Hydraulic Fracture Height Growth Research Articles

Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs

In this study, a fully coupled hydromechanical model within the extended finite element method (XFEM)-based cohesive zone method (CZM) is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast. The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment. Then, the fracture geometry (e.g. height, aperture, and area) and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model. The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented. The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’ tips when propagating in soft layers, which impedes the simultaneous height growth. It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures. After that, the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented, and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing. Finally, it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures. The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.

Laboratory demonstration of the impact of weak interfaces and layered rock properties on hydraulic fracture containment and height growth

Hydraulic fracturing and waterflooding are both widely applied methods for improving the recovery of oil and gas resources. These methods have increasing commonality because many waterfloods are being carried out at high enough pressure to generate hydraulic fractures. Even so, it is challenging for engineers to make an optimal wellbore pressure design for layered and otherwise complex underground formations. An overly aggressive injection pressure may lead to uncontrollable fracture height growth into non-producing layers adjacent to the reservoir. In contrast, when using classical but highly simplified height growth models, the pressure limits can be far too conservative which may lead to lower recovery rates and inefficient use of resources invested in developing producing reservoirs. Therefore, it is necessary to investigate the mechanism of fracture height growth while considering the coupling effect from multiple dominated factors. This research contributes an experimental approach to evaluating the role of stresses, weak interfaces, and mechanical properties of a three-layer system in promoting or containing hydraulic fracture height growth from a central reservoir into neighboring barrier layers. In all cases, the experiments agree that the pressure required to induce substantial height growth exceeds the stress applied to the barrier layers and is far above classical predictions. Additionally, when the reservoir layer is softer than the barriers, the containment is sustained to even higher pressures than for layers with similar material properties. Finally, the experiments show that permeability of the barrier layer can induce a more sudden transition to uncontrolled height growth when fracture reaches the bedding interfaces. Hydraulic fracture height growth is mitigated by weak interfaces between layers. Unstable height growth typically requires fluid pressure to exceed the in-situ stress in the bounding layer(s). Contrasting layer stiffness and permeability often leads to further mitigation of height growth.

Numerical investigation of hydraulic fracture height growth in layered rock based on peridynamics

In this study, we explore hydraulic fracture (HF) propagation and fracture height growth in layered rocks using a self-developed three-dimensional hydraulic fracturing model based on peridynamics. The influences of the rock dip angle, rock interface strength and in-situ stress distribution on the HF propagation in the height direction and the fracture distribution are studied. In horizontally layered rock formations, the in-situ stress distribution significantly affects the HF propagation pattern. The HF preferentially propagates into the rock layer with lower horizontal stress. In inclined layered rock formations, the interaction between the HF and the interfaces controls fracture propagation in the height direction. A smaller layer dip angle and larger vertical stress enables the HF to penetrate the interface and propagate in the height direction. A larger layer dip angle and lower interface strength (toughness) causes the HF to be more easily captured by the interfaces and further promotes fracture propagation in the height direction. Furthermore, we simulated fracture propagation in a thin-interbedded reservoir. The simulation results show that the fracture propagation pattern in the thin-interbedded reservoir is very complex due to the anisotropy of the formation, and the HFs in the thin-interbed are usually rough surfaces.

Anisortopic Modeling of Hydraulic Fractures Height Growth in the Anadarko Basin

Correct estimation of hydraulic fracture height growth is a critical step in the design of Hydraulic Fracturing (HF) treatment, as it maximizes the reservoir stimulation and returns on investment. The height of the fractures is governed by several in situ conditions, especially stress variation with depth. The common workflow to estimate stress is by building the mechanical earth model (MEM) and calibrating it using the Diagnostic Fracture Injection Test (DFIT). However, DFIT interpretation is a complex task, and depending on the method used, different results may be obtained that will consequently affect the predicted hydraulic fracture height. This work used the tangent and compliance methods for DFIT interpretation, along with isotropic and anisotropic stress profiles, to estimate the HF height growth using numerical modeling in a 3D planar HF simulator. Data from two wells in the Anadarko Basin were used in this study. The predicted height was compared with microseismic data. The results showed that even though the tangent method fits better to the isotropic stress profile, HF did not match with the microseismic data. On the contrary, the anisotropic stress profile showed a good match between the compliance DFIT model and the microseismic events. Based on the discussions presented in this study, the validity of the DFIT interpretation is debatable, and when the formations are anisotropic, the isotropic model fails to correctly estimate the minimum stress profile, which is the main input for the estimation of the fracture height. This is in addition to the fact that some researchers have questioned the use of the tangent method in low-permeability formations.

Numerical Simulation on Hydraulic Fracture Height Growth across Layered Elastic–Plastic Shale Oil Reservoirs

Shale oil reservoirs are characterized by having various types of vertical sublayers, a large contrast in rock mechanical properties, well-developed bedding, and high clay content, which are likely to cause rock elastic–plastic deformation. In numerical simulations of hydraulic fracture (HF) propagation in the shale oil reservoirs, the effects of rock elastic–plastic deformation and complex bedding structure on the layer-crossing behavior of HF are not considered. To understand the mechanism of HF height growth in shale oil reservoirs, we used the cohesive zone method to establish an elastic–plastic finite element model of HF propagation by considering the effects of shell limestone interlayers, the Mohr–Coulomb yield criterion for shear–plastic failure, the cross-mechanical interaction between bedding and shale oil reservoir, and the complex situations such as the HF height across high-electrical resistivity bedding and high-conductivity fractures. The effects of internal friction angle, cohesion, layer stress contrast, fracture toughness, bedding bond strength, injection rate, elastic modulus, and bedding shear strength on HF height growth in shale oil reservoirs are studied, and the characteristics of HF width profile, injection pressure, failure mode, and maximum HF width are compared. Compared with the layer stress contrast, cohesion, internal friction angle, and fracture toughness, the injection rate, elastic modulus, and bedding shear strength and bond strength have a larger effect on the vertical HF width. Increment of the injection rate, decrease of the elastic modulus, and increment of the bedding shear strength and bond strength are favorable for HF height growth in the shale oil reservoir. As rock cohesion and internal friction angle increase, the HF width decreases. At the initial stage of fracturing fluid injection, the maximum HF height and injection pressure fluctuate. Lower cohesion and internal friction angle promote rock shear failure in HF height growth. Our study provides guidance for the stimulation of fracture crossing layers in the shale oil reservoirs.

An Efficient Model for Hydraulic Fracture Height Growth Considering the Effect of Bedding Layers in Unconventional Shale Formations

Summary Understanding and quantifying the effect of the weak bedding layers on the hydraulic fracture height growth in shale formations has always been challenging during the hydraulic fracturing design and operations. This work introduces a comprehensive and nonintrusive hydraulic fracture height growth model that accounts for both formation rock properties and the weak interfaces and can be incorporated into pseudo-3D hydraulic fracture simulators. The formation rock properties are handled by the equilibrium fracture height model. The shear slippage of the weak bedding layers is simulated by an efficient 2D higher-order displacement discontinuity method (HDDM), and the effectiveness on the hydraulic fracture height is quantified by correcting the stress intensity factors (SIFs) at the hydraulic fracture tips. The model is applied in the Permian Basin Wolfcamp formation to quantitatively investigate the effect of bedding layers on the hydraulic fracture height growth. Numerical studies show that the shear slippage of the beddings can significantly slow down the hydraulic fracture height growth and that the shear fracture toughness of the bedding layers and the spacing between the laminations have a considerable impact on the effectiveness of the shear slippage on the fracture height growth. Larger shear fracture toughness and smaller spacing of the bedding layers add more resistance to the fracture height propagation and require larger pressure to breakthrough. Additional results show that the effect of bedding layers is more significant in formations with low-stress contrast but less obvious in formations with high-stress contrast. The impact of the landing depth on the hydraulic fracture height growth is also investigated to provide crucial insights into the optimization of the landing depth in laminated formations.

A Review on Hydraulic Fracture Height Growth for Layered Formation

A Review on Hydraulic Fracture Height Growth for Layered Formation

Three-dimensional hydraulic fracturing modeling based on peridynamics

We established a three-dimensional (3D) hydraulic fracturing model based on peridynamics and subsequently validated it against an analytical solution. The 3D peridynamics model is based on a stress-based bond breaking criterion and contact-friction constitutive model. Parallel computing is used for this model to improve the computational efficiency. Furthermore, we studied the hydraulic fracture height growth and explored the interaction between the hydraulic fracture and the natural fracture in 3D space. The result shows from the 3D model and the 2D model are significantly different because the 3D model takes into account the fracture propagation in the height direction. Our model is capable of simulating the propagation of 3D hydraulic fractures.

Exploring the effect of engineering parameters on the penetration of hydraulic fractures through bedding planes in different propagation regimes

Bedding planes have a significant effect on the behaviour of hydraulic fracture height growth, increasing the complexity of understanding hydraulic fractures. At the same time, hydraulic fracture height growth is of pivotal importance for successful stimulation in shale reservoirs. This paper aims to explore the influence of engineering parameters on the behaviour process of hydraulic fractures penetrating bedding planes. The block discrete element method is used to investigate the penetration ability of hydraulic fractures under different fracturing fluid viscosities and injection rates. The results show that a high viscosity and high injection rate are beneficial for producing hydraulic fractures that penetrate bedding planes. The mechanism of the penetration behaviour of hydraulic fractures is investigated based on the analysis of stress evolution curves. The evaluation standard of penetrating ability is established based on the dimensionless Τ value in the established propagation regimes, which is useful to evaluate the interaction behaviour between hydraulic fractures and bedding planes. A close relationship is demonstrated between the Τ value and the stress curve. This study establishes a concise evaluation criterion for the penetrating behaviour of hydraulic fractures, which has theoretical significance for the study of hydraulic fracturing of shale reservoirs with bedding planes.

The study of hydraulic fracture height growth in coal measure shale strata with complex geologic characteristics

The coal measure shale strata (CMSS) is rich in coalbed methane and shale gas. However, different thicknesses and high heterogeneity between the coal and shale typically result in difficultly predicting hydraulic fracture height growth. The feasibility of multi-gas production and the optimal layer for fracturing in CMSS requires a better understanding of fracture vertical propagation mechanism. In this paper, a three-dimensional model of a hydraulic fracture crossing CMSS layer was built according to geological characteristics, based on the rock seepage-stress-damaged coupled finite element method. The influence of geological factors and construction factors on the hydraulic fracture expansion was investigated. The results showed that (1) The physical property and geological conditions presented a huge difference between different lithological rock with various depth; (2) The increase of displacement and fracturing fluid viscosity, the inhibition effect on vertical fracture extension became weak. The augment of displacement was more helpful to the vertical propagation of fracture; (3) Under low permeability difference and small horizontal minimal principal stress difference, fracture length propagated enough distance and fracture height extension gap connected more the production layer. Therefore, the favorable conditions for forming balanced fracture geometry were as follows: permeability difference from 0–3 and stress difference from 1–2 MPa. (4) The 11th layer was chosen as the best fracturing layer in Shanxi Formation. The fracture height was about 26.13 m and the thickness of pay layers accounted for 42.32% of the height. The research results provide theoretical guidance for the optimal fracturing layer and fracturing construction parameters in CMSS.

Hydraulic fracture height growth in layered rocks: Perspective from DEM simulation of different propagation regimes

A propagating fluid driven fracture in a rock mass is expected to interact with geological interfaces on a wide variety of length scales. The vertical growth of hydraulic fractures in layered rocks is of pivotal importance for the successful stimulation in reservoir development. In this study, 2D discrete element modeling is used to investigate the influence of the stiffness and toughness ratio, as well as stress contrast between layers on the hydraulic fracture height growth. In particular, the ultimate goal is to better understand mechanisms of the fracture height containment by contrasts of different rock properties and to quantitatively determine which parameters provide a stronger influence. In addition, the analysis is performed in the context of hydraulic fracture regimes, whereby the dominant dissipation mechanism in the system can either be associated with fracture toughness or viscous fluid flow. As a starting point, we investigated the propagation of a plane strain hydraulic fracture from a low stiffness layer to a high stiffness layer and vice versa, while keeping the stress constant. The influence of stress on hydraulic fracture propagation in layered rocks is investigated afterwards. The numerical results demonstrate that the hydraulic fracture can either directly pass through the geological interface, be arrested at the interface, or stop before reaching the interface. The interface itself is assumed to be perfectly bonded, therefore no slippage is considered. Ability of the hydraulic fracture to approach the interface is first determined by the elastic modulus ratio of the two adjacent layers. Once reached the interface, the further growth is then affected by the toughness ratio between the layers. After that, if the fracture crosses the interface, then it is affected by the stress contrast. The propagation regime has an important influence on the fracture propagation in layered rocks. If the propagation regime is closer to the viscosity dominated, the hydraulic fracture is likely to cross the interface. In contrast, it is more difficult for a fracture to cross the barrier if the propagation regime is near the toughness dominated. A map of fracture crossing behavior versus propagation regime and contrast in properties has been constructed, that can be used to quantify strength of mechanical barriers and to deduce hydraulic fracture height growth behavior for various scenarios.

The Impact of Layering and Permeable Frictional Interfaces on Hydraulic Fracturing in Unconventional Reservoirs

Summary The impacts of formation layering on hydraulic fracture containment and on pumping energy are critical factors in a successful stimulation treatment. Conventionally, it is considered that the in-situ stress is the dominant factor controlling the fracture height. The influence of mechanical properties on fracture height growth is often ignored or is limited to consideration of different Young’s moduli. Also, it is commonly assumed that the interfaces between different layers are perfectly bounded without slippage, and interface permeability is not considered. In-situ experiments have demonstrated that variation of modulus and in-situ stress alone cannot explain the containment of hydraulic fractures observed in the field (Warpinski et al. 1998). Enhanced toughness, in-situ stress, interface slip, and energy dissipation in the layered rocks should be combined to contribute to the fracture containment analysis. In this study, we consider these factors in a fully coupled 3D hydraulic fracture simulator developed based on the finite element method. We use laboratory and numerical simulations to investigate these factors and how they affect hydraulic fracture propagation, height growth, and injection pressure. The 3D fully coupled hydromechanical model uses a special zero-thickness interface element and the cohesive zone model (CZM) to simulate fracture propagation, interface slippage, and fluid flow in fractures. The nonlinear mechanical behavior of frictional sliding along interface surfaces is considered. The hydromechanical model has been verified successfully through benchmarked analytical solutions. The influence of layered Young’s modulus on fracture height growth in layered formations is analyzed. The formation interfaces between different layers are simulated explicitly through the use of the hydromechanical interface element. The impacts of mechanical and hydraulic properties of the formation interfaces on hydraulic fracture propagation are studied. Hydraulic fractures tend to propagate in the layer with lower Young’s modulus so that soft layers could potentially act as barriers to limit the height growth of hydraulic fractures. Contrary to the conventional view, the location of hydraulic fracturing (in softer vs. stiffer layers) does affect fracture geometry evolution. In addition, depending on the mechanical properties and the conductivity of the interfaces, the shear slippage and/or opening along the formation interfaces could result in flow along the interface surfaces and terminate the fracture growth. The frictional slippage along the interfaces can serve as an effective mechanism of containment of hydraulic fractures in layered formations. It is suggested that whether a hydraulic fracture would cross a discontinuity depends not only on the layers’ mechanical properties but also on the hydraulic properties of the discontinuity; both the frictional slippage and fluid pressure along horizontal formation interfaces contribute to the reinitiation of a hydraulic fracture from a pre-existing flaw along the interfaces, producing an offset from the interception point to the reinitiation point.

A semi-analytical model for estimation of hydraulic fracture height growth calibrated with field data

The vertical growth of hydraulic fractures in layered formations has been a topic of interest amongst researchers because of its critical influence on well performance. The analytical solution to the fracture vertical growth in layered formations is primarily based on force balance amongst various formation layers of segments that the vertical fracture intersects. The pressure associated with fluid movement in the vertical direction in a hydraulic fracture is generally ignored in most semi-analytical solutions to height-growth problems, especially if the vertical growth occurs at a slow pace. For a slow advancing vertical fracture, the tips are assumed to be near stationary, and the assumption is termed as equilibrium-height model. The model was first conceptualized for a simple 3-layered problem and later extended to multi-layered applications. The available literature shows model-derived solution for simple cases but lack in-depth study of real-world examples, which in doing so could highlight some of the model limitations.The semi-analytical model presented in the study, was first benchmarked by replicating the data published in the existing literature, and then applied to the field cases to compare its output with the observed data. Unlike the typical approach taken in the literature where the location of one of the tips of the fracture is assigned and the position of other tip is determined, the current model determines the most suitable position for a fracture of given height and stress profile. Additionally, new features were added to the model when evaluating the field cases. These include, incorporating calculation procedures that provide accurate fracture placement for given conditions, handling layered property inputs up to 100 layers, and the ability to include variable fracture pressure as opposed to a constant pressure approach.The model was applied on several cases from the field, four of which are presented here. The analysis showed that there is a close agreement between the predicted and the observed fracture heights. The hybrid feature of the model with inclusion of non-uniform pressure drop profile in the fracture, also helped in calibrating a case where a mismatch was observed. It was concluded that this model can predict fracture height growth with reasonable accuracy for cases with low injection rates where low viscosity fluid is used and requires calibration in cases where high net pressures are expected.The newly developed model is simple to program and can assist in making quick estimates of fracture vertical growth in vertical wells with low-rate fracture stimulation treatments.

Height Growth in Layered Unconventional Reservoirs: The Impact of Formation Moduli, Interfaces, and In-Situ Stress

Summary In recent years, much research effort has focused on hydraulic fracture (HF) height growth because height containment is needed to ensure effective stimulation of target zones. In many cases, fracture height growth determines the success or failure of a hydraulic stimulation. For layered rock systems, material properties, interface mechanical characteristics and permeability, and in-situ stresses influence both the lateral and height growth of HFs. It is generally believed that stress contrast is a dominant factor that directly controls the fracture height. The influence of Young's modulus contrast on height growth is usually ignored. Simplified “average methods” are often proposed and used to homogenize layered modulus. Also, it is commonly assumed that the layer interfaces are perfectly bonded without slippage even when high stress contrast exits. The above assumptions are made partially due to the difficulty in handling all the factors (e.g., layered modulus and stress contrast between adjacent layers) involved in simulations. In this study, a fully coupled 3D HF simulator that is based on the finite element method (FEM) is used to investigate the above factors and study how they impact HF propagation and height growth. The influence of modulus contrast, interface conditions, and in-situ stress on hydraulic fracturing and especially on fracture height growth is analyzed. The numerical approach is a 3D FEM with a special zero-thickness interface element based on the cohesive zone model (CZM) to simulate the fracture propagation and fluid flow in fractures. A local traction-separation law with strain-softening is used to capture tensile cracking. The nonlinear mechanical behavior of frictional sliding along interface surfaces is also considered. Because discontinuities are explicitly simulated through using the interface elements, details of the deformation processes are captured and revealed. For example, information related to aperture opening/sliding and stress distribution along the discontinuities is obtained in the simulations. After verification and validation of the numerical model, it is used to simulate height growth in layered rock of practical interest. The numerical model is evaluated through a commonly used crossing/arrest criterion. Laboratory experiments on fracture-discontinuity interaction under triaxial stress conditions are also studied. Numerical results match well with predictions from theoretical formulations and with laboratory observations. Typical processes associated with fracture-discontinuity interaction are revealed. The recorded injection pressure increases when the HF reaches a bedding interface (or other discontinuities). Continuous opening and/or sliding along the interface requires higher injection pressure. With the existence of a horizontal interface, the influence of modulus contrast and stress contrast on HF height growth is analyzed. The combined effects of rock properties, mechanical properties of the interfaces, and in-situ stress can effectively inhibit HF height growth. Analyzing pressure and aperture responses during fracture/interface interaction, it is revealed that the injection net pressure in the case where an offset exists along the interface is larger than that required if the HF could propagate continuously across the interface (no offset from the intersection point to the flaw along the interface). Whenever the free propagation of fracture tips is limited, either by horizontal formation interface or displacement constraints set intentionally to prevent fracture propagation, the injection net pressure and aperture at the injection point exhibit increase.

Three dimensional finite element simulations of hydraulic fracture height growth in layered formations using a coupled hydro-mechanical model

In this paper, we treat the important problem of hydraulic fracturing in the presence of elastic modulus and stress contrast in layered rock systems encountered in petroleum resources development using a fully coupled 3D hydro-mechanical model. First, the model is validated by simulating a laboratory hydraulic fracturing experiment dealing with the influence of stress contrast. Good agreements in the distribution of fracture aperture, injection pressure and fracture footprint have been achieved. Then, numerical analyses are performed to investigate the influence of in-situ stress and formation layer properties, such as Young's modulus and fracture energy release rate on the height growth and containment of hydraulic fractures. Comparing the results of simulations using conventional thickness-weighted Young's modulus to those from explicit modeling of layers' Young's moduli, it is found given that for the same amount of injection volume, the thickness-weighted modulus generates a higher injection pressure. Explicit modeling of the layers influences the hydraulic fracture aperture distribution in the pay zone as well as in the surrounding layers. A relatively large fracture aperture is observed in the layer with the lower Young's modulus. Also, the hydraulic fracture tends to propagates mainly in the lower Young's modulus layers which could facilitate containment of the hydraulic fracture by limiting height growth in the stiffer layers. When considering the influence of stress contrast on height growth, the conventional equilibrium height model produces a relatively large aperture and overestimates the fracture height. Simulations using typical injection rate, fluid viscosity, and in-situ stress, show stress contrast larger than a certain value, for example 30% of the in-situ minimum horizontal stress, can effectively inhibit height growth. When the payzone is bounded by ductile layers, the injection pressure is higher and the corresponding aperture at the injection point is larger than those obtained using uniform rock properties.

The Effect of Layered Modulus on Hydraulic-Fracture Modeling and Fracture-Height Containment

Summary Oil and gas production from unconventional reservoirs, which are usually stratified with layers having different mechanical properties, generally requires the aid of hydraulic–fracturing technology. Predicting hydraulic–fracture–height growth is one of the critical factors in designing successful hydraulic–fracturing treatments. It has been well–documented that the in–situ–stress contrast between adjacent layers and interface properties are the dominating factors in fracture–height containment, whereas the modulus contrast between adjacent layers is generally considered to be of secondary importance in the direct control of fracture–height containment. However, the arrest of fluid–driven fractures at soft layers is often observed in outcrops and hydraulic–fracture–diagnostic field tests. The objective of this study is to investigate fracture–height containment resulting from the modulus contrast between adjacent layers. To illustrate the effect of modulus contrast on fracture–height containment, this study proposes a new approach that uses the effective modulus of a layered reservoir. We use 2D finite–element models to evaluate the effective modulus of a layered reservoir, considering the effects of modulus values, fracture–tip location, height percentage of each rock layer, layer location, the number of layers, and the mechanical anisotropy. Then, the effect of modulus contrast on fracture–height growth is investigated with an analysis of the stress–intensity factor, taking into account the change of the effective modulus as the fracture tip propagates from the stiff layer to the soft layer. This study shows that the detail of layering does not affect the effective modulus and the only important parameters are fracture–tip locations, modulus values, and the height percentage of each rock layer. In addition, this study empirically derives two approximations of effective moduli depending on fracture–tip locations: the modified height–weighted mean and the modified height–weighted harmonic average. Results from combining linear–elastic fracture mechanics with the effective–modulus approximations show that height growth will be inhibited by the soft layer because of a reduced stress–intensity factor. The effective moduli can be applied to other hydraulic–fracture models to take into account the layering effect. This study also shows that soft layers inhibit hydraulic–fracture–height growth in layered reservoirs. As a result, hydraulic–fracture–height containment within a stratified rock stack can be better evaluated by comparing the modulus contrast between adjacent layers.

Uncertainty analysis of hydraulic fracture height containment in a layered formation

The prediction of hydraulic fracture height growth is of extreme interest in various engineering practices. To fully understand the dependence of the fracturing height in complex underground geological structures, it is crucial to develop theoretical and numerical hydraulic fracturing models to identify the key variables and their interactions to hydraulic fracture height containment. In this work, we adopt a three-dimensional hydro-mechanical coupling cohesive zone finite element model supported by logging data from a practical engineering project. A novel response surface method with Box–Behnken design is introduced to evaluate the statistical significance of tested variables and to forecast the optimal variable combinations for hydraulic fracture height. The key controlling variables are sorted according to their statistical significance from the analysis of variance, and only the minimum lateral stress ratios in mudstone layer and conglomerate layer are highly statistically significant. The minimum lateral in situ stress contrast is the predominant influence of fracture height containment regarding to their significant negative correlation, while the Young’s modulus contrast is probably not an important parameter in terms of direct control of fracture height. Upon optimization, 41 optimized variable combinations were achieved and could be served as references in regulating this engineering practice or even similar events.

Laboratory demonstration of hydraulic fracture height growth across weak discontinuities

Decades of research have led to numerous insights in modeling the impact of stresses and rock properties on hydraulic fracture height growth. However, the conditions under which weak horizontal interfaces are expected to impede height growth remain for the most part unknown. We have developed an experimental study of the impact of weak horizontal discontinuities on hydraulic fracture height growth, including the influences of (1) abrupt stress contrasts between layers, (2) material fracture toughness, and (3) contrasts of stiffness between the reservoir and bounding layers. The experiments are carried out with an analog three-layered medium constructed from transparent polyurethane, considering toughnesses resisting vertical fracture growth. There are four observed geometries: containment, height growth, T-shape growth, and the combination of height growth and T-shape. Results are developed in a parametric space embodying the influence of the horizontal stress contrast, vertical stress, and horizontal barrier stress contrast, as well as the fluid pressure. The results indicate that these cases fall within distinct regions when plotted in the parametric space. The locations in the parametric space of these regions are strongly impacted by the vertical fracture toughness: Increasing the value of the vertical interface fracture toughness leads to a suppression of height growth in favor of containment and T-shaped growth. Besides providing detailed experimental data for benchmarking 3D hydraulic fracture simulators, these experiments show that the fracture height is substantially less than would be predicted in the absence of the weak horizontal discontinuities.

Experimental and numerical study of hydraulic fracture geometry in shale formations with complex geologic conditions

Strike-slip fault geostress and dipping laminated structures in Lujiaping shale formation typically result in difficultly predicting hydraulic fracture (HF) geometries. In this study, a novel 3D fracture propagation model based on discrete element method (DEM) is established. A series of simulations is performed to illustrate the influence of vertical stress difference (△σv = σv−σh), fluid viscosity, and injection rate, on HF growth geometry in the dipping layered formation. Results reveal that the fracturing fluid can easily infiltrate the dipping bedding plane (BP) interfaces with low net pressure for △σv = 1 MPa. HF height growth is also restricted. With increased △σv, fracture propagation in the vertical direction is enhanced, and a fracture network is formed by VF and partially opened dipping BPs. However, it is likely to create simple VF for △σv = 20 MPa. Appropriately increasing fracturing fluid viscosity and injection rate is conductive to weakening the containment effect of BPs on HF growth by increasing the fluid net pressure. However, no indication is found on whether a higher fracturing fluid viscosity is better. Higher viscosity can reduce the activation of BPs, so a stimulated reservoir volume is not necessarily increased. All these results can serve as theoretical guidance for the optimization of fracturing treatments in Lujiaping shale formation.

Hydraulic Fracture Height Growth Containment by Artificial Barrier: Experimental Studies

It is necessary to control hydraulic fracture height growth by creating artificial barrier for reservoir with thin payzone or weak overburdens and underburdens. In this paper, the influential factors on resistance role of artificial barrier were firstly identified and the parameters value range was determined. Then, an affixing intermediate container was combined into the core flow test device in order to ensure buoyant diverter well dispersed into carrying fluid in experiment test, and the particle size distribution of buoyant additives was tested by Malvern laser counter. The crack was made about 2/3 length in artificial core for simulating artificial barrier process by core flow test which were accomplished in base of recommendation practice of petroleum industry. Lastly, successive regression method was applied and a statistical relationship of the barrier strength with carrying fluid viscosity, floating additives concentration and core permeability. Then scouring experiments are made under modeling hydraulically fracturing treatment conditions. It was proven that the artificial barrier was steady at current treatment parameters and that could be effectively controlled hydraulic fracture height growth.