An Improved Equilibrium-Height Model for Predicting Hydraulic Fracture Height Migration in Multi-Layer Formations

2015 ◽  
Author(s):  
Songxia Liu ◽  
Peter P. Valkó
Keyword(s):  
Fracture Toughness ◽  
Hydraulic Fracture ◽  
3D Models ◽  
In Situ Stress ◽  
Height Growth ◽  
Net Pressure ◽  
Fracture Height ◽  
Layer Problem ◽  
Equilibrium Height

Abstract Fracture height is a critical input parameter for 2D hydraulic fracturing design models, and also an important output result of 3D models. While many factors may influence fracture height evolution in multi-layer formations, the consensus is that the so called “equilibrium height belonging to a certain treating pressure” provides an upper limit, at least for non-naturally fractured media. How to solve the “equilibrium height” problem has been known since the 1970s. However, because of the complexity of the algebra involved, published equations are overly simplified and do not provide reliable results. We revisited the equilibrium height problem, and our theoretical and numerical investigations led to a new model that fully characterizes height evolution amid various formation properties (fracture toughness, in-situ stress, thickness, etc.). The new model, for the first time, rigorously solves the equilibrium height mathematically. With the help of computer algebra software, we applied a definition of fracture toughness, incorporated the effects of hydrostatic pressure, and considered non-symmetric variations of layered formation properties. Results were determined for the classic 3-layer problem and then were extended to 6 layers. The effects of reservoir and fluid properties on the fracture height growth were investigated. Tip jump is caused by low in-situ stress; tip stability is imposed by large fracture toughness and/or large in-situ stress. If the fluid density is ignored, the result regarding to which tip will grow into infinity could be totally different. For any multi-layer formation problem, two, 3-layer pseudo problems were constructed to create an outer and inner height envelope, in order to assess the potential effects of reservoir parameter uncertainties on height profile. Second solution pair in the 3-layer problem was investigated numerically and analytically, to avoid misleading results in the 3D models. This improved model can rapidly (in seconds) and reliably calculate the theoretical maximum equilibrium fracture height in layered formations with various rock mechanical properties. Then, the equilibrium height can be used to (1) provide input data for 2D model, (2) improve 3D model governing equations, (3) determine the net pressure needed to achieve a certain height growth, and (4) obtain the maximum net pressure assuring no fracture invasion into aquifers. This model may be incorporated into current hydraulic fracture simulation software to yield more accurate and cost-effective hydraulic fracturing designs.

scholarly journals Apparent Toughness Anisotropy Induced by “Roughness” of In-Situ Stress: A Mechanism That Hinders Vertical Growth of Hydraulic Fractures and Its Simplified Modeling

SPE Journal ◽  
2019 ◽  
Vol 24 (05) ◽  
pp. 2148-2162 ◽  
Author(s):  
Pengcheng Fu ◽  
Jixiang Huang ◽  
Randolph R. Settgast ◽  
Joseph P. Morris ◽  
Frederick J. Ryerson
Keyword(s):  
Hydraulic Fracture ◽  
High Stress ◽  
In Situ Stress ◽  
Height Growth ◽  
Hydraulic Fractures ◽  
Simple Relationship ◽  
Vertical Growth ◽  
Stress Profiles ◽  
Fracture Height

Summary The height growth of a hydraulic fracture is known to be affected by many factors that are related to the layered structure of sedimentary rocks. Although these factors are often used to qualitatively explain why hydraulic fractures usually have well–bounded height growth, most of them cannot be directly and quantitatively characterized for a given reservoir to enable a priori prediction of fracture–height growth. In this work, we study the role of the “roughness” of in–situ–stress profiles, in particular alternating low and high stress among rock layers, in determining the tendency of a hydraulic fracture to propagate horizontally vs. vertically. We found that a hydraulic fracture propagates horizontally in low–stress layers ahead of neighboring high–stress layers. Under such a configuration, a fracture–mechanics principle dictates that the net pressure required for horizontal growth of high–stress layers within the current fracture height is significantly lower than that required for additional vertical growth across rock layers. Without explicit consideration of the stress–roughness profile, the system behaves as if the rock is tougher against vertical propagation than it is against horizontal fracture propagation. We developed a simple relationship between the apparent differential rock toughness and characteristics of the stress roughness that induce equivalent overall fracture shapes. This relationship enables existing hydraulic–fracture models to represent the effects of rough in–situ stress on fracture growth without directly representing the fine–resolution rough–stress profiles.

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

2021 ◽  
pp. 1-14
Author(s):  
Qian Gao ◽  
Ahmad Ghassemi
Keyword(s):  
Mechanical Properties ◽  
Hydraulic Fracture ◽  
Fracture Propagation ◽  
In Situ Stress ◽  
Height Growth ◽  
Interface Element ◽  
Hydraulic Fractures ◽  
Hydraulic Fracture Propagation ◽  
Fracture Height

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.

scholarly journals A new chart of hydraulic fracture height prediction based on fluid–solid coupling equations and rock fracture mechanics

2018 ◽  
Vol 5 (10) ◽  
pp. 180600 ◽  
Author(s):  
Xiaoqiang Liu ◽  
Zhanqing Qu ◽  
Tiankui Guo ◽  
Dongying Wang ◽  
Qizhong Tian ◽  
...  
Keyword(s):  
Fracture Mechanics ◽  
Hydraulic Fracture ◽  
Rock Fracture ◽  
Shielding Effect ◽  
Stress Difference ◽  
Coupling Equations ◽  
Rock Fracture Mechanics ◽  
Net Pressure ◽  
Fracture Height

The conventional method to predict hydraulic fracture height depends on linear elastic mechanics, and the typical Gulrajani–Nolte chart fails to reflect fracture height when the net pressure in the fracture is too high. Based on fluid–solid coupling equations and rock fracture mechanics, a new chart is obtained by the ABAQUS extended finite-element method. Compared with the Gulrajani–Nolte chart, this new chart shows that longitudinal propagation of hydraulic fracture is still finite when the net pressure in the fracture is higher than in situ stress difference between reservoir and restraining barrier. The barrier has a significant shielding effect on the longitudinal propagation of hydraulic fracture, and there is a threshold for an injection rate of fracturing fluid to ensure hydraulic fracture propagates in the barrier. Fracture height decreases with the increase of in situ stress difference. When the ratio of net pressure to in situ stress difference is less than 0.56, the propagation of hydraulic fracture is completely restricted in the reservoir. Hydraulic fracturing parameters in Well Shen52 and Well Shen55 are optimized by using the new chart. Array acoustic wave logging shows that the actual fracture height is at an average error within 14.3% of the theoretical value, which proves the accuracy of the new chart for field application.

Laboratory demonstration of hydraulic fracture height growth across weak discontinuities

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. MR93-MR105 ◽  
Author(s):  
Pengju Xing ◽  
Keita Yoshioka ◽  
Jose Adachi ◽  
Amr El-Fayoumi ◽  
Andrew P. Bunger
Keyword(s):  
Fracture Toughness ◽  
Hydraulic Fracture ◽  
Fluid Pressure ◽  
Height Growth ◽  
Rock Properties ◽  
Vertical Fracture ◽  
Parametric Space ◽  
Fracture Height ◽  
Stress Contrast ◽  
The Impact

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.

Hydraulic-Fracture-Height Growth: Real Data

2012 ◽  
Vol 27 (01) ◽  
pp. 8-19 ◽  
Author(s):  
M. Kevin Fisher ◽  
Norman R. Warpinski
Keyword(s):  
Hydraulic Fracture ◽  
Real Data ◽  
Height Growth ◽  
Fracture Height

Interpretation of Hydraulic Fracturing Pressure in Tight Gas Formations1

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Gun-Ho Kim ◽  
John Yilin Wang
Keyword(s):  
Hydraulic Fracturing ◽  
In Situ Stress ◽  
Pressure Effects ◽  
Tight Gas ◽  
New Methods ◽  
Accurate Interpretation ◽  
Fracture Fluid ◽  
Net Pressure ◽  
Property Changes

The interpretation of hydraulic fracturing pressure was initiated by Nolte and Smith in the 1980s. An accurate interpretation of hydraulic fracturing pressures is critical to understand and improve the fracture treatment in tight gas formations. In this paper, accurate calculation of bottomhole treating pressure was achieved by incorporating hydrostatic pressure, fluid friction pressure, fracture fluid property changes along the wellbore, friction due to proppant, perforation friction, tortuosity, casing roughness, rock toughness, and thermal and pore pressure effects on in-situ stress. New methods were then developed for more accurate interpretation of the net pressure and fracture propagation. Our results were validated with field data from tight gas formations.

Hydraulic Fracture Geometry: Fracture Containment in Layered Formations

1982 ◽  
Vol 22 (03) ◽  
pp. 341-349 ◽  
Author(s):  
H.A.M. van Eekelen
Keyword(s):  
Stress Field ◽  
Cross Section ◽  
Horizontal Plane ◽  
Fluid Pressure ◽  
Vertical Plane ◽  
Fracture Propagation ◽  
In Situ Stress ◽  
Design Procedures ◽  
Fracture Height

Abstract One of the main problems in hydraulic fracturing technology is the prediction of fracture height. In particular, the question of what constitutes a barrier to vertical fracture propagation is crucial to the success of field operations. An analysis of hydraulic fracture containment effects has been performed. The main conclusion is that in most cases the fracture will penetrate into the layers adjoining the pay zone, the depth of penetration being determined by the differences in stiffness and in horizontal in-situ stress between the pay zone and the adjoining layers. For the case of a stiffness contrast, an estimate of the penetration depth is given. Introduction Current design procedures for hydraulic fracturing of oil and gas reservoirs are based predominantly on the fracturing theories of Perkins and Kern, Nordgren, and Geertsma and de Klerk. In the model proposed by Perkins and Kern, and improved by Nordgren, the formation stiffness is concentrated in vertical planes perpendicular to the direction of fracture propagation, The fracture cross section in these planes is assumed elliptical, and the stiffness of the formation in the horizontal plane is neglected. In the model proposed by Geertsma and de Klerk, the stiffness of the formation is concentrated in the horizontal plane. The fracture cross section in the vertical plane is assumed rectangular, and the stiffness in the vertical plane is neglected. In both models, the fluid pressure is assumed a function of the distance from the borehole, independent of the transverse coordinates. The theory by Perkins and Kern is more appropriate for long fractures (L/H >1, where L and H are length and height of the fracture), whereas the model by Geertsma and de Klerk is applicable for short fractures, L/H less than 1. The main shortcoming of these fracture-design procedures is that they assume a constant, preassigned fracture height. H. The value of H has a strong influence on the result, for fracture length, fracture width, and proppant transport. Usually, the estimated fracture height is based on assumed "barrier action" of rock layers above and below the pay zone. This situation is rather unsatisfactory. Moreover, if these layers do not contain the fracture, large volumes of fracturing fluid may be lost in fracturing unproductive strata, and communication with unwanted formations may be opened up. Whether an adjacent formation will act as a fracture barrier may depend on a number of factors: differences in in-situ stress, elastic properties, fracture toughness, ductility, and permeability; and the bonding at the interface. We analyze these factors with respect to their relative influence on fracture containment. Differences in in-situ stress and differences in elastic properties affect the global or overall stress field around the fracture, and, hence, the three-dimensional shape of the fracture. This shape, together with the horizontal and vertical fracture propagation rates, determines the fluid pressure distribution in the fracture, which in turn affects the stress field around the fracture. Consequently, the elastic stress field, the fluid pressure field, and the fracture propagation pattern are intimately coupled, which makes the fracture propagation problem a complicated one. Whether at a certain point of the fracture edge the fracture will propagate is determined by the intensity of the stress concentration at that point. This stress concentration depends on the global stress distribution in and around the fracture, but it also is affected directly by local ductility, permeability, and elastic modulus in the tip region. SPEJ P. 341^

scholarly journals Laboratory Investigation on the -Effect of In-Situ Stresses on Hydraulic Fracture Containment

1982 ◽  
Vol 22 (03) ◽  
pp. 333-340 ◽  
Author(s):  
Norman R. Warpinski ◽  
James A. Clark ◽  
Richard A. Schmidt ◽  
Clarence W. Huddle
Keyword(s):  
Pore Pressure ◽  
Hydraulic Fracture ◽  
Laboratory Experiments ◽  
In Situ Stress ◽  
Enhanced Production ◽  
In Situ Stresses ◽  
Extensive Growth ◽  
Stress Variations ◽  
Fracture Growth

Abstract Laboratory experiments have been conducted to determine the effect of in-situ stress variations on hydraulic fracture containment. Fractures were initiated in layered rock samples with prescribed stress variations, and fracture growth characteristics were determined as a function of stress levels. Stress contrasts of 300 to 400 psi (2 to 3 MPa) were found sufficient to restrict fracture growth in laboratory samples of Nevada tuff and Tennessee and Nugget sandstones. The required stress level was found not to depend on mechanical rock properties. However, permeability and the resultant pore pressure effects were important. Tests conducted at biomaterial interfaces between Nugget and Tennessee sandstones show that the resultant stresses set up near the interface because of the applied overburden stress affect the fracture behavior in the same way as the applied confining stresses. These results provide a guideline for determining the in-situ stress contrast necessary to contain a fracture in a field treatment. Introduction An under-standing of the factors that influence and control hydraulic fracture containment is important for the successful use of hydraulic fracturing technology in the enhanced production of natural gas from tight reservoirs. Optimally, this understanding would provide improved fracture design criteria to maximize fracture surface area in contact with the reservoir with respect to volume injected and other treatment parameters. In formations with a positive containment condition (i.e., where fracturing out of zone is not anticipated), long penetrating fractures could be used effectively to develop the resource. For the opposite case, the options would beto use a small treatment so that large volumes are not wasted in out-of-zone fracturing and to accept a lower productivity improvement, orto reject the zone as uneconomical. These decisions cannot be made satisfactorily unless criteria for vertical fracture propagation are developed and techniques for readily measuring the important parameters are available. Currently, both theoretical and experimental efforts are being pursued to determine the important parameters and their relative effects on fracture growth. Two modes of fracture containment are possible. One is the situation where fracture growth is terminated at a discrete interface. Examples of this include laboratory experiments showing fracture termination at weak or unbonded interfaces and theoretical models that predict that fracture growth will terminate at a material property interface. The other mode may occur when the fracture propagates into the bounding layer, but extensive growth does not take place and the fracture thus is restricted. An example is the propagation of the fracture into a region with an adverse stress gradient so that continued propagation results in higher stresses on the fracture, which limits growth, as suggested by Simonson et al. and as seen in mineback experiments. Another example is the possible restriction caused by propagation into a higher modulus region where the decreased width results in increased pressure drop in the fracture, which might inhibit extensive growth into that region relative to the lower modulus region. Other parameters, such as natural fractures, treatment parameters, pore pressure, etc., may affect either of these modes. Laboratory and mineback experiments have shown that weak interfaces and in-situ stress differences are the most likely factors to contain the fracture, and weak interfaces are probably effective only at shallow depths. Thus, our experiments are being performed to determine the effect of in-situ stresses on fracture containment, both in a uniform rock sample and at material properly interfaces. SPEJ P. 333^

Some Effects of Stress, Friction, and Fluid Flow on Hydraulic Fracturing

1982 ◽  
Vol 22 (03) ◽  
pp. 321-332 ◽  
Author(s):  
M.E. Hanson ◽  
G.D. Anderson ◽  
R.J. Shaffer ◽  
L.D. Thorson
Keyword(s):  
Fluid Flow ◽  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Research Program ◽  
In Situ Stress ◽  
Material Interfaces ◽  
Fracture Geometry ◽  
Funded Research ◽  
Fracturing Process

Abstract We are conducting a U.S. DOE-funded research program aimed at understanding the hydraulic fracturing process, especially those phenomena and parameters that strongly affect or control fracture geometry. Our theoretical and experimental studies consistently confirm the well-known fact that in-situ stress has a primary effect on fracture geometry, and that fractures propagate perpendicular to the least principal stress. In addition, we find that frictional interfaces in reservoirs can affect fracturing. We also have quantified some effects on fracture geometry caused by frictional slippage along interfaces. We found that variation of friction along an interface can result in abrupt steps in the fracture path. These effects have been seen in the mineback of emplaced fractures and are demonstrated both theoretically and in the laboratory. Further experiments and calculations indicate possible control of fracture height by vertical change in horizontal stresses. Preliminary results from an analysis of fluid flow in small apertures are discussed also. Introduction Hydraulic fracturing and massive hydraulic fracturing (MHF) are the primary candidates for stimulating production from tight gas reservoirs. MHF can provide large drainage surfaces to produce gas from the low- permeability formation if the fracture surfaces remain in the productive parts of the reservoir. To determine whether it is possibleto contain these fractures in the productive formations andto design the treatment to accomplish this requires a much broader knowledge of the hydraulic fracturing process. Identification of the parameters controlling fracture geometry and the application of this information in designing and performing the hydraulic stimulation treatment is a principal technical problem. Additionally, current measurement technology may not be adequate to provide the required data. and new techniques may have to be devised. Lawrence Livermore Natl. Laboratory has been conducting a DOE-funded research program whose ultimate goal is to develop models that predict created hydraulic fracture geometry within the reservoir. Our approach has been to analyze the phenomenology of the fracturing process to son out and identify those parameters influencing hydraulic fracture geometry. Subsequent model development will incorporate this information. Current theoretical and stimulation design models are based primarily on conservation of mass and provide little insight into the fracturing process. Fracture geometry is implied in the application of these models. Additionally, pressure and flow initiation in the fractures and their interjection with the fracturing process is not predicted adequately with these models. We have reported previously on some rock-mechanics aspects of the fracturing process. For example, we have studied, theoretically and experimentally, pressurized fracture propagation in the neighborhood of material interfaces. Results of interface studies showed that natural fractures in the interfacial region negate any barrier effect when the fracture is propagating from a lower modulus material toward a higher modulus material. On the other hand, some fracture containment could occur when the fracture is propagating from a higher modulus into a lower modulus material. Effect of moduli changes on the in-situ stress field have to be taken into consideration to evaluate fracture containment by material interfaces. Some preliminary analyses have been performed to evaluate how stress changes when material properties change, but we have not evaluated this problem fully. SPEJ P. 321^

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