scholarly journals On the simultaneous growth of multiple hydraulic fractures emanating from an inclined well

2021 ◽  
Vol 2057 (1) ◽  
pp. 012079
Author(s):  
A V Valov
Keyword(s):  
Inclination Angle ◽  
Stress Component ◽  
Hydraulic Fractures ◽  
Multiple Fractures ◽  
Time Step ◽  
Stress Shadow ◽  
Large Perforation ◽  
Primary Focus ◽  
The Mathematical Model ◽  
Previous Time Step

Abstract The primary focus of this paper is to investigate the interaction between simultaneously propagating multiple fractures, initiated from an inclined well. In particular, the aim is to better understand the influence of the well inclination angle on the stress shadow between the fractures and on the overall resulting geometry of individual cracks. To simplify the analysis, the paper assumes the limit of large perforation friction, which leads to a uniform flux distribution between the fractures. The mathematical model for multiple hydraulic fractures is constructed by coupling together the respective models for individual fractures, each representing a single planar fracture model. In this approach, the fracture induced stress or stress shadow from a previous time step is used as an input for a given single hydraulic fracture to propagate independently. Further, to reduce computational burden, the effects associated with tangential stresses and displacements are neglected, whereby the stress interaction between the fractures is solely described by the normal opening and the normal stress component. Numerical results are presented for the storage viscosity dominated regime, whereby the effects of toughness and leak-off are negligible. An interesting behaviour is observed, demonstrating that the well inclination angle plays a significant role on the overall fracture symmetry. For zero inclination, all the fractures are nearly symmetrical and identical. However, once well inclination is introduced, this breaks the symmetry, making a profound effect on the final result.

scholarly journals Impact of geomechanical heterogeneity on multiple hydraulic fracture propagation

2021 ◽  
Vol 18 (6) ◽  
pp. 954-969
Author(s):  
Yunlin Gao ◽  
Huiqing Liu ◽  
Chao Pu ◽  
Huiying Tang ◽  
Kun Yang ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Fracture Propagation ◽  
Poisson's Ratio ◽  
Sequential Gaussian Simulation ◽  
Hydraulic Fractures ◽  
Multiple Fractures ◽  
Shadow Effect ◽  
Stress Shadow

Abstract To extract more gas from shale gas reservoirs, the spacing among hydraulic fractures should be made smaller, resulting in a significant stress shadow effect. Most studies regarding the stress shadow effect are based on the assumption of homogeneity in rock properties. However, strong heterogeneity has been observed in shale reservoirs, and the results obtained with homogeneous models can be different from practical situations. A series of case studies have been conducted in this work to understand the effects of mechanical heterogeneity on multiple fracture propagation. Fracture propagation was simulated using the extended finite element method. A sequential Gaussian simulation was performed to generate a heterogeneous distribution of geomechanical properties. According to the simulation results, the difficulty of fracture propagation is negatively correlated with the Young's modulus and Poisson's ratio, and positively correlated with tensile strength. When each of the multiple fractures propagates in a homogeneous area with different mechanical properties, the final geometry of the fracture is similar to homogeneous conditions. When the rock parameter is a random field or heterogeneity perpendicular to the propagation direction of fracture, the fracture will no longer take the wellbore as the center of symmetry. Based on the analysis of fracture propagation in random fields, a small variance of elastic parameters can result in asymmetrical propagation of multiple fractures. Moreover, the asymmetrical propagation of hydraulic fractures is more sensitive to the heterogeneity of Poisson's ratio than Young's modulus. This study emphasises the importance of considering geomechanical heterogeneity and provides some meaningful suggestions regarding hydraulic fracturing designs.

scholarly journals Modeling Simultaneous Multiple Fracturing Using the Combined Finite-Discrete Element Method

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Quansheng Liu ◽  
Lei Sun ◽  
Pingli Liu ◽  
Lei Chen
Keyword(s):  
Hydraulic Fracturing ◽  
Solid Phase ◽  
Horizontal Wells ◽  
In Situ Stress ◽  
Gas Production ◽  
Hydraulic Fractures ◽  
Multiple Fractures ◽  
Fracture Geometry ◽  
Stress Shadow ◽  
Oil Gas

Simultaneous multiple fracturing is a key technology to facilitate the production of shale oil/gas. When multiple hydraulic fractures propagate simultaneously, there is an interaction effect among these propagating hydraulic fractures, known as the stress-shadow effect, which has a significant impact on the fracture geometry. Understanding and controlling the propagation of simultaneous multiple hydraulic fractures and the interaction effects between multiple fractures are critical to optimizing oil/gas production. In this paper, the FDEM simulator and a fluid simulator are linked, named FDEM-Fluid, to handle hydromechanical-fracture coupling problems and investigate the simultaneous multiple hydraulic fracturing mechanism. The fractures propagation and the deformation of solid phase are solved by FDEM; meanwhile the fluid flow in the fractures is modeled using the principle of parallel-plate flow model. Several tests are carried out to validate the application of FDEM-Fluid in hydraulic fracturing simulation. Then, this FDEM-Fluid is used to investigate simultaneous multiple fractures treatment. Fractures repel each other when multiple fractures propagate from a single horizontal well, while the nearby fractures in different horizontal wells attract each other when multiple fractures propagate from multiple parallel horizontal wells. The in situ stress also has a significant impact on the fracture geometry.

scholarly journals The Effect of Perforation Spacing on the Variation of Stress Shadow

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 4040
Author(s):  
Weige Han ◽  
Zhendong Cui ◽  
Zhengguo Zhu
Keyword(s):  
Compressive Stress ◽  
Reservoir Rock ◽  
Hydraulic Fractures ◽  
Extended Finite Element ◽  
Gas Reservoir ◽  
Fracture Length ◽  
Shadow Effect ◽  
Stress Shadow ◽  
Initiation Pressure ◽  
Small Perforation

When the shale gas reservoir is fractured, stress shadows can cause reorientation of hydraulic fractures and affect the complexity. To reveal the variation of stress shadow with perforation spacing, the numerical model between different perforation spacing was simulated by the extended finite element method (XFEM). The variation of stress shadows was analyzed from the stress of two perforation centers, the fracture path, and the ratio of fracture length to spacing. The simulations showed that the reservoir rock at the two perforation centers is always in a state of compressive stress, and the smaller the perforation spacing, the higher the maximum compressive stress. Moreover, the compressive stress value can directly reflect the size of the stress shadow effect, which changes with the fracture propagation. When the fracture length extends to 2.5 times the perforation spacing, the stress shadow effect is the strongest. In addition, small perforation spacing leads to backward-spreading of hydraulic fractures, and the smaller the perforation spacing, the greater the deflection degree of hydraulic fractures. Additionally, the deflection angle of the fracture decreases with the expansion of the fracture. Furthermore, the perforation spacing has an important influence on the initiation pressure, and the smaller the perforation spacing, the greater the initiation pressure. At the same time, there is also a perforation spacing which minimizes the initiation pressure. However, when the perforation spacing increases to a certain value (the result of this work is about 14 m), the initiation pressure will not change. This study will be useful in guiding the design of programs in simultaneous fracturing.

A Modular Code for Real Time Dynamic Simulation of Gas Turbines in Simulink

2002 ◽  
Vol 128 (3) ◽  
pp. 506-517 ◽  
Author(s):  
S. M. Camporeale ◽  
B. Fortunato ◽  
M. Mastrovito
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Gas Turbine ◽  
Dynamic Behavior ◽  
Gas Turbines ◽  
Simulation Software ◽  
Computational Time ◽  
High Fidelity ◽  
Time Step ◽  
The Mathematical Model

A high-fidelity real-time simulation code based on a lumped, nonlinear representation of gas turbine components is presented. The code is a general-purpose simulation software environment useful for setting up and testing control equipments. The mathematical model and the numerical procedure are specially developed in order to efficiently solve the set of algebraic and ordinary differential equations that describe the dynamic behavior of gas turbine engines. For high-fidelity purposes, the mathematical model takes into account the actual composition of the working gases and the variation of the specific heats with the temperature, including a stage-by-stage model of the air-cooled expansion. The paper presents the model and the adopted solver procedure. The code, developed in Matlab-Simulink using an object-oriented approach, is flexible and can be easily adapted to any kind of plant configuration. Simulation tests of the transients after load rejection have been carried out for a single-shaft heavy-duty gas turbine and a double-shaft aero-derivative industrial engine. Time plots of the main variables that describe the gas turbine dynamic behavior are shown and the results regarding the computational time per time step are discussed.

Can We Engineer Better Multistage Horizontal Completions? Evidence of the Importance of Near-wellbore Fracture Geometry from Theory, Lab and Field Experiments

2015 ◽  
Author(s):  
B.. Lecampion ◽  
J.. Desroches ◽  
X.. Weng ◽  
J.. Burghardt ◽  
J.E.. E. Brown
Keyword(s):  
Pressure Drop ◽  
Field Experiments ◽  
Horizontal Wells ◽  
Fracture Plane ◽  
Hydraulic Fractures ◽  
Multiple Fractures ◽  
Fracture Geometry ◽  
Complex Fracture ◽  
Limited Entry ◽  
The Impact

Abstract There is accepted evidence that multistage fracturing of horizontal wells in shale reservoirs results in significant production variation from perforation cluster to perforation cluster. Typically, between 30 and 40% of the clusters do not significantly contribute to production while the majority of the production comes from only 20 to 30% of the clusters. Based on numerical modeling, laboratory and field experiments, we investigate the process of simultaneously initiating and propagating several hydraulic fractures. In particular, we clarify the interplay between the impact of perforation friction and stress shadow on the stability of the propagation of multiple fractures. We show that a sufficiently large perforation pressure drop (limited entry) can counteract the stress interference between different growing fractures. We also discuss the robustness of the current design practices (cluster location, limited entry) in the presence of characterized stress heterogeneities. Laboratory experiments highlight the complexity of the fracture geometry in the near-wellbore region. Such complex fracture path results from local stress perturbations around the well and the perforations, as well as the rock fabric. The fracture complexity (i.e., the merging of multiple fractures and the reorientation towards the preferred far-field fracture plane) induces a strong nonlinear pressure drop on a scale of a few meters. Single entry field experiments in horizontal wells show that this near-wellbore effect is larger in magnitude than perforation friction and is highly variable between clusters, without being predictable. Through a combination of field measurements and modeling, we show that such variability results in a very heterogeneous slurry rate distribution; and therefore, proppant intake between clusters during a stage, even in the presence of limited entry techniques. We also note that the estimated distribution of proppant intake between clusters appears similar to published production log data. We conclude that understanding and accounting for the complex fracture geometry in the near-wellbore is an important missing link to better engineer horizontal well multistage completions.

Near-Wellbore Hydraulic Fracture Non-Planar Propagation and Torturous Morphology in Tight Sandstone Formation

2021 ◽  
Author(s):  
Ruxin Zhang ◽  
Qinglin Shan ◽  
Wan Cheng
Keyword(s):  
Stress Distribution ◽  
Fracture Initiation ◽  
Damage Mechanism ◽  
Fracture Morphology ◽  
Propagation Model ◽  
Hydraulic Fractures ◽  
Tight Sandstone ◽  
Propagation Behavior ◽  
Stress Shadow ◽  
Sandstone Formation

Abstract In this paper, a 3D near-wellbore fracture propagation model is established, integrating five parts: formation stress balance, drilling, casing and cementing, perforating, and fracturing, in order to investigate fracture initiation characteristics, near-wellbore fracture non-planar propagation behavior, and torturous hydraulic fracture morphology for cased and perforated horizontal wellbores in tight sandstone formation. The method is based on the combination of finite element method and post-failure damage mechanism. Finite element method is used to determine the coupling behavior between the pore fluid seepage and rock stress distribution. Post-failure damage mechanism is adopted to test the evolution of hydraulic fractures through simulating rock damage process. Moreover, a user subroutine is introduced to establish the relation between rock strength, permeability, and damage, in order to solve the model. This model could simulate the interaction between fractures during their propagation process because of the stress shadow. The simulation results indicate that each operation could cause redistribution and reorientation of near-wellbore stress. Therefore, it is important to know the real near-wellbore stress distribution that affects near-wellbore fracture initiation and propagation. Initially, hydraulic fractures initiate independently from each perforation and propagate along the direction of maximum horizontal stress. However, hydraulic fractures divert from original direction gradually to interconnect and overlap with each other, because of stress shadow, resulting in non-planar propagation behavior. Individual fractures coalesce into a spiral-shaped fracture morphology. In addition, a longitudinal fracture could be observed because of wellbore effect, which is a result of weak cementing strength or near-wellbore weak plane. Finally, the complex and torturous fracture morphologies are created near the wellbore, incorporating Multi-spiral shaped fracture and horizontal-vertical crossing shaped fracture. However, the propagation behavior of fracture far away from wellbore is controlled by in-situ stress, forming a planar fracture. The highlights of this 3D near-wellbore fracture propagation model are following: 1) it considers near-wellbore stress change caused by each construction to ensure the accuracy of near-wellbore stress distribution; 2) it achieves 3D simulation of fracture initiation and near-wellbore propagation from perforations; 3) the interaction between fractures is involved, resulting in complex and torturous morphology. This model provides the theoretical basis for fracture initiation and propagation, which also could be applied into heterogenous formations considering the effect of discontinuities.

scholarly journals Assessment of Susceptibility to Liquefaction of Saturated Road Embankment Subjected to Dynamic Loads

2014 ◽  
Vol 36 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Anna Borowiec ◽  
Krzysztof Maciejewski
Keyword(s):  
Factor Of Safety ◽  
Stress Component ◽  
Critical Time ◽  
Water Reservoir ◽  
Constitutive Relationship ◽  
Plastic Behavior ◽  
Shear Stresses ◽  
Time Step ◽  
The Road ◽  
Liquefaction Susceptibility

Abstract Liquefaction has always been intensely studied in parts of the world where earthquakes occur. However, the seismic activity is not the only possible cause of this phenomenon. It may in fact be triggered by some human activities, such as constructing and mining or by rail and road transport. In the paper a road embankment built across a shallow water reservoir is analyzed in terms of susceptibility to liquefaction. Two types of dynamic loadings are considered: first corresponding to an operation of a vibratory roller and second to an earthquake. In order to evaluate a susceptibility of soil to liquefaction, a factor of safety against triggering of liquefaction is used (FSTriggering). It is defined as a ratio of vertical effective stresses to the shear stresses both varying with time. For the structure considered both stresses are obtained using finite element method program, here Plaxis 2D. The plastic behavior of the cohesionless soils is modeled by means of Hardening Soil (HS) constitutive relationship, implemented in Plaxis software. As the stress tensor varies with time during dynamic excitation, the FSTriggering has to be calculated for some particular moment of time when liquefaction is most likely to occur. For the purposes of this paper it is named a critical time and established for reference point at which the pore pressures were traced in time. As a result a factor of safety distribution throughout embankment is generated. For the modeled structure, cyclic point loads (i.e., vibrating roller) present higher risk than earthquake of magnitude 5.4. Explanation why considered structure is less susceptible to earthquake than typical dam could lay in stabilizing and damping influence of water, acting here on both sides of the slope. Analogical procedure is applied to assess liquefaction susceptibility of the road embankment considered but under earthquake excitation. Only the higher water table is considered as it is the most unfavorable. Additionally the modified factor of safety is introduced, where the dynamic shear stress component is obtained at a time step when its magnitude is the highest - not necessarily at the same time step when the pore pressure reaches its peak (i.e., critical time). This procedure provides a greater margin of safety as the computed factors of safety are smaller. Method introduced in the paper presents a clear and easy way to locate liquefied zones and estimate liquefaction susceptibility of the subsoil - not only in the road embankment.

Optimization of In-Stage Diversion To Promote Uniform Planar Multifracture Propagation: A Numerical Study

SPE Journal ◽  
2020 ◽  
Vol 25 (06) ◽  
pp. 3091-3110
Author(s):  
Ming Chen ◽  
Shicheng Zhang ◽  
Tong Zhou ◽  
Xinfang Ma ◽  
Yushi Zou
Keyword(s):  
Numerical Study ◽  
High Stress ◽  
In Situ Stress ◽  
Stress Difference ◽  
Multiple Fractures ◽  
Stress Shadow ◽  
Limited Entry ◽  
Fully Coupled ◽  
Flux Redistribution

Summary Creating uniform multiple fractures is a challenging task due to reservoir heterogeneity and stress shadow. Limited-entry perforation and in-stage diversion are commonly used to improve multifracture treatments. Many studies have investigated the mechanism of limited-entry perforation for multifracture treatments, but relatively few have focused on the in-stage diversion process. The design of in-stage diversion is usually through trial and error because of the lack of a simulator. In this study, we present a fully coupled planar 2D multifracture model for simulating the in-stage diversion process. The objective is to evaluate flux redistribution after diversion and optimize the dosage of diverters and diversion timing under different in-stage in-situ stress difference. Our model considers ball sealer allocation and solves flux redistribution after diversion through a fully coupled multifracture model. A supertimestepping explicit algorithm is adopted to solve the solid/fluid coupling equations efficiently. Multifracture fronts are captured by using tip asymptotes and an adaptive time-marching approach. The modeling results are validated against analytical solutions for a plane-strain Khristianovic-Geertsma de Klerk (KGD) model. A series of numerical simulations are conducted to investigate the multifracture growth under different in-stage diversion operations. Parametric studies reveal that the in-stage in-situ stress difference is a critical parameter for diversion designs. When the in-situ stress difference is larger than 2 MPa, the fracture in the high-stress zone can hardly be initiated before diversion for a general fracturing design. More ball sealers are required for the formations with higher in-stage in-situ stress difference. The diverting time should be earlier for formations with high in-stage stress differences as well. Adding more perforation holes in the zone with higher in-situ stress is recommended to achieve even flux distribution. The results of this study can help understand the multifracture growth mechanism during in-stage diversion and optimize the diversion design timely.

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