the main factors influencing the gas production rate of tightsandstone fracturing. An integrated model combining geological engineering and numerical simulation of fracturepropagation and production was completed. Based on data analysis, the hydraulic fracture parameters wereoptimized to develop a differentiated fracturing treatment adjustment plan. The results indicate that the influenceof geological and engineering factors in the X1 and X2 development zones in the study area differs significantly.Therefore, it is challenging to adopt a uniform development strategy to achieve rapid production increase. Thedata analysis reveals that the variation in gas production rate is primarily affected by the reservoir thickness andpermeability parameters as geological factors. On the other hand, the amount of treatment fluid and proppantaddition significantly impact the gas production rate as engineering factors. Among these factors, the influence ofgeological factors is more pronounced in block X1. Therefore, the main focus should be on further optimizing thefracturing interval and adjusting the geological development well location. Given the existing well location, thereis limited potential for further optimizing fracture parameters to increase production. For block X2, the fracturingparameters should be optimized. Data screening was conducted to identify outliers in the entire dataset, and adata-driven fracturing parameter optimization method was employed to determine the basic adjustment directionfor reservoir stimulation in the target block. This approach provides insights into the influence of geological,stimulation, and completion parameters on gas production rate. Consequently, the subsequent fracturing parameteroptimization design can significantly reduce the modeling and simulation workload and guide field operations toimprove and optimize hydraulic fracturing efficiency.

Productivity model for gas reservoirs with open-hole multi-fracturing horizontal wells and optimization of hydraulic fracture parameters

Multi-fractured horizontal wells are commonly employed to improve the productivity of low and ultra-low permeability gas reservoirs.However,conventional productivity models for open-hole multi-fractured horizontal wells do not consider the interferences between hydraulic fractures and the open-hole segments,resulting in significant errors in calculation results.In this article,a novel productivity prediction model for gas reservoirs with open-hole multi-fractured horizontal wells was proposed based on complex potential theories,potential superimposition,and numerical analysis.Herein,an open-hole segment between two adjacent fractures was regarded as an equivalent fracture,which was discretized as in cases of artificial fractures.The proposed model was then applied to investigate the effects of various parameters,such as the angle between the fracture and horizontal shaft,fracture quantity,fracture length,diversion capacity of fractures,horizontal well length,and inter-fracture distance,on the productivity of low permeability gas reservoirs with multi-fractured horizontal wells.Simulation results revealed that the quantity,length,and distribution of fractures had significant effects on the productivity of low permeability gas reservoirs while the effects of the diversion capacity of fractures and the angle between the fracture and horizontal shaft were negligible.Additionally,a U-shaped distribution of fracture lengths was preferential as the quantity of fractures at shaft ends was twice that in the middle area.

Estimation of Fracture Geometry Parameters and Characterization of Rock Mass Structure for the Beishan Area,China

The accurate estimation of fracture geometry parameters and the characterization of rock mass structure are two important topics in the geological disposal system of high-level radioactive waste(HLW).The Beishan area,as the current preselected area for China’s HLW disposal,has three subareas considered to be the key survey area at the stage of site selection.In this paper,a comprehensive survey method conducted on the outcrop is developed to estimate fracture geometry parameters.Results show that fracture occurrence obeys a Fisher distribution,fracture trace length obeys a normal distribution,and the distribution of spacing obeys a negative exponential distribution.An evaluation index,Rock Mass Structure Rating(RMSR),is proposed to characterize rock mass structure for the three subareas.The results show that the Xinchang area is more suitable to act as China’s HLW disposal repository site.At the same time,the index can also be applied to characterize surface rock mass structure and rock mass integrity at the site selection phase of HLW disposal.

DICE:An open-source MATLAB application for quantification and parametrization of digital outcrop model-based fracture datasets

An open-source MATLAB application(app)named Discontinuity Intensity Calculator and Estimator(DICE)was developed in order to quantitatively characterize the fractures,or in more general,discontinuities within a rocky outcrop in three-dimensional(3D)digital data,such as digital outcrop model(DOM).The workflow proposed for the parametrization of the discontinuities consists of the following steps:(1)Analysis and mapping of the fractures detected within the 3D DOMs;(2)Calculation of the orientation,position and dimensions of discontinuities that are represented by best-fit circular planes;(3)Determining the discontinuity parameters(dimension,distribution,spacing and intensity)by the DICE algorithm using different 3D oriented sampling techniques(3D oriented scanline,3D oriented circular scan window and spherical scan volume).Different sampling methods were bench tested with a synthetic,as well as a natural case study,and compared in order to understand the advantages and limitations of each technique.The 3D oriented circular scan window appears to be the most effective method for fracture intensity estimation with high accuracy(error 0.4%)and stability with variations in scan radius.

Effects of strength matching and crack depth on the fracture parameters for welded joints

Fracture parameters of welded joints with different strength matching and crack depth in weld metal are investigated by using the methods of elastoplastic finite element analysis and three point bend specimen test. The results show that for shallow crack, the plastic zone turns large in loading process, and the fracture toughness turns high. The extent of the plastic zone of overmatched joint is larger than that of undermatched joint because it will extends to parent metal from the weld metal in loading process for the same CTOD value. The plastic zone of undermatched joint is restricted within the weld, and the size of that is small. Overmatched joint shows the fracture behaviour of shallow crack may more easily than the undermatched joint, while the two sorts of joint specimens have the same crack depth. Therefore, the fracture-resistant capability of overmatched weld is better than that of undermatched weld. when the toughness of weld metals is similar for both overmatched and undermatched joints.

Fracture propagation,proppant transport and parameter optimization of multi-well pad fracturing treatment

This paper establishes a 3D multi-well pad fracturing numerical model coupled with fracture propagation and proppant migration based on the displacement discontinuity method and Eulerian-Eulerian frameworks,and the fracture propagation and proppant distribution during multi-well fracturing are investigated by taking the actual multi-well pad parameters as an example.Fracture initiation and propagation during multi-well pad fracturing are jointly affected by a variety of stress interference mechanisms such as inter-cluster,inter-stage,and inter-well,and the fracture extension is unbalanced among clusters,asymmetric on both wings,and dipping at heels.Due to the significant influence of fracture morphology and width on the migration capacity of proppant in the fracture,proppant is mainly placed in the area near the wellbore with large fracture width,while a high-concentration sandwash may easily occur in the area with narrow fracture width as a result of quick bridging.On the whole,the proppant placement range is limited.Increasing the well-spacing can reduce the stress interference of adjacent wells and promote the uniform distribution of fractures and proppant on both wings.The maximum stimulated reservoir volume or multi-fracture uniform propagation can be achieved by optimizing the well spacing.Although reducing the perforation-cluster spacing also can improve the stimulated reservoir area,a too low cluster spacing is not conducive to effectively increasing the propped fracture area.Since increasing the stage time lag is beneficial to reduce inter-stage stress interference,zipper fracturing produces more uniform fracture propagation and proppant distribution.

Optimization of Gas-Flooding Fracturing Development in Ultra-Low Permeability Reservoirs

Ultra-low permeability reservoirs are characterized by small pore throats and poor physical properties, which areat the root of well-known problems related to injection and production. In this study, a gas injection floodingapproach is analyzed in the framework of numerical simulations. In particular, the sequence and timing of fracturechanneling and the related impact on production are considered for horizontal wells with different fracturemorphologies. Useful data and information are provided about the regulation of gas channeling and possible strategiesto delay gas channeling and optimize the gas injection volume and fracture parameters. It is shown that inorder to mitigate gas channeling and ensure high production, fracture length on the sides can be controlled andlonger fractures can be created in the middle by which full gas flooding is obtained at the fracture location in themiddle of the horizontal well. A Differential Evolution (DE) algorithm is provided by which the gas injectionvolume and the fracture parameters of gas injection flooding can be optimized. It is shown that an improvedoil recovery factor as high as 6% can be obtained.

Calculation Model of Equivalent Strength for Induced Crack Based on Double-K Fracture Theory and Its Optimizing Setting in RCC Arch Dam

By means of fracture testing on roller-compacted concrete （RCC） three-point bending beams with two different specimen sizes, the P-CMOD complete curve for RCC was gained. Furthermore, by applying double-K fracture theory, KiniⅠC,KunⅠC, as well as the critical effective crack length and the critical crack tip opening displacement, were evaluated. Based on the double-K fracture parameters above, the calculation model of equivalent strength for induced crack was established, thus the calculation method on its initiation, stable propagation and unstable fracture was ascertained. Moreover, the finite element simulation analysis of stress field in ShaPai arch dam and the on-site observational splaying points of induced crack at different altitudes validated the reliability of the model. Finally, crack inducer′s optimal setting in RCC arch dam was studied. It improves the design level of induced crack in RCC arch dam and satisfies the necessity of engineering practice.

An Integrated Optimization Method for CO_(2) Pre-Injection during Hydraulic Fracturing in Heavy Oil Reservoirs

CO_(2) pre-injection during hydraulic fracturing is an important method for the development of medium to deep heavy oil reservoirs.It reduces the interfacial tension and viscosity of crude oil,enhances its flowability,maintains reservoir pressure,and increases reservoir drainage capacity.Taking the Badaowan Formation as an example,in this study a detailed three-dimensional geomechanical model based on static data from well logging interpretations is elaborated,which can take into account both vertical and horizontal geological variations and mechanical characteristics.A comprehensive analysis of the impact of key construction parameters on Pre-CO_(2) based fracturing(such as cluster spacing and injection volume),is therefore conducted.Thereafter,using optimized construction parameters,a non-structured grid for dynamic development prediction is introduced,and the capacity variations of different production scenarios are assessed.On the basis of the simulation results,reasonable fracturing parameters are finally determined,including cluster spacing,fracturing fluid volume,proppant concentration,and well spacing.

Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media

An accurate and straightforward symplectic method is presented for the fracture analysis of fractional two-dimensional(2D)viscoelastic media.The fractional Kelvin-Zener constitutive model is used to describe the time-dependent behavior of viscoelastic materials.Within the framework of symplectic elasticity,the governing equations in the Hamiltonian form for the frequency domain(s-domain)can be directly and rigorously calculated.In the s-domain,the analytical solutions of the displacement and stress fields are constructed by superposing the symplectic eigensolutions without any trial function,and the explicit expressions of the intensity factors and J-integral are derived simultaneously.Comparison studies are provided to validate the accuracy and effectiveness of the present solutions.A detailed analysis is made to reveal the effects of viscoelastic parameters and applied loads on the intensity factors and J-integral.

A novel approach of tight oil reservoirs stimulation based on fracture controlling optimization and design

To deal with the stress interference caused by simultaneous propagation of multiple fractures and the wettability reversal and physical property changes of the reservoir caused by fracturing fluid getting in during large-volume fracturing of tight oil reservoirs through a horizontal well, a non-planar 3D fracture growth model was built, wettability reversal characterizing parameters and change of relative permeability curve were introduced to correct the production prediction model of fractured horizontal well, a fracturing design optimization software(Fr Smart) by integrating geological and engineering data was developed, and a fracturing design optimization approach for tight oil reservoirs based on fracture control was worked out. The adaptability of the method was analyzed and the fracture parameters of horizontal wells in tight oil reservoirs were optimized. The simulation results show that fracturing technology based on fracture control is suitable for tight oil reservoirs, and by optimizing fracture parameters, this technology makes it possible to produce the maximum amount of reserves in the well-controlled unit of unconventional reservoirs. The key points of fracturing design optimization based on fracture control include increasing lateral length of and reducing the row spacing between horizontal wells, increasing perforation clusters in one stage to decrease the spacing of neighboring fractures, and also avoiding interference of old and new fracturing wells. Field tests show that this technology can increase single well production and ultimate recovery. Using this technology in developing unconventional resources such as tight oil reservoirs in China will enhance the economics significantly.

A review of the effect of a/W ratio on fracture toughness (Ⅲ)——theoretical analysis

In part I and II of this series, experimental investigation in both EPFM and LEFM had been discussed. In this part, further theoretical analysis is given. The theoretical development of Two Parameter Fracture Mechanics by Hancock etc, has rationalized our experimental results. This method can be applied to engineering practice, and will allow the advantage of enhanced toughness for specimens with low levels of constraint to be taken into account for defect assessment.

Experimental Research on Supercritical Carbon Dioxide Fracturing of Sedimentary Rock:A Critical Review

Supercritical carbon dioxide(ScCO_(2))fracturing has great advantages and prospects in both shale gas exploitation and CO_(2)storage.This paper reviews current laboratory experimental methods and results for sedimentary rocks fractured by ScCO_(2).The breakdown pressure,fracture parameters,mineral composition,bedding plane angle and permeability are discussed.We also compare the differences between sedimentary rock and granite fractured by ScCO_(2),ultimately noting problems and suggesting solutions and strategies for the future.The analysis found that the breakdown pressure of ScCO_(2)was reduced 6.52%–52.31%compared with that of using water.ScCO_(2)tends to produce a complex fracture morphology with significantly higher permeability.When compared with water,the fracture aperture of ScCO_(2)was decreased by 4.10%–72.33%,the tortuosity of ScCO_(2)was increased by 5.41%–70.98%and the fractal dimension of ScCO_(2)was increased by 4.55%–8.41%.The breakdown pressure of sandstone is more sensitive to the nature of the fracturing fluid,but fracture aperture is less sensitive to fracturing fluid than for shale and coal.Compared with granite,the tortuosity of sedimentary rock is more sensitive to the fracturing fluid and the fracture fractal dimension is less sensitive to the fracturing fluid.Existing research shows that ScCO_(2)has the advantages of low breakdown pressure,good fracture creation and environmental protection.It is recommended that research be conducted in terms of sample terms,experimental conditions,effectiveness evaluation and theoretical derivation in order to promote the application of ScCO_(2)reformed reservoirs in the future.

Progress and prospects of horizontal well fracturing technology for shale oil and gas reservoirs

By systematically summarizing horizontal well fracturing technology abroad for shale oil and gas reservoirs since the “13th Five-Year Plan”, this article elaborates new horizontal well fracturing features in 3D development of stacked shale reservoirs, small well spacing and dense well pattern, horizontal well re-fracturing, fracturing parameters optimization and cost control. In light of requirements on horizontal well fracturing technology in China, we have summarized the technological progress in simulation of multi-fracture propagation, horizontal well frac-design, electric-drive fracturing equipment, soluble tools and low-cost downhole materials and factory-like operation. On this basis, combined with the demand analysis of horizontal well fracturing technology in the “14th Five-Year Plan” for unconventional shale oil and gas, we suggest strengthening the research and development in the following 7 aspects:(1) geology-engineering integration;(2) basic theory and design optimization of fracturing for shale oil and gas reservoirs;(3) development of high-power electric-drive fracturing equipment;(4) fracturing tool and supporting equipment for long horizontal section;(5) horizontal well flexible-sidetracking drilling technology for tapping remaining oil;(6) post-frac workover technology for long horizontal well;(7) intelligent fracturing technology.

Complex variable approach in studying modified polarization saturation model in two-dimensional semipermeable piezoelectric media

A modified polarization saturation model is proposed and addressed math- ematically using a complex variable approach in two-dimensional （2D） semipermeable piezoelectric media. In this model, an existing polarization saturation （PS） model in 2D piezoelectric media is modified by considering a linearly varying saturated normal electric displacement load in place of a constant normal electric displacement load, applied on a saturated electric zone. A centre cracked infinite 2D piezoelectric domain subject to an arbitrary poling direction and in-plane electromechanical loadings is considered for the analytical and numerical studies. Here, the problem is mathematically modeled as a non-homogeneous Riemann-Hilbert problem in terms of unknown complex potential functions representing electric displacement and stress components. Having solved the Hilbert problem, the solutions to the saturated zone length, the crack opening displace- ment （COD）, the crack opening potential （COP）, and the local stress intensity factors （SIFs） are obtained in explicit forms. A numerical study is also presented for the proposed modified model, showing the effects of the saturation condition on the applied electrical loading, the saturation zone length, and the COP. The results of fracture parameters obtained from the proposed model are compared with the existing PS model subject to electrical loading, crack face conditions, and polarization angles.

Optimization of fracturing parameters for tight oil production based on genetic algorithm

It is difficult to determine the main controlling factors of tight oil production.In addition to the problem of uncontrollable prediction accuracy,the numerical prediction model established by the main controlling factors will also make the correctly predicted low production samples lose the value of development.Applying the optimization algorithm with fast convergence speed and global optimization to optimize the controllable parameters in the high-precision numerical prediction model can effectively improve the productivity of low production wells with timeliness,and bring greater economic value while saving development cost.Using PCA-GRA method,the sample weight and the weighted correlation ranking results of parameters affecting tight oil production were obtained.Thereupon then the main controlling factors of tight oil production were determined.Then we set up a BP neural network model with by taking the main controlling factors as input and tight oil production as output.The prediction effect of the network was good and can be put into use.The results of sensitivity analysis showed that the network was stable,and the total fracturing fluid volume had the greatest impact on the production of tight oil.Finally,by using genetic algorithm,we optimized the fracturing parameters of all low production well samples in the field data.Combined with the fracturing parameters of all high production well samples and the optimized fracturing parameters of low production wells,the optimal interval of fracturing parameters was given,which can provide guidance for the field fracturing operation.