Average Fracture Width Research Articles

Propagation of multiple hydraulic fractures in a transversely isotropic shale formation

Shale anisotropy can lead to deviated patterns of hydraulic fractures in multi-stage hydraulic fracturing (MSHF) operations, significantly hindering hydrocarbon production. Such deviation usually occurs in formations where the induced fractures interfere with natural bedding planes or where the stress shadow is created. In this work, the elastic behavior of a transversely isotropic shale rock during MSHF is investigated using the extended finite element method (XFEM) in conjunction with the cohesive zone model (CZM) in ABAQUS. In comparison to the linear elastic fracture mechanics approach, the CZM considers the plasticity and softening effects at the fracture tip, and therefore, leads to a more accurate prediction of fracture geometry. The XFEM model is capable of simulating fractures with an arbitrary path without requiring re-meshing. The 2D numerical model is first verified against the Kristianovich-Geertsma-de Klerk (KGD) analytical solutions. Five injection clusters in a single fracturing stage are simulated to analyze the effects of the material isotropy, the dip angle of shale bedding, and the fracture spacing on the geometry of multiple hydraulic fractures. The transversely isotropic poroelasticity model predicts narrower and longer hydraulic fractures than the isotropic poroelasticity model. The bedding dip angle plays a crucial role in the deviation and the shape of multiple hydraulic fractures. Increasing the dip angle from zero to 90° results in an increase in the average fracture width and an increase-peak-decrease trend in the fracture length. A strong correlation is observed between the fracture spacing and the fracture geometry, and a spacing of 75 m is considered optimal because it results in no discernible stress shadow at all dip angle cases.

A Study on the Migration Rule and Flow Conductivity of Multi-particle Size Proppant in Shale Reservoir

To solve the problem that it is difficult to realize efficient prop of fracture network system in the volume fracturing process of shale reservoir, the migration and settlement mechanism of proppant in fractures is analyzed, the migration law of proppant under different particle size and different combination conditions is studied by using true three-dimensional simulation software, and the distribution of proppant concentration and fracture conductivity are simulated. On this basis, the applicability of proppant with different particle sizes under different fracture morphology is judged, and the combination of proppant particle sizes is optimized to maximize the full prop of the fracture network system, improve the conductivity of the fracture network system, and realize efficient fracturing stimulation of shale reservoirs. The research shows that when the fracture width is very small and the average fracture width is less than 1mm, it is difficult for medium/large size proppant to enter the fracture network and achieve effective fracturing prop. Therefore, it is recommended to use small/micro size proppant. Under the condition that the average fracture width is greater than 1mm and the proppant with large particle size can effectively enter the fracture, the combination of large size + medium size proppant particles settle quickly, and the porosity of the sand dike is large, which can reach a larger equilibrium height, increase the effective support width of the fracture, and improve the conductivity of the fracture network. The fracture conductivity is not only related to the proppant placement concentration, but also depends on the proppant placement structure in the fracture. After the fracture is effectively propped, further increasing the proppant concentration will block the fracture system and reduce the conductivity. Therefore, it is not suitable to pump small size proppant after pumping large/medium size proppant, so as to avoid unnecessary plugging to the proppant. Small size proppant is suitable for use in the early pumping phase.

Study on the influence of temperature on fracture propagation in ultra-deep shale formation

Creating a complex fracture network by hydraulic fracturing was an essential technic for the development of ultra-deep reservoirs. Due to the effect of thermal stress field on fracture propagation was unclear, it was necessary to understand the interaction mechanism between hydraulic fracture and bedding plane in layered formation. Combined with the experiments, the numerical simulation model was proposed based on the damage mechanics theory to illustrate the fracture propagation mechanism under high temperature. The simulations indicated that the reservoir temperature was a predominant factor affecting the fracture propagation when the temperature was over 200 ℃. Under high reservoir temperature, the breakdown pressure and extension pressure reduced by 7.61 % and 8.44 % compared with the reservoir temperature was 25 ℃, and the average fracture width increased by 23 %. Combined with the triaxial rock mechanics test and CT scanning, it indicated that the increased temperature difference between reservoir and fracturing fluid contributed the degradation mechanism of rock mechanical properties, the main reason was that the higher temperature difference induced the growth of micro fracture system in the reservoir, making the opening of micro fracture larger and the number of micro fracture increased, so the mechanical strength of rock experienced a dramatically decrease. With the degradation mechanism of rock mechanical properties, the mechanical strength difference between rock and bedding plane was reduced, thus the hydraulic fracture was more easily cross the bedding plane.

Hydraulic and Mechanical Coupling Analysis of Rough Fracture Network under Normal Stress and Shear Stress

The hydraulic and mechanical coupling characteristics of fracture networks under normal stress and shear stress were studied in this paper. The hydraulic and mechanical coupling model of the fracture network comprehensively considers the normal stress, shear stress, seepage pressure and roughness characteristics. Based on the boundary conditions and reasonable assumptions, COMSOL Multiphysics software was used to develop the hydraulic and mechanical coupling finite element model of the fracture network with different intersection points under normal stress and shear stress, focusing on the study of the effect of normal stress and shear stress on the fracture permeability. The degree of permeability change caused by the normal stress and shear stress is different. The shear stress has a significant influence on the fracture permeability, and when the normal stress is low, the relationship between the fracture permeability and shear stress can be described by a linear relationship. Then, the influence of the number of intersection points in the fracture network on the average fracture width, average water pressure, average seepage velocity and seepage passage of the fractured rock mass was analyzed. The number of intersections in the fracture network has little influence on the average fracture gap width and average water pressure but has a great influence on the flow velocity. The analysis in this paper is very helpful to understand the seepage characteristics in rough fractures under normal stress and shear stress.

Poroelastoplastic Modeling of Complex Hydraulic-Fracture Development in Deep Shale Formations

Summary In this paper, we propose a hydromechanical model to simulate hydraulic fracture propagation in deep shale formations. The Drucker-Prager plasticity theory, Darcy’s law, Reynolds lubrication theory, and Kirchoff’s laws are adopted to describe the plastic deformation, matrix flow, fracture flow, and wellbore flow, respectively. A global embedded cohesive zone model is constructed to achieve the free evolution of hydraulic fractures and the characterization of natural fractures. The finite element method (FEM) and finite volume method (FVM) are used for the spatial discretization of the stress field and pressure field. On the basis of Newton-Raphson iteration, fixed-stress iteration, and Picard iteration, a mixed numerical scheme is built up to solve the strong nonlinear coupling problem. The proposed model is verified against several reference cases and experimental results. Finally, some numerical cases are carried out to investigate the influences of rock properties, natural fracture distribution, and fracturing fluid properties on the complex hydraulic fracture development. The results show that rock plasticity leads to a decrease in stimulated fracture area, an increase in average fracture width, and an increase in propagation pressure. As the cluster number increases, the adverse effect of rock plasticity on multiple hydraulic fracturing in deep shale formations increases significantly. In addition, appropriate optimization of cluster spacing could weaken the adverse effect of rock plasticity on fracturing treatment to a certain extent by using the stress interference effect.

Optimizing selection method of continuous particle size distribution for lost circulation by dynamic fracture width evaluation device

The increase in the pressure bearing capacity is critical for mitigation of lost circulation, and to do so the strength of the plugging zone should be increased via picking an effective evaluation method and choosing the proper particle size distribution (PSD). Therefore, in order to successfully investigate this process, the traditional evaluation device of lost circulation should be improved for dynamic variation of fracture width to find the optimized plugging materials. This means, a new testing apparatus device capable of testing dynamic fracture width should be developed. Additionally, commonly used selection criteria of PSD are incapable of providing us with a continuous PSD curve since they only fulfill discrete PSDs. To overcome these two obstacles, a variety of continuous PSD models based on a new testing device and method are examined. Likewise, the impact of governing parameters and an optimized PSD selection criterion were studied with a specific lost circulation material (calcium carbonate) and concentration in a water-based drilling fluid. The experimental results demonstrate that the normal distribution model provides the best selection result while the sensitive analysis indicate that the factors influencing pressure bearing capacity in a sequential order are: minimum particle size, standard deviation, maximum particle size and average value. Besides, the optimized experiments illustrated that the maximum particle size should be 1.3 times of the maximum fracture width and the minimum particle size should be 0.8 times of the average fracture width. Moreover, the average value should be equal to the optimal particle average size and the standard deviation should be 0.3 times of the particle average size. It was found that the optimized selection method results in the highest plugging efficiency compared to conventional selection criteria. Collectively, the new device and optimal assessing approach would improve the prediction accuracy of pressure bearing capacity to select an appropriate PSD with varying of fracture width in field operations.

New algorithm to simulate fracture network propagation using stationary and moving coordinates in naturally fractured reservoirs

AbstractInfluenced by natural fractures, fracture networks may be created when hydraulic fractures propagate in naturally fractured reservoirs. Simulating fracture network propagation is crucial to fracture design. In this paper, a two‐dimensional mathematical model for the direct simulation of fracture network propagation that considers fluid filtration and reservoir fluid flow is developed, and a simulation method is proposed based on the coupled flow idea of natural fractures and matrices in dual‐porosity media. The model uses dynamic coordinates to represent the extended hydraulic fracture network and static coordinates to describe natural fractures that have not been activated. The activation of natural fractures by a hydraulic fracture is determined according to the hydraulic fracture propagation scenario after an intersection with natural fractures. The geometric shape and size of the network fracture are obtained by changing the size of the simulated area and solving the mass balance, fracture width, and reservoir fluid flow equations numerically in a coupled manner. After validating the new model, a parameter sensitivity analysis is conducted to study the effects of injected fluid volume, fracture height, fracture spacing, elastic modulus, horizontal principal stress difference, pumping rate, and fracturing fluid viscosity on the fracture network shape, fracture network size, average fracture width, and fracture‐reservoir contact area. The numerical results indicate that the model can be directly used to simulate the propagation of fracture networks. The volume of injected fluid is the most critical factor affecting the fracture network size. Increasing the fluid viscosity and injection rate can increase the width of the fracture network and the average width of a secondary fracture. However, the total contact area of the reservoir and fracture will decrease, and the reservoir‐fracture contact area and fracture network size will increase with a decrease in the horizontal stress difference and increase in elastic modulus. Decreasing a fracture's height can significantly increase the size of the fracture network and reservoir‐fracture contact area.

Experimental study on the effect of fracture surface morphology on plugging efficiency during temporary plugging and diverting fracturing

Temporary-plugging-and-diverting fracturing (TPD fracturing) is widely used to enhance hydrocarbon recovery from unconventional reservoirs. During TPD fracturing, diverters are injected to prevent the propagation of the previously formed fractures, then divert the fracturing fluid into the unstimulated zones. However, the influence of the fracture morphology on the diversion remains unknown. This study examined the characteristics of diversion under the influence of fracture undulation and roughness. The fracture surface was represented through the application of the 3D scanning and printing method. The digitized scan data is used to characterize the roughness and undulation of the fracture surface. Moreover, the width in the normal direction (normal width) of the fracture surface is used to measure the width of the flow channel in the fracture. A new method for describing the characteristics of fracture plugging location based on the normal width of the fracture is established. Besides, we chose a combination of particles with a diameter of 1 mm and fibers and studied its plugging behavior in a fracture with a width of 2 mm under the carrying of cross-linked guar fracturing fluid. Parallel experimental results suggest the presence of the characteristic plugging position, which is the narrow area inside the fracture. A fracture shape parameter quantitatively describing the characteristics of the region was established. It can be used to predict the inflection point in the pressure response of the diversion process. The research results show that the shape and distribution of the narrow areas in the fracture have a great impact on the plugging behavior. Even with similar average fracture width or the degree of normal width variation, there are significant differences in plugging efficiency. This study deepens the understanding of the plugging behavior of diverters in rough fractures.

Implementation of Hydraulic Fracturing Operation for a Reservoir in KRG

This study focuses on procedures to enhance permeability and flow rate for a low permeability formation by creating a conductive path using the hydraulic fracturing model. Well data are collected from the Qamchuqa KRG oil field formation. A Fracpro simulator is used for modelling the hydraulic fracturing process in an effective way. The study focuses on an effective hydraulic fracturing design procedure and the parameters affecting the fracture design. Optimum design of fracturing is achieved by selecting the proper fracturing fluid with a suitable proppant carried in a slurry, determining the formation fracturing pressure, selection of a fracture propagation fluid, and also a good proppant injection schedule, using a high pump rate and good viscosity. Permeability and conductivity are calculated before and after applying the hydraulic fracturing. Fracture height, length, and width are calculated from the Fracpro software, among other parameters, and the production rate changes. From the results, it is observed that by using hydraulic fracturing technology, production will increase and permeability will be much higher. The original formation permeability is 2.55 md, and after treatment, the average fracture conductivity has significantly increased to 1742.3 md-ft. The results showed that average fracture width is 0.187 inch. The proppant used in this treatment has a permeability of 122581 md. The suitable fluid choice is hyper with an apparent viscosity of 227.95 cp, and the proper proppant type is Brady sand with a conductivity of 2173.41 md-ft. Fracture orientation from the Khurmala oil field in Kurdistan is vertical fractures produced at a depth of 1868 m. Fracture half-length, total fracture height, and average fracture width are 220 ft, 42 ft, and 0.47 inch, respectively. After fracturing, the maximum and average area of fracture are 33.748 and 17.248 ft2, respectively. The recommended pump hydraulic horse power is 3200 HHP, and the total required fluid is 1076.3 bbl. In this study, hydraulic fracture is designed, and then, it has been analyzed after that production is optimized.

A 3D CT-based fracture map study of intra-articular distal radial fractures

Objective To map OTA/AO type B and type C distal radial fractures according to three-dimensional (3D) CT scan data, and to describe the morphological distribution of fracture lines. Methods A total of 468 cases of distal radius fractures admitted to the Affiliated Hospital of Chengdu University from January 2016 to March 2019 were analyzed and AO classification were performed. AO type B and type C fractures meet the inclusion criteria and then CT data were 3D reconstructed, and morphological description were performed on the fracture lines of each joint surface, including fracture shape angle, fracture area and fracture ratio. At the same time, the articular surface fracture model was superimposed on the standard model, then fracture line and fracture area distribution map were drawn to create the fracture map of intra-articular distal radial fractures. Result Intra-articular fractures of the distal radius were 209 cases, accounting for 44.7% (209/468) of the distal radius fractures, among which 67 cases of AO type B fracture. In type B fractures, average fracture height were 20.30±11.26 mm, average fracture width were 12.24±6.83 mm, average fracture area were 189.61±101.84 mm2, average angle were 57.23°±14.95°, and average area ratio of fracture (fracture zone area/joint surface area ratio) were 32.42%±10.24%. 142 cases were OA type C fracture, the average fracture height were 24.43±11.37 mm, average fracture width were 20.38±7.59 mm, average fracture area were 425.26±314.31 mm2, average angle were 51.26°±13.17°, and average area ratio of fracture were 73.81%±26.29%. According to fracture map formed by main fracture lines, five different fracture areas were identified: ① 63 cases in central area; ② 25 cases in Lister's nodule area; ③ 59 cases in scaphoid area; ④ 36 cases in lumbar fossa area; ⑤ 26 cases in lower iliac area. Main fracture lines were concentrated in the area on the dorsal side of the central area and the scaphoid area. The fracture lines of type B fracture mainly concentrated in scaphoid region, which accounted for 29.85% (20/67), and dorsal side and central area accounted for 26.87% (18/67). The fracture lines of type C fracture accounted for 27.46% (39/142) in scaphoid area and 31.69% (45/142) in central area. The fracture line of type C fracture increased in the lumbar fossa region (17.61%, 25/142) and the lower ulnar region (12.68%, 18/142) compared with type B fracture (28.69%). Compared with the type B fracture, the overall distribution of the fracture line of the type C fracture is more central. Conclusion The map of intra-articular fracture of distal radius was drawn and morphological distribution of fracture lines were quantified. Fracture-prone site and shape of fracture line were visually recognized. At the same time, description of articular surface fracture line and fracture area of type B and type C fractures of OA classification were improved, which may help with new classification and diagnosis. Key words: Radius fractures; Intra-articular fractures; Imaging, three-dimensional; Maps

An equivalent mathematical model for 2D stimulated reservoir volume simulation of hydraulic fracturing in unconventional reservoirs

ABSTRACT Stimulated reservoir volume (SRV) is a key parameter affecting the post-fracturing production of ultra-low permeability reservoirs. Accurate prediction of the SRV shape and size is of vital significance for pre-fracturing stimulation design and post-fracturing effect evaluation. In this paper, an equivalent mathematical model for simulating two-dimensional SRV growth is proposed by integrating the fracture width equation, tensor permeability conversion, cubic law and calculation method of fracture porosity with mass conservation equation of injected fluid in natural fracture system. The finite difference method is used to derive the numerical discrete equation, and the fluid pressure and average fracture width in each grid block are obtained by solving the coupled fluid conservation equation and fracture width equation. The model is validated by comparing the results obtained from this work with others from literature. A parametric sensitivity study was performed to analyze the effects of some factors incorporating approaching angle, natural fracture spacing, horizontal principal stress difference, pumping rate and fracturing fluid viscosity on the SRV (including size, aspect ratio, and arithmetic mean fracture width in SRV region). The results show that SRV increases with the decrease of approaching angle, principal stress difference, injection rate, viscosity of fracturing fluid and fracture density. The width of branch fracture decreases with the increasing approaching angle and principal stress difference but increases with the increasing pumping rate and fluid viscosity.

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

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.

Calculation Method of Overburden Damage Height Based on Fracture Mechanics Analysis of Soft and Hard Rock Layers

Under the geological condition of soft and hard rock interaction stratum, the overburden damage height can provide a quantitative support for the design of the locations of gas drainage boreholes in the roof mining fracture zone and the determination of the hydraulic fracture zone in coal seam mining. The interbedded structure of overlying mud rock and sandstone in the Lu’an mining area in Shanxi is a typical soft and hard rock interaction stratum. In view of the lack of soft rock fracture mechanics analysis and the improper calculation of the damage height of overburden rock caused by constant rock residual bulking coefficient to be used regularly in the analysis, in this paper, we constructed a fracture model of soft and hard strata by giving a quantitative classification criterion of soft and hard rocks and introducing a fracture failure criterion of soft rock strata and the space constraint condition of broken-expansion rock formation. Aiming at improving the calculation precision of overburden damage height, we presented a calculation method based on fracture mechanics analysis of soft and hard strata, which could delineate the extent of intact rock in overlying strata from bottom to top to determine the damage height of overburden rock. This research took Yuwu coal mine in Lu’an mining area as an example. Results showed that (1) by the calculation method, the overburden damage height of the N1102 fully mechanized caving face in Yuwu coal mine was 51.44 m, which was less than the value obtained by an actual borehole TV method as well as the numerical simulation result of 53.46 m, with a calculation accuracy about 96.22%, which is quite high for both. The calculation accuracy of the proposed method was higher than that of the three conventional theoretical methods, and it effectively solved the limitation of the fracture analysis method without the inclusion of the soft rock layer in design and the distortion problem due to the residual bulking coefficient to be improperly used in simulation. (2) There was no noticeable fractures in the broken soft rock zone, and the whole fractures were mainly low-angle rupture; the fractures in hard rock layer had obvious ruptures and multiangle cracks, and the average fracture width of soft rock was 2.8 mm smaller than that of hard rock. The fracture modes of soft rock and hard rock were mainly tensile failure and tensile shear failure, which verified the correctness of the fracture mechanics model of soft and hard rock layers constructed in this paper. (3) It is noticed that the tensile strength of rock in this method needs to be obtained through rock mechanics experiment on overlying strata in the study area, and our proposed method was applicable to the mining conditions of near horizontal coal seam. The calculation accuracy of this method meets the engineering error requirements and can be applied to the prediction of overburden damage height in near horizontal coal seam mining.

Optimization of the Horizontal-Well Hydraulic-Fracture Geometry From Caprock-Integrity Point of View Using Fully Coupled 3D Cohesive Elements

Summary Pre-analysis of the geometry of a hydraulically induced fracture, including fracture width, length, and height, plays a crucial role in a successful hydraulic-fracturing (HF) operation. Besides the geometry of the fracture, the injection rate should be optimal for obtaining desired results such as maintaining sufficient aperture for proppant placement, avoiding screenouts or proppant bridging, and also preventing caprock-integrity failure as a result of an extensively uncontrolled fracture in reservoirs. A sophisticated numerical model derived from the cohesive-elements method has been developed and validated using field data to obtain an insight on the optimal fracture geometry and injection rate that can lead to a safe and efficient operation. The HF operation has been conducted in an oil field in the Persian Gulf with the aim of enhanced oil recovery (EOR) from a limestone reservoir with low matrix permeability in a horizontal wellbore. The concept of the cohesive-elements method with pore pressure as an additional degree of freedom has been applied to a 3D fully coupled HF model to estimate fracture geometry, specifically fracture height as a function of the optimal injection rate in a reservoir porous medium. It was observed that by increasing injection rate, all the fracture-geometry parameters steeply increased, but the fracture height must be controlled to be in the reservoir domain and not surpass the caprock and sublayer. For the reservoir under study with the maximum height of 100 m, length of 250 m, width of 100 m, permeability of 2 md, and porosity of 10%, the optimal fracture height is 73.4 m; the average fracture width and half-length are 12.8 mm and 55.4 m, respectively. Therefore, the optimal injection rate derived from the fracture height and geometry is in this case 4.5 bbl/min. The computed fracture pressure (49.55 MPa = 7,283.85 psi) has been compared with the field fracture pressure (51.02 MPa = 7,500 psi), and the error obtained for these two values is 2.88%, which showed a very good agreement.

Quantitative fracture evaluation method based on core-image logging: A case study of Cretaceous Bashijiqike Formation in ks2 well area, Kuqa depression, Tarim Basin, NW China

A quantitative evaluation method of fracture is established based on core observation and image logging, and is used to characterize the distribution feature of fractures in Bashijiqike Formation of ks2 well area. This method gets the empirical corrections of fracture parameters between cores and image logging in the same depth, and these empirical values will be used in other depth where cores are not acquired to obtain all the fracture parameters per meter of the target layer. The study shows the fractures in ks2 well area are mainly high angle structural fractures between 45°−75°, and their strikes are near SN or near EW. The fracture linear density values are 0.11−1.30/m, the fracture area ratio is 0.027%−0.130%, the average fracture width is 0.13−0.55 mm, and the fracture length is 0.39−1.20 m. The development of fracture is divided into three levels (I-developed, II – relatively developed, III-poorly developed) based on the linear density value and surface area ratio. Fractures in this well area are most abundant in sandstones of 1st and 2nd members of Bashijiqike Formation, forming 4-6 fracture segments with good continuity. The thicknesses, development levels, parameters of fracture segments decrease exponentially with the increase of distance to fault and to anticline axis. The most favorable area (I – II) is within 800 m from the fault, or within 1 800 m from the anticlinal axis. It is predicted the fractures in ks2 well area, are more developed in the eastern area than the middle-western area, and more developed in the southern area than the northern area, and that the linear fracture density can be up to 1.0/m around Well ks201, Well ks207-ks2-12, Well ks203 and areas near faults.

Optimal Fracturing Parameters Condition of Integrated Model Development for Tight Oil Sands Reservoir with 2D Fracture Geometry Using Response Surface Methodology

In this study, oil production in tight oil reservoir was declined due to high heterogeneity, complicated and complexity of reservoir of the low permeability reservoir ranges from 0.1 md to 5 md and reservoir porosity ranges from 10 to 18% lead to low fracture conductivity among the fractures. The challenge deal with this problem is to stimulate the reservoir of hydraulic fracturing for maximum oil production is necessary for the study. The application of the central composite design and response surface are the best tool in order to optimize the operating parameters based on the maximum net present value and through the series calculation, the optimal operating parameters of hydraulic fracturing have been determined of 46 bpm of injection rate, 88.5 min of the injection time and 0.002 ft/min0.5 of the leak-off coefficient and the maximum net present value of 46.5 $mm. Finally, the integrated model development of hydraulic fracturing includes of the normal faulting stress regime, fracturing fluid selection and fluid model, proppant selection, fracture geometry, pressure model, material balance, fracture conductivity and simulation production of fractured well and unstimulated well that have been presented in this study. With the using two dimensional Perkins-Kern-Nordgren fracture geometry models coupled with carter leak-off as the 2D PKN-C has been used to account for leak-off coefficient, spurt loss in term of power law parameters to propagate the fracture half-length, fracture width. The result of the fracture conductivity of fractured well at the fracture half-length of 1,940 ft and average fracture width of 0.32 in by series calculated propped fracture concentration of 1.63 lb/ft2 and fracture closure pressure of 4,842.59 psi to fracture conductivity of 6,200 md-ft, which value is measured by the laboratory experiment. The post-fracture production has been shown the fold of increase oil of 18.7 and the oil production rate of fractured well demonstrated much rising compared to oil production rate of unstimulated case.

Application of Ultra High Toughness Cementitious Composites to Tunnel Lining

Ultra high toughness cementitious composites (UHTCC) demonstrates the properties of non-linear and hardening under load. Its tensile strain may reach over 3%, whereas its average fracture width is only about 60m which shows excellent ability in controlling crack. Tunnel lining is usually made of moulded concrete. One way it endure all the pressures from surrounding rock to guarantee tunnel stability, on the other hand also has low permeability to resist groundwater seepage, while UHTCC has the special advantages in this respect. By analyzing the pressures applied to tunnel lining in one tunnel section, discussion of how UHTCC is applied to lining is done, and some related questions about its application are explained by calculation.

A Computer Study of Horizontal Fracture Treatment Design

Abstract Published correlations for the principal aspects of hydraulic fracturingwere combined into a digital computer program to facilitate the study ofinterrelated variables. The computer program includes individual relationshipsfor fracture width during pumping, fracture area generated, propping agentembedment, flow capacities of propped fractures and transport of proppingagents in horizontal fractures. The effects of more than 20 treatment andformation parameters on the predicted results of hydraulic fracturingtreatments were studied. The effects of these parameters were determined forfracture width during injection,fracture width after the overburdencomes to rest on the propping agents, assumed not to be crushed,generatedand propped fracture area,location and concentration of propping agents inthe fracture when injection ceases,flow capacities of the various proppedsections of the fracture andexpected increase in the well productivity. The effects of propping agent, formation and fracturing fluid parameters onwell productivity are discussed. The parameters that were found to have themost pronounced effects on hydraulic fracturing treatments are injection rate, treatment volume, fracturing fluid coefficient, size and amount of proppingagent, spearhead volume, well damage radius and formation capacity. Introduction Many correlations have been published for predicting effects of variousparameters that are considered in the design of hydraulic fracturingtreatments. The Carter equation can be used to predict generated fractureradius as a function of fracture width, fracturing fluid leakoff and otherparameters. Fracture width can be determined by use of the Perkins and Kerncorrelation in which the fracture width is related to the fracture radius, fluid injection rate and certain formation and fracturing fluid parameters. Wahl and Lowe et al. have reported methods of predicting the location ofpropping agents in fractures when pumping ceases. The former study isapplicable to the case where the ratio of propping agent diameter to fracturewidth is less than 0.1. The latter is applicable when this ratio is greaterthan 0.1. These studies showed that the propping agent placement inhorizontal-radial fractures depends principally on how the individual particlesare transported in the fracture by the carrying fluid. Particle transport infractures is determined by local fluid velocity in the fracture, fluid andparticle properties, and the size of the particle relative to the fracturewidth. The distribution of propping agents, effective overburden pressure andformation rock strength control the propped fracture width by controlling theextent to which the propping agent particles embed into the fracture faces. From the distribution of propping agents and the propped fracture width, fracture flow capacities can be calculated for the various regions of thefracture. The flow capacities and the radial extent of these regions can becombined with reservoir information to predict the productivity increases forfractured wells. In all these studies, the effects of certain treatment and/orreservoir parameters on one facet of fracturing can be predicted only if otherfacets which the parameters affect are fixed. For instance, fracture width andradius are interrelated; that is, to calculate the value of one, the value ofthe other must be known. Also, some parameters influence more than one aspectof fracturing. For example, proppant transport is a function of both fracturewidth and fluid viscosity, but fracture width is itself a function of fluidviscosity. Since these calculations are complex and the parametersinterrelated, it is not possible to write an equation with which the over-alleffects of treatment parameters can be solved explicitly. For these reasons, the correlations for determining the effects of the parameters which are mostsignificant in hydraulic fracturing treatments have been incorporated into adigital computer program. Computer Program The program, which was written for an IBM 7094 computer, can be used topredict results of most of the combinations and values for the treatmentparameters that are ordinarily considered for fracturing treatments. Aspearhead of fracturing fluid and a propping agent-carrying fluid withdifferent fluid properties can be taken into account. Also, the total volumesand relative amounts of the spearhead and carrying fluids can be varied. Twodifferent propping agents (as used in tail-in operations) and a wide range offormation properties and injection rates are considered. The computer program(Fig. 12) consists of several sets of calculations. First, the final floodedfracture radius and average fracture width at the cessation of pumping arecalculated. This is done by simultaneous solution of the Perkins and Kernfracture width equation and the Carter equation for flooded fracture radius(equations used in the computer program appear in the Appendix). The next stepis to determine local fluid velocity in the fracture as a function of time andradius. Since it is, not possible to write this function in closed formexpression, a table of velocity values is generated by the program and storedfor subsequent use.