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ABSTRACT: Controlled fracture geometry is one of the most important criteria that measure the success of a hydraulic fracturing treatment. Typical stress conditions often lead to generation of a planar vertical fracture. Even for this simple geometry, fracture growth in a multilayered rock depends on many factors, such as stress, toughness and modulus contrasts across layers, fracturing fluid viscosity and injection rate. In the present work, a new cell-based pseudo-3D (P3D) model, which uses plane strain deformation in each vertical cross-section and simplified 2D flow assumptions, is described, with an aim to extend the classical P3D model to consider the effect of multiple elastic layers. To capture the effect of viscous fluid flow on height growth, the flow direction at a point along a cell is taken either lateral or vertical, depending on the local pressure level. The lateral flow region is divided into a so called central part that is subject to the maximum fluid pressure in a cell and the vertical flow region which is called the filling segment or part of the cell. The vertical and lateral fracture growth is controlled by the toughness criterion, and, the lateral stress intensity factor is used to convert a filling segment into the central part so as to accelerate lateral fracture growth by changing the local pressure level to the maximum of the cell. The governing equations associated with the problem are provided. A comparison is made between numerical results and the fully 3D (F3D) simulations for a vertically planar fracture propagating in a homogeneous rock subject to stress contrast. The numerical results appear reasonably acceptable. Some solution features associated with the proposed model are delineated. In addition, a special example for hydraulic fracture propagation in a layered rock is examined and the fracture height is found to increase much slower than the fracture length.
Hydraulic fracture treatments in multiple-layer, low- permeability unconventional gas reservoirs provide an important stimulation technology. In a layered rock formation, there are dissimilarities in confining stresses and material properties across the layers. The fracture height growth can be enhanced or constrained by these stress and material property changes (Palmer and Kutas, 1991; Gu and Siebrits, 2008; Gu et al., 2008), as well as by any slippage along the interfaces (Gu et al., 2008; Fan et al., 2014; Chuprakov et al., 2015;). Fracture containment or limited fracture height growth may result in dominant lateral fracture growth with fluid flow localized in the lower-modulus, lower-stress layers (Jeffrey et al., 1993).
Copyright 2011, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Denver, Colorado, USA, 30 October-2 November 2011. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract Much public discourse has taken place regarding hydraulic-fracture growth in unconventional reservoirs and whether fractures could potentially grow up to the surface and create communication pathways for frac fluids or produced hydrocarbons to pollute groundwater supplies. Real fracture-growth data mapped during thousands of fracturing treatments in unconventional reservoirs are presented along with the reported aquifer depths in the vicinity of the fractured wells. These data are supplemented with an in-depth discussion of fracture-growth limiting mechanisms augmented by mineback tests and other studies performed to visually examine hydraulic fractures. These height-growth limiting mechanisms, which are supported by the mapping data, provide insight into why hydraulic fractures are longer laterally and more constrained vertically. This information can be used to improve models, optimize fracturing, and provide definitive data for regulators and interest groups.
Abstract There is compelling evidence that majority of industrial hydraulic fractures have limited vertical growth (height). Theoretical and experimental work on fracture extension show that limiting the fracture height will result in continuously increasing fluid pressure during the treatment. Yet, field data does not support this point. This paper resolves the contradiction between theoretical and experimental data and field evidence. In the past, three mechanisms have been offered for fracture containment. These are stress contrast, modulus contrast, and fracture slippage. This paper shows that stress and modulus contrast do not stop the fracture height growth by themselves. They mainly change the fracture width and conductivity. Shear failure (slippage), on the other hand, results in blunting of the fracture tip and completely stops its local growth. This has important implications for the length and width of the fracture; the former becoming shorter and latter wider. A new mechanism offered for fracture containment is fracture re-orientation near an interface. Although the mechanism for such behavior is not well-defined, its presence has been observed directly in coal mines, and anecdotally by microseismic and tiltmeter surveys. The long length of the tip area means that different mechanisms may account for containment of the same fracture at different points and times. Contrast between the Young's moduli and stresses of the bounding layers may sometimes be enough to hald local fracture growth. Due to formation inhomogeneity the fracture may be contained at a given point and time, but cross the interface at a later time. General Background Estimation or determination of fracture height has been the most difficult technical question in hydraulic fracturing. The significance of the subject spans issues related to containment of reservoir fluid, production of unwanted water or gas, as well as optimizing the reservoir production. There is strong evidence suggesting that the vertical extent of many industrial hydraulic fractures is much less than their lateral growth. Such evidence consists of production mixture (absence or smaller than expected flow of water or gas), temperature and tracer logs, and seismic and tiltmeter fracture mapping. The early attempts to address fracture containment were focused on formation elastic properties. Using stress intensity computations for a fracture approaching an interface, Simonson et al argued that a formation with a higher Young's modulus can act as a barrier for a fracture propagating in a lower modulus rock. However, laboratory experiments conducted by Daneshy and field experiments by Sandia National Laboratory at Nevada Test Site showed that contrast in elastic moduli is not sufficient to stop the growth of a hydraulic fracture across an interface. Daneshy also introduced the concept of shear sliding of the fracture at interfaces and argued that blunting of the fracture tip due to sliding is a more plausible mechanism for fracture containment. The significance of shear sliding at the interface was later confirmed by the experimental work of Anderson.
The propagation of a single fluid-filled fracture from the surface of a semi-infinite isotropic elastic solid, subjected to both a transient temperature field and a constant source fluid pressure that is less than the confining stress, is studied using a boundary element method. Fluid flow in fractures is described by the lubrication equation, while the local pressure is determined by the strong coupling between elastic deformation, heat conduction and fluid pressure. Numerical results show that the combination of cooling-induced tensile stress and the source pressure can enhance the propagation speed. Parametric studies are carried out for identifying speed regimes and show the importance of the initial fracture aperture. Three speed regimes are found to exist. If the fluid penetration into the fracture is heavily restricted, the fracture length grows exponentially at early time, and then it suddenly reaches a large speed and progressively decelerates in a finite transition time as fluid diffusion speed varies, but eventually it follows the exponential fracture growth curve at a higher index for stable fluid flow in high-permeability fractures. The time-dependent crack growth behavior does not show any signs of unstable growth, even in the high-speed transition regime. The predictions of crack growth kinetics show a good agreement with some published experimental results and highlight the stabilizing effect of fluid transport on crack growth.
Hydraulic fracture geometry (i.e., critical results of length and proppant placement) is driven by four major in situ parameters: Fracture Height (H), Modulus (E), Fluid Loss (C), and "Apparent" Fracture Toughness (KI c-app ). In many (even most) cases, "Height" is the most important of these parameters - due to the need for some height confinement to achieve long fractures, or the need for height growth to insure good pay coverage. Due to this importance, industry research effort and most field measuring techniques concentrate on "Height." In particular, the growing use of seismic imaging is offering a tool to measure height growth away from the wellbore. Results from such diagnostics have often shown, as one expects, that in situ stress variations control height. However, results have also shown situations where this is apparently not the case.
This paper examines another in situ parameter, "Layered Modulus," which also affects height. In addition, by controlling the "local" width of a fracture, layered modulus (i.e., layered formations with different layers having significantly different modulus) can have a critical effect on final proppant placement.
The importance of layered modulus in directly controlling fracture height is illustrated in this paper, and this is compared with published solutions. In general, it is found that, just as concluded in the past, modulus contrast is probably not an important parameter in terms of direct control of fracture height. The greater importance lies in the effects on local fracture width. These local width changes can have a significant influence on controlling proppant placement - and this can be critical for low net pressure cases such as "water fracs" or fracturing in "soft" formations. It is also noted that layered modulus significantly impacts the average width of a fracture, and thus impacts the critical material balance aspects of fracture modeling if not properly accounted for.
Finally, some of the theoretical solution problems created by "Layered Modulus" formations for fracture modeling are discussed and compared. This is done by comparing with 3-D Finite Element (static) solutions, and shows how some common industry "approximations" for layered modulus give incorrect results. Based on this, examples with a fracture propagation model using a finite element-generated stiffness matrix are used to define types of cases where a simple "average" modulus is acceptable, versus cases where more complex calculations are needed.
Six major variables control hydraulic fracturing, fracture geometry, proppant placement, etc. Two of these are the "controllable" variables of fluid viscosity, µ, and pump rate, Q. The remaining four variables are "natural" variables and include:
Height. Fracture height (or more generally fracture geometry) is possibly the most important unknown for fracture design and post-frac production success. Generally, it is recognized that in situ stress differences (the in situ stress profile) is the major controlling factor for this behavior.  At a minimum, in situ stress differences control the maximum fracture height, i.e., if the net pressure is not available to grow through high stress shale layers, then fracture height must be contained. The importance of fracture height/geometry is clear, and there are many research efforts and technical publications addressing this issue. [1-6]
Fluid Loss. Fluid loss is typically characterized for hydraulic fracturing by a fluid loss coefficient, C, which characterizes linear flow fluid loss out of the fracture. This gives the familiar C/ (t-t) form of fluid loss behavior. Again, this variable has been exhaustively discussed in the literature including wall building characteristics of specific fluid systems, effects of natural fractures, behavior of fluid loss additives, etc. [7-16]