Modeling of interactions of hydraulic fractures in complex fracture networks

Description [1] This patent application claims the priority of US Provisional Application No. 61/900479 registered on November 6, 2013, the entire content of which is incorporated herein by citation. This patent application is a continuation in part of US patent application no. 11/356369 registered on November 2, 2012, the entire content of which is incorporated herein by citation.

[2] The present invention relates generally to methods and systems for performing well site operations. More specifically, this invention is directed to methods and systems for performing fracturing operations, such as investigating underground formations and characterizing hydraulic fracturing networks from an underground formation.

[3] In order to facilitate the recovery of hydrocarbons from oil and gas wells, the underground formations surrounding these wells can be hydraulically fractured. Hydraulic fracturing can be used to create cracks in underground formations to allow oil and gas to move to the well. A formation is fractured by introducing a specially designed fluid (referred to as "fracture fluid" or "fracture suspension" in the front frame) at high pressure and high flow rates within the formation through one or more drilling holes. The hydraulic fractures can extend from the drill hole to hundreds of feet in two opposite directions according to the natural efforts within the formation. In certain circumstances, they may form a network of complex fractures. Complex fracture networks may include induced hydraulic fractures and natural fractures, which may or may not intersect, along several azimuths, in several planes and directions and in several regions.

[4] Current methods and systems for monitoring hydraulic fractures can map locations where fractures occur and fracture size. Some micro-seismic monitoring methods and systems can process the locations of seismic events by mapping seismic arrival times and polarizing information in the three-dimensional space by using travel times and / or modeled ray paths. These methods and systems can be used to infer the propagation over time of hydraulic fractures.

[5] The models of hydraulic fractures created by the stimulation of the fracture can be complex and they can form a network of fractures, as indicated, through a distribution of events.

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Λ; 2 ο 1 6 - - 0 0 3 2 3 0 6 -11- 20Η associated micro-seismic. Complex networks of hydraulic fractures were developed to represent the hydraulic fractures created. Examples of fracture models are provided in US Patent / Patent Applications 6101447, 7363162, 7788074, 20080133186, 20100138196 and 20100250215.

[6] In at least one aspect, the present invention relates to methods for performing a fracture operation in a well location. The well location is positioned around an underground formation having a drill hole through it and a network of fractures in it. The fracture network has natural fractures in it. The well location can be stimulated by injecting a supporting fluid into the fracture network. The methods involve obtaining data about the well location including the parameters of natural fractures and obtaining a mechanical ground model of the underground formation and generating a model of hydraulic fracture development for the fracture network over time. Generation involves the extension of hydraulic fractures from the borehole and within the fracture network of the underground formation to form a network of hydraulic fractures including natural and hydraulic fractures, determining the parameters of hydraulic fractures after expansion, determining the transport parameters for the passing support agent. through the hydraulic fracturing network, and determining the dimensions of the hydraulic fractures from the determined parameters of the hydraulic fractures, the determined transport parameters and the mechanical soil model. The method also involves conducting efforts on hydraulic fractures to determine the interference of efforts between hydraulic fractures at different depths, conducting additional efforts on hydraulic fractures to determine the interference of efforts between hydraulic fractures at different depths, and repeat generation based on interference. determined efforts. The method may also include analyzing stress interference between hydraulic fractures to evaluate the development of the height of each fracture.

[7] Effort tracking may involve performing a first effort tracking to determine interference between hydraulic fractures and / or conducting a second pursuit to determine interference between hydraulic fractures at different depths. Effort tracking can involve performing a two-dimensional displacement discontinuity method and / or performing a three-dimensional displacement discontinuity method.

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ο 1 6 - - 0 0 3 2 3 0 6 -π- 23Η [8] If the hydraulic fracture encounters a natural fracture, the method may also involve determining the intersecting behavior between the hydraulic fractures and a fracture encountered based on determined stress interference, and repetition may involve repetition of generation based on determined effort interference and intersecting behavior. The method may also involve stimulating the well location by injecting a supporting fluid into the fracture network.

[9] The method may also involve, if the hydraulic fracture encounters a natural fracture, determining the intersecting behavior to the natural fracture encountered, and in which the repetition comprises the repetition of the generation based on the determined stress interference and the intersecting behavior. The model of development of hydraulic fractures can be influenced or not influenced by the intersecting behavior. A fracture pressure in the hydraulic fracture network can be greater than an effort acting on the fracture encountered, and the fracture development model can propagate along the fracture encountered. The fracture development model can continue to propagate along the fracture encountered until one end of the natural fracture is reached. The fracture development model can change its direction at the end of the natural fracture, and the fracture development model can extend in a normal direction with minimal effort at the end of the natural fracture. The fracture development model can normally propagate on a local main effort according to the efforts tracking.

[10] Effort tracking may involve achieving discontinuity of movement for each of the hydraulic fractures. Effort tracking may involve tracking efforts around multiple drill holes in a well location and repeating the generation using effort tracking performed on multiple drill holes. Effort tracking can involve conducting efforts in several simulation stages in the drill hole.

[11] The method may also involve validating the fracture development model. Validation may involve comparing the fracture development model with at least one simulation of fracture network stimulation. The method may also involve adjusting the stimulation (for example, pumping rate and / or fluid viscosity) based on effort tracking.

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-2016-- 003230 6 -11- 2014 [12] The extension may involve the extension of hydraulic fractures along a model of fracture development based on the parameters of natural fractures and minimal effort and maximum effort on the underground formation. Determination of fracture dimensions may include one of the evaluation of seismic measurements, tracking of ants, sonic measurements, geological measurements and combinations thereof. The well location data may include at least one of the geological, geophysical, geomechanical, diagraphic, extension, historical, and combinations thereof. The parameters of natural fractures can be generated by observing the diagrams that make up the image of the drill hole, estimating the fracture dimensions from the measurements of the drill hole, obtaining the microseismic images and combinations thereof.

[13] Examples of embodiment of the system and method for characterizing the stresses in the drill hole are described with reference to the following figures. The same reference numbers are used throughout the figures to designate the same characteristics and components.

[14] FIG. 1.1 is a schematic illustration of a hydraulic fracturing location illustrating a fracturing operation;

[15] FIG. 1.2 is a schematic illustration of a hydraulic fracturing location with micro-seismic events illustrated therein;

[16] FIG. 2 is a schematic illustration of a 2D fracture;

[17] FIG. 3.1 and 3.2 are schematic illustrations of an effort tracking effect;

[18] FIG. 4 is a schematic illustration comparing 2D DDM and Flac3D for two straight parallel fractures;

[19] FIG. 5.1-5.3 are graphs illustrating 2D DDM and Flac3D of extended fractures for efforts at various positions;

[20] FIG. 6.1-6.2 are graphs illustrating propagation paths for two initially parallel fractures in isotropic and anisotropic stress fields;

[21] FIG. 7.1-7.2 are graphs illustrating propagation paths for two initially fractured fractures in isotropic and anisotropic stress fields;

[22] FIG. 8 is a schematic illustration of parallel transverse fractures along a horizontal well;

[23] FIG. 9 is a graph illustrating lengths for five parallel fractures;

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^- 2 0 1 6 -- 0 0 3 2 3 ^ν Ο 6 -ii- 2014 [24] Fig. 10 is a schematic diagram illustrating the geometry of the UFM fractures and the width for the parallel fractures in Figure 9;

[25] FIG. 11.1-11.2 are schematic diagrams illustrating the fracture geometry for a high perforation friction case and a large fracture spacing case respectively;

[26] FIG. 12 is a graph illustrating microseismic mapping;

[27] FIG. 13.1-13.4 are schematic diagrams illustrating a simulated fracture network compared to the microseismic measurements respectively for steps 1-4;

[28] FIG. 14.1-14.4 are schematic diagrams illustrating a network of fractures distributed in various stages;

[29] FIG. 15 is a block diagram illustrating a method of performing a fracturing operation; and [30] Fig. 16.1-16.4 are schematic illustrations showing the development of fractures around a borehole during a fracturing operation.

[31] FIG. 17 is a schematic diagram showing a coordinate system attached to a rectangular 3D DDM element.

[32] FIG. 18-20 are schematic diagrams showing two vertical fractures at different depths and affecting the increase of the height of each fracture due to the efforts tracking.

[33] FIG. 21 is a block diagram illustrating another method of performing a fracturing operation.

[34] The following description includes exemplary apparatus, methods, techniques and sequences that implement the techniques according to the object of the invention. However, it is understood that the embodiments described can be implemented without these specific details.

[35] Models have been developed to understand underground fracture networks. The models can take into account various factors and / or data, but they cannot be constrained by taking into account the quantity of fluid pumped or the mechanical interactions between fractures and the injected fluid and between fractures. Limited models can be provided to provide a basic understanding of the mechanisms involved, but may be complex in terms of mathematical description and / or may require computer and time processing resources to provide accurate simulations of fracture propagation.

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² Ο 1 6 - - 0 0 3 2 3 0 6 -11- 20Η hydraulic. A limited model can be configured to perform simulations to take into account factors such as the interaction between fractures, over time and under desired conditions.

[36] An unconventional fracture model (UFM) (or complex model) can be used to simulate complex propagation of the fracture network in a formation with pre-existing natural fractures. Multiple branches of fractures can propagate simultaneously and intersect / intersect with each other. Each open fracture may exert additional efforts on the surrounding rock and adjacent fractures, which may be referred to as the "effort tracking" effect. Effort tracking can cause a restriction of fracture parameters (for example, width), which can lead, for example, to a higher risk of filtering the supporting agent. Effort tracking can also alter the propagation path of fractures and affect fracture network models. Effort tracking can affect the modeling of fracture interactions in a complex fracture model.

[37] A method for calculating the effort tracking in a complex network of hydraulic fractures is presented. The method can be performed based on a 2D Displacement Discontinuity Method (2D DDM) with correction for finite fracture height or 3D Displacement Discontinuity Method (3D DDM). The stress field calculated from 2D DDM can be compared with 3D numerical simulation (3D DDM or flac3D) to determine an approximation for the 3D fracture problem. This calculation of the effort tracking effect can be incorporated into the UFM. The result for the simple cases of two fractures shows that the fractures can be drawn or rejected one another depending on, for example, their initial relative positions and can be compared with an independent 2D non-plane hydraulic fracture model. The effort tracking effect can also be ensured by using, for example, 3D DDM to consider the interaction of fractures at different depths.

[38] Further examples of flat and complex fracture propagation from multiple drill groups are also presented, showing that fracture interaction can control fracture size and propagation pattern, in a reduced stress anisotropy formation, fracture interaction can lead to fracture interaction. to the dramatic divergence of the fractures because they may tend to reject each other. However, even when the anisotropy of the efforts is large and the return of the fractures due to the interactions of the fractures is limited, the tracking effect of

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efforts can have an effect on the width of the fractures, which can affect the distribution of the injection rate in the multiple perforation groups, and thus the overall geometry of the fracture network and the placement of the support agent.

[39] Figures 1.1 and 1.2 illustrate the propagation of fractures around a well location 100. The well location has a drill hole 104 that extends from a well hole 108 into a surface location and through an underground formation 102 from below. A fracture network 106 extends around the borehole 104. A pumping system 129 is positioned around the well head 108 for fluid passage through the tubing 142.

[40] The pumping system 129 is illustrated as being operated by a field operator 127 for recording maintenance and operational data and / or performing the operation in accordance with a prescribed pumping program. The pumping system 129 pumps from the surface into the drill hole 104 during the fracturing operation.

[41] The pumping system 129 may include a water source, such as a plurality of water tanks 131, which feeds water to a gel hydration unit 133. The gel hydration unit 133 combines the water in the tanks 131 with a water treatment agent. gelling to form a gel. The gel is then sent to a mixer 135 in which it is mixed with a backing agent from a means of transporting the backing agent 137 to form a fracturing fluid. The gelling agent can be used to increase the viscosity of the fracturing fluid, and to allow the supporting agent to be suspended in the fracturing fluid. It can also act as a friction reduction agent to allow higher pumping rates with less friction pressure.

[42] The fracturing fluid is then pumped from the mixer 135 to the treatment trucks 120 with the piston pumps, as shown by the continuous lines 143. Each treatment truck 120 receives the fracturing fluid at a low pressure and discharges it into a common manifold 139 (sometimes referred to as a projectile or projectile trailer) at high pressure, as shown with broken lines 141. The projectile 139 then directs the fracturing fluid from the treatment trucks 120 to the borehole 104, as shown by the continuous line 115. One or more treatment trucks 120 may be used to feed the fracturing fluid at a desired flow rate.

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4 ^ 2016--00323Ο 6 -11- 20Η [43] Each truck 120 can be operated normally at any flow, such as well below its maximum operating capacity. Operating the treatment trucks 120 to their operating capacity may allow one to fail, and the rest to operate at a higher speed to compensate for the absence of the defective pump. A computer control system 149 can be used to direct the entire pumping system 129 during the fracturing operation.

[44] Various fluids, such as conventional pacing fluids with supporting agents, can be used to create fractures. Other fluids, such as viscous gels, "slushy water" (which may have a friction reducing agent (polymer) and water) can also be used for hydraulic fracturing of shale shafts. This "lunge water" can be in the form of a thin fluid (for example, almost at the same viscosity as water) and can be used to create more complex fractures, such as multiple micro-seismic fractures detectable by monitoring.

[45] As also shown in Figures 1.1 and 1.2, the fracture network includes fractures located at various positions around the borehole 104. The various fractures may be natural fractures 144 present prior to fluid injection, or hydraulic fractures 146 generated in around formation 102 during injection. Figure 1.2 shows an illustration of the fracture network 106 based on seismic events 148 obtained using conventional means.

[46] Multi-stage stimulation may be the standard for unconventional tank development. However, an obstacle to optimizing the extensions in the shale reservoirs may involve a lack of hydraulic fracture models that can adequately simulate the propagation of complex fractures often observed in these formations. A complex fracture network (or UFM) model has been developed (see, for example, Weng, X, Kresse, O., Wu, R., ŞÎGu, H, Modeling of Hydrauiic Fracture Propagation in a Naturally Fracturad Formation. SPE 140253 presented at SPE Hydrau / ic Fracturing Conference and Exhibition, Woodlands, Texas, USA, January 24-26 (2011) (hereafter "Weng 2011") / Kresse, O., Cohen, C., Weng, X , Wu, P., and Gu, H. 2011 (hereafter "Kresse 2011"). Numerical! Modeling of Hydrau / ic Fracturing in Naturally Fracturad Formations. 45th US Rock Mechanics / Geomechanics Symposium, San Francisco, CA June 26-29, whose entire content is incorporated here).

<img file="RO131506A2_D0009.tif" />

^ 2 0 1 6 -- 00323⁰ * -11- 20 «[47] Existing models can be used to simulate fracture propagation, rock deformation and fluid flow in the complex fracture network created during treatment. The model can also be used to solve the completely related problem of fluid flow in the fracture network and elastic deformation of fractures, which may have presumptions and governing equations similar to conventional pseudo3D fracture models. Transport equations can be solved for each component of pumped fluids and support agents.

[48] ​​Conventional plane fracture models can model various aspects of the fracture network. The predicted UFM model may also imply the ability to simulate the interaction of hydraulic fractures with pre-existing natural fractures, namely determining whether a hydraulic fracture propagates through or is stopped by a natural fracture when they intersect and subsequently propagate along the fracture. natural. The branching of the hydraulic fracture at the intersection with the natural fracture can give rise to the development of a complex fracture network.

[49] An intersection model can be extended from the interface intersection criterion of Renshaw and Pollard (see, for example, Renshaw, EC and Pollard, DD 1995, An Experimentally Verified Criterion for Propagation across Unbounded Frictionai interfaces in Brittie, Linear Elastic Materials, Inc. J. Pock Mech. Min. Sci. &amp; Geomech. Abstr., 32: 237-249 (1995) whose entire content is incorporated herein), intended to be applied at any angle of intersection, and can be developed (see, for example, Gu, H. and Weng, X. Criterion for Fractures Crossing Frictionai interfaces at Non-orthogonal Angies. 44th US Rock symposium, Salt Lake City, Utah, June 27-30, 2010 (hereinafter "Gu and Weng 2010"), the entire content of which is incorporated herein by citation) and validated on the basis of experimental data (see, by for example, Gu, H., Weng, X., Lund, J., Mack, M., Gangu / y, U. and Suarez-Rivera R. 2011. Hydraulic Fracture Crossing Natural Fracture at NonOrthogonai Angies, A Criterion, its Vaiidation and Applications. Paper SPF 139984 presented at SPE Hydraulic Fracturing Conference and Exhibition, Woodiands, Texas, January 24-26 (2011) (hereinafter "Gu et al. 2011"), the entire content of which is incorporated herein by citation), and incorporated into UFM.

[50] To adequately simulate the propagation of multiple or complex fractures, the fracture model may take into account an interaction between adjacent branches of

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single flat hydraulic fracture is opened under a net pressure of finite fluid, it can exert a field of stress on the surrounding rock which is proportional to the net pressure.

[51] in the limiting case of an infinitely long vertical fracture with a constant finite height, an analytical expression of the stress field exerted by the open fracture can be provided. See, for example, Warpinski, NF and Teufe! LW, Influence of Geologic Discontinuities on Hydrauiic Fracture Propagation, JPT, Feb., 209-220 (1987) (hereafter "Warpinski and Teufel") and Warpinski, NR, and Branagan, P. T, AiteredStress Fracturing. SPE JPT, September, 1989, 990-997 (1989), the entire contents of which are incorporated herein by citation. The net pressure (or more precisely, the pressure that causes the given fracture to open) can exert a compression effort in the normal direction on the fracture above the minimum in-situ stress, which can be equal to the net pressure on the face of the fracture, but decreases rapidly with distance fracture.

[52] At a distance above the fracture height, the induced stress may be a small fraction of the net pressure. Thus, the term "effort tracking" can be used to describe this increase in effort in the region surrounding the fracture. If a second hydraulic fracture is created parallel to an existing open fracture, and this falls within the "effort tracking" (ie the distance to the existing fracture is smaller than the fracture height), the second fracture may therefore observe an effort of closure greater than the original in-situ effort. As a result, higher pressure may be required for fracture propagation and / or the fracture may be smaller in width, compared to the corresponding individual fracture.

[53] An application of the effort tracking study may involve designing and optimizing fracture spacing between multiple fractures that propagate simultaneously from a horizontal drill hole. In shale formations with ultra low permeability, fractures can be spaced close together for efficient drainage of the reservoir. However, the effort tracking effect may prevent a fracture that propagates in the immediate vicinity of other fractures (see, for example, Fisher, MK, JR Heinze, CD Harris, BM Davidson, CA Wright, and KP Dunn, Optimizing horizontal compietion techniques in the Barnett Shaie using microseismic Fracture mapping SPE 90051 presented at SPE Annua! Technica! Conference and Exhibition, Houston, 26-29

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¢ -2016-- 0 0 3 2 3 0 6 -11- 20Η

September 2004, the entire content of which is incorporated herein by citation as a whole).

[54] Interference between parallel fractures has been studied in the past (see, for example,

Warpinski and Teufei; Britt, LK and Smith, MB, Horizontai Weii Compietion, Stimuiation Optimization, and Risk Mitigation. Paper SPE 125526 presented at the 2009 SPE Eastern Regional Meeting, Charleston, September 23-25, 2009; Cheng, Y. 2009. Boundary Element Analysis of the Stress Distribution around Multiple Fractures: Implications for the Spacing of Perforation Ciusters of Hydrauiicaiiy Fracturad Horizontai Wells. Paper SPE 125769 presented at the 2009 SPE Eastern Regional Meeting, Charleston, September 23-25, 2009; Meyer, BR and Bazan, LW, A Discrete Fracture NetWork Mode for Hydrauiicaiiy induced Fractures: Theory, Parametric and Case Studies. Paper SPE 140514 presented to SPE Hydrauiic Fracturing Conference and Exhibition, Woodiands,

Texas, USA, January 24-26, 2011; Roussei, NP and Sharma, MM, Optimizing Fracture Spacing and Sequencing in Horizontai-Weii Fracturing, SPE PE, May, 2011, pp. 173-184, the entire content of which is incorporated herein by citation). Studies may involve parallel fractures under static conditions.

[55] An effect of effort tracking may be that fractures in the median region of multiple parallel fractures may be smaller in width due to increased compression efforts from neighboring fractures (see, for example, Germanovich, LN and AstakhovD., Ciosure Fracture in Extension and Mechanicai interaction of Paraiiei Joints.

J. Geophys. Res., 109, B02208, doi: 10.1029 / 2002 JB002131 (2004); O / son, JE, MuitiFractura Propagation Mode / ing: Applications to Hydrauiic Fracturing in Shaies and Tight Sands. 42nd US Rock Mechanics Symposium and 2nd US-Canada Rock Mechanics Symposium, San Francisco, CA, June 29 - July 2, 2008, the entire content of which is incorporated herein by citation). When several fractures propagate simultaneously, distribution of the flow rate within the fractures can be a dynamic process and may be affected by the net pressure of the fractures. The net pressure can be strongly dependent on the width of the fracture and thus, the effect of tracking the efforts on the distribution of the flow rate and the size of the fractures warrants further study.

[56] The dynamics of the simultaneous propagation of several fractures may also depend on the relative positions of the initial fractures. If the fractures are parallel, for example in the case of several fractures that are orthogonal to a horizontal borehole, # V £ ROMINVEtroil 5 S, A. fW \\ O Or

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fractures can be repelled with each other, resulting in fractures that bend outwards. However, if several fractures are arranged under a stepped pattern, for example for fractures initiated from a horizontal borehole, which is not orthogonal to the fracture plane, the interaction between adjacent fractures may be such that their peaks are attracted to one another and they even come together (see, for example, Oison, JE Fracture Mechanics Analysis of Joints and Veins. PhD dissertation, Stanford University, San Francisco, California (1990); Yew, CH, Mear, ME, Chang, CC, and Zhang, XC On Perforating and Fracturing of Deviated Cased Weiibores. Paper SPE 26514 presented by SPE 68th Annual Technicat Conference and Exhibition, Houston, TX, Oct. 3-6 (1993); Weng, X, Fracture tnitiation and Propagation from Deviated Weiibores. SPE Paper 26597 presented by SPE 68th Annual Technicat Conference and Exhibition, Houston, TX, Oct. 3-6 (1993), the entire content of which is incorporated herein by citation).

[57] When a hydraulic fracture intersects a secondary fracture oriented in a different direction, it may exert an additional closing effort on the secondary fracture that is proportional to the net pressure. This effort can be derived and taken into account in calculating the crack opening pressure from the pressure-dependent leakage analysis of the cracked formation (see, for example, No / te, K, Fracturing Pressure Analysis for nonideai behavior. JPT, Feb. 1991, 210-218 (SPE 20704) (1991) (hereinafter referred to as "Nolte 1991"), the entire content of which is incorporated herein by citation).

[58] For more complex fractures, a combination of various fracture interactions may be present, as discussed above. To adequately account for these interactions and to remain computationally efficient, so that they can be incorporated into a complex fracture network model, an appropriate modeling framework can be built. A method based on a 2D Displacement Discontinuity Method (2D DDM) can be used to calculate the stresses induced on a given fracture and rock from the rest of the complex fracture network (see, for example, O / son, JE, Predicting Fracture Swarms - The tnftuence of Sub Critical Crack Growth and the Crack-Tip Process Zone on Joints Spacing in Rock. In The initiation, Propagation and Arrest of Joints and Other Fractures, ed. JWCosgrove and T.Engeider, Geologica! Soc. Special Pubiications, London, 231, 73-87 (2004fyr \ hereafter "Olson 2004"), the entire content of which is incorporated herein by citation). The return of the fracture can also be modeled based on the direction of local effort modified before

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by propagating the tip of the fracture due to the effort tracking effect. The simulation results from the UFM model incorporating the modeling of fracture interactions are presented.

Description of the UFM Model [59] In order to simulate the propagation of a complex fracture network consisting of many intersecting fractures, the equations governing the basic physical phenomena of the fracturing process can be used. Basic governing equations may include, for example, the equations governing fluid flow in the fracture network, the equation governing fracture deformation, and the fracture propagation / interaction criterion.

[60] The continuity equation considers that fluid flow propagates along a fracture network with the following mass conservation:

dq 3 (//_{/ z}w) ds dt (1) where q is the local flow rate inside the hydraulic fracture along the length, w is a width or average opening at the fracture cross-section at position s = s (x, y), Hn is the height of the fluid in the fracture, and q_IT is the rate of leakage volume through the hydraulic fracture wall in matrix per unit height (the rate at which the fracture fluid seeps into the permeable environment), which is expressed by Carter's drainage pattern. Fracture peaks propagate as a sharp front, and the hydraulic fracture length at any time / is defined as Kfi.

[61] The properties of the drive fluid can be defined by the exponent of the energy law exponent n '(fluid behavior index) and the consistency index K'. Fluid flow may be laminar, turbulent, or Darcy flow through the mass of the supporting agent, and may be suitably described by different laws. For the general case, of the 1D laminar flow of the fluid from the energy law in any given branch of the fracture, the Poiseuille law can be used (see, for example, Nolte, 1991):

3 ^ ds = -a,

<td>1 q</td><td>q</td>

<td>w²”’⁺¹ H_fl</td><td></td>

do it (1) where

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o 1 6 - - 0 0 3 2 3 0 6 -11- 2014 οχ =

ΊΚ '(4 «' + 2Y

2 " '+ l

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(2) here w (z) represents the width of the fracture as a function of depth in the current position and a is coefficient, n 'is the exponent of the energy law (fluid consistency index), φ is the shape function, and dz is the increment of integration along the fracture height in the formula.

[62] The width of the fracture can be associated with fluid pressure through the elasticity equation. The elastic properties of the rock (which can be considered a linear, isotropic, homogeneous elastic material) can be defined by Young E's module and Poissonv's report. For a vertical fracture in a stratified environment with the minimum horizontal variable stress Oh (x, y, z) and the fluid pressure p, the width profile (w) can be determined from an analytical solution given as:

w (x, y, z) = w (p (x, y), H, z) ₍₃₎ where W is the width of the fracture at a point with the spatial coordinates x, y, z (the coordinates of the center of the fracture element): p (x, y) is the pressure of the fluid, H is the height of the fracture element and z is the vertical coordinate along of the fracture element at point (x, y).

[63] Because the height of the fractures may vary, the set of governing equations may also include the calculation of height increase as described, for example, in Kresse 2011.

[64] In addition to the equations described above, the equilibrium condition of the global volume can be satisfied:

t L (t) t L (t)

J (? (/) £ // = H (s, t) w (s, t) ds + JJ ^ 2g_ITdsdtdh_t ooh_it oo (4) where g_IT is the fluid flow rate, Q (t) is the injection rate dependent on

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α: 2 0 1 6 - 0 0 3 2 3 0 6 -11- 20Η time, H (s, t) fracture height at space point s (x, y) and at time t, ds is the increase in length for integration along the fracture length, d_t is the increase in time, dhi is the height of leakage, H_IT is the height of the drain, and s₀is a loss coefficient of the jet. Equation (5) ensures that the total volume of fluid pumped during / is equal to the volume of fluid in the fracture network and the volume of the fractured volume up to time t. In this case, L (t) represents the length of HFN at time of time t and So is the loss coefficient of the jet. The boundary conditions may require that the flow rate, net pressure, and fracture width be zero at all fracture points.

[65] The system of equations 1 - 5, together with the initial and boundary conditions, can be used to represent a set of governing equations. Combining these equations and discretizing the fracture network into small elements can lead to a nonlinear system of equations in terms of fluid pressure for each element, simplified as / tp) = 0, which can be solved by using a damped Newton-Raphson method.

[66] The interaction of fractures can be considered for modeling the propagation of hydraulic fracture in naturally fractured reservoirs. This includes, for example, the interaction between hydraulic fractures and natural fractures, as well as the interaction between hydraulic fractures. For the interaction between hydraulic and natural fractures, a semi-analytical intersection criterion can be implemented in the UFM using, for example, the approach described in Gu and Weng 2010, and Gu and others 2011.

Modeling the effort tracking effect [67] For parallel fractures, the effort tracking can be represented by overlapping efforts from neighboring fractures. Fig. 2 is a schematic illustration of a 2D 200 fracture around a coordinate system having an x-axis and a y-axis. The various points along the 2D fractures, such as a first limb at h / 2, a second limb at -h / 2, and a midpoint are extended to an observation point (x, y). Each line L extends at angles θι, θ2 with respect to the points along the 2D fracture at the observation point.

[68] The stress field around a 2D fracture with internal pressure p can be calculated using, for example, the techniques described in Warpinski and Teufel. The effort that affects the width of the fracture is σ_χ, and can be calculated from:

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Λ_- 2 Ο 1 6 - - 003230 β -11- 2014 where σ_χ = Ρ 1 θ = arcta.

= arcta

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(5)

Θ_Λ - ar at I -— = 1

Vy / (6) and in which a_x is the effort in the x direction, p is the internal pressure, and x, y, L, Li, L_t are the coordinates and distances in Figure 2 normalized with half the height of the fracture h / 2. Because σ_χ varies in the y direction, as well as in the x direction, a weighted stress on fracture height can be used to calculate the stress tracking effect.

[69] The analytical equation given above can be used to calculate an effective average fracture effort on an adjacent parallel fracture and can be included in the closure effort v effects on that fracture.

[70] For more complex fracture networks, fractures may be oriented in different directions and may intersect with each other. Figure 3.1 shows a complex fracture network 300 illustrating the effects of effort tracking. Fracture network 300 includes hydraulic fractures 303 extending from a borehole 304 and intersecting with other fractures 305 from fracture network 300.

[71] A more general approach can be used to calculate the actual effort on each given branch of fracture relative to the rest of the fracture network. In the UFM model, mechanical interactions between fractures can be modeled on the basis of an improved 2D displacement discontinuity (DDM) method (Olson 2004) for calculating the stresses introduced (see, for example, Figure 3.2).

[72] in a solution of discontinuity of displacement, plane deformation, 2D (see, for example, Crouch, SL and Starfield, AM, Boundary ElementMethods in SolidMechanics, George Alieri &amp; Unwin Ltd, London. Fisher, MK (1983) (in following Crouch and Starfield 1983), whose entire content is incorporated herein by citation) can be used

<img file="RO131506A2_D0022.tif" />

(λ- 2 Ο 1 6 - - 0 0 3 2 3 0 6 -li- 20Η to describe normal and shear stresses (σ_π and a_s) acting on a fracture element induced by the opening and shear displacement discontinuities (Z7_n and Ds) from all fracture elements. To account for the 3D effect due to finite fracture height, Olson 2004 can be used to provide a 3D correction factor to influence the C coefficients.¹ in combination with the modified elasticity equations of 2D DDM, as follows:

NN σ^ι = YA^j C^ij From + V Ab^jC^ij D 'n ns s nn n

7=1 7=1 ^NN σ^ι = \ A^yC^ylD^j + \ A^ylC^ylD^{J (7)} s ss s sn n

7 = 1 7 = 1 where A is a matrix of the influence coefficients described in ec. (9), N is a total number of elements of the network whose interaction is considered, i is the element considered, and j = 1, N are the other elements of the network whose influence on the efforts on the element / is calculated; and in which C^] are the coefficients of elastic influence, plane deformation, 2D. These expressions can be found in Crouch and Starfield 1983.

[73] The elements / and j in Figure 3.2 schematically illustrate the variables i and j in equation (8). Discontinuities D_s and D_n applied to Elem j are also illustrated in Figure 3.2. Dn can be the same as the width of the fracture, and the shear stress can be 0 as illustrated. The displacement discontinuity from Elem j creates an effort on Elem i, as illustrated by c._s and c_n.

The 3D correction factor suggested by Olson 2004 can be represented as follows:

^^=1_^₊(Xr ^&lt;8&gt; where h is the height of the fracture, dj is the distance between the elements / and / a and β are the adjustment parameters. Ec. 9 shows that the 3D correction factor can lead to

TO·

V * ^ - 2 0 1 6 - 003230 6 -11- 20Η

WT decomposes the interaction between any two fracture elements as the distance increases.

[75] in the UFM model, at each time step, the additional efforts induced due to the effort tracking effects can be calculated. It can be considered that at any given time, the width of the fracture is equal to the normal displacement discontinuities (Z7_n) and the shear stress at the fracture surface is zero, ie, Df = wj, o_s^z = 0. by replacing these two conditions in Eq. 8, the shear displacement discontinuities (Z?) Can be found._s) and the normal stress induced on each fracture element (o_n).

[76] The effects of effort-induced efforts on the fracture network propagation model can be described in two ways. First, during the pressure and width iteration, the original in-situ stresses on each fracture element can be modified by adding the normal strain due to the strain tracking effect. This can directly affect the fracture pressure and the width distribution that can result in a change in fracture development. Second, by including effort-induced efforts (normal and shear stresses), the local stress fields in front of the propagation peaks can also be modified, which may cause the direction of the local main effort to deviate from the original direction of in-situ effort. This altered direction of the local main effort may result in the return of the fracture from its original propagation plane and may further affect the propagation module of the fracture network.

3D Displacement Discontinuity Method (3D DDM) [77] In addition to the 2D DDM method described here, a 3D DDM based method can be used for various applications. For a given hydraulic fracture network that is discretized into small connected rectangular elements, any given rectangular element can be subjected to a discontinuity of displacement between two sides of the rectangular element represented by Dx, Dyş \ Dz, and rock-induced stresses at any point. (x, y, 2) can be calculated using the 3D DDM solution presented here.

[78] Figure 17 shows a schematic diagram 1700 of a local coordinate system x, y, z for a rectangular element 1740 in a plane xy. This figure illustrates a fracture plane around the coordinate axis. Induced displacement and effort field can be expressed as:

<img file="RO131506A2_D0023.tif" />

2016-- 00323a E -11- 2014 k · (10) (11) (12) (13) (14) (15) (16) (17) and_x = [2 (1 - v) /₂ - z / „] Z&gt;, - zjpy - [(1- 2ν) Λ + zf ^ D, u, = -zf _r.D_t + [2 (1 - v) f _t - zf "] O, - [(1 - 2 v) /, + z /"] Z&gt;₂«, = [(1 - 2v) f _x - zf „] 25, + [(1 - 2v) /, - z /,₂ ] 2), + [2 (1 - v} f ₂ - zf_S] D, σ „= 2G {[2 /„ -z / ^ JD, + [2i /,₂ -ς / „] Ζ&gt;, + [/₌ + (1 -2i /) / „- z /„] Z&gt;₂} σ ,, = 2G [[2i /₌ - ζ / ,, ρ, + [2 / „- z /,„ p, + [/ „+ (1-2v) /_n-z /, „] /),} σ_α = 2Gz-z /_mn, -z /, JZ&gt;, + [/₂₂ - zf ^ Df, r, = 2G [[(lv) / ^ -z / „p, + 1 (1-¾. -ζ / ,, ρ, - [(1 -2v) /„ + ζ /,.₂Ρ₂} r,₂ = 2G {- [i /_1} + zf „] Z&gt;, + [/_of + vf „- z /„ JZ&gt;, - zf ^ D,} = 2θ {[(/_κ + 1 &lt;J, - [1 &lt;_W + z / "JA" "^zZ = A)

Where a and b are half the lengths of the edges of the rectangle, the induced displacement and the field of requests can be expressed as follows:

/ (*, y, ri =; fÎK¹ - Oh¹ + (y-ri + rirri / fAl, 41 &lt;a, | η | S b

Wv) " ₍₁₉₎ where A is the area of ​​the rectangle, (x, y, z) is the coordinate system initiated at the element, (ξ, η, Ο) are the coordinates at point P, and v is the Poisson's ratio.

[79] For any given observation point P (x, y, z) in 3D space, the effort induced at the point P (x, y, z) with the production rate Ο (ξ, η, Ο) can be calculated by superposition efforts from all fracture elements, and by applying a coordinate transformation. Exemplary techniques involving 3D DDM are provided in Crouch, SL and Starfield, AM (1990), Boundary Element Methods in Solid Mechanics, Unwin Hyman, London, all of which is incorporated herein by citation.

[80] The interaction between the multiple propagating hydraulic fractures or in this case called the effort tracking effect, may influence the increase of the fracture height.

<img file="RO131506A2_D0024.tif" />

AJ ² 6 1 6 - - 0 0 3 2 3 0 6 -11- 2014 for fractures that propagate in the same layer or different layers in depth, which may have implications for the success of a fracture treatment.

[81] in at least one embodiment of the hydraulic fracturing model described herein, the model may further integrate the 3D DDM method for calculating the 3D stress field induced by the propagating hydraulic fractures, and may incorporate the stress modification induced by -along the vertical depth in a calculation of the fracture height of the fracture model.

[82] For example, for two parallel fractures 1811.1, 1811.2, as illustrated in the schematic diagram 1800 of Fig. 18, the height increase may be promoted or eliminated depending on the relative height of the fracture. For fractures initiated from different depths, the presence of the adjacent fracture can help prevent a fracture from developing in the layer occupied by the other fracture due to the effect of tracking vertical efforts. For example, due to the interaction between fractures 1811.1, 1811.2 at different depths, fracture 1811.1 may increase in an upward direction and fracture

1811.1 may increase in a downward direction, as indicated by arrows.

Validation of the Effort Tracking Model [83] The validation of the UFM model for two-wing fracture cases can be done using, for example, Weng 2011 or Kresse 2011. Validation can also be done using the stress tracking modeling approach. For example, the results can be compared using 2D DDM to Flac 3D as provided in Itasca Consulting Group Inc., 2002, FLAC3D (Fast Lagrangian Analysis of Continuous in 3 Dimensions), Version 2.1, Minneapoiis: ICG (2002) ( in the following Itasca, 2002 ”).

Comparison of improved 2D DDM to Flac3D [84] The 3D correction factors suggested by Olson 2004 contain two empirical constants α and β. The values ​​of α and β can be calibrated by comparing the efforts obtained from the enhanced 2D DDM numerical solutions) to the analytical solution for a fracture with plane deformation with infinite length and finite height. The model can be further validated by comparing the results of the 2D DDM method with complete three-dimensional numerical solutions, using, for example, the FLAC3D method, for two parallel fractures with finite lengths and heights.

[85] The issue of validation is presented in Figure 4. Figure 4 illustrates a diagram

<img file="RO131506A2_D0025.tif" />

&lt;^ 2 0 1 6 - 0 0 3 2 3 - Ζ &amp; 20 6 -11- 20Η schematic 400 comparing the improved 2D DDM method with the Flac3D method for two straight parallel fractures. As shown in diagram 400, two parallel fractures 407.1,407.2 are subjected to a_x, o_y along an x, y coordinate axis. Fractures are 2L in length_xF, and fracture pressure p₁₍ P2, respectively. The fractures are at a distance s.

[86] The fracture from the Flac3D method can be simulated as two surfaces in the same location but with unattached network points. The pressure of the internal, constant fluid can be applied as the normal effort on the networks. Fractures can also be subjected to remote efforts o_x and a_y. Two fractures can have the same length and height with the ratio height / half length = 0.3.

[87] Efforts along the x (y = 0) and y (x = 0) axes can be compared. Two close fractures (s / h = 0.5) can be simulated as shown in the comparison in Figures 5.1-5.3. These figures provide a comparison of the extended 2D DDM method with the Flac3D method: Efforts along the x (y = 0) and y (x = 0) axes.

[88] These figures include graphs 500.1, 500.2, 500.3, respectively, illustrating the 2D DDM method and Flac3D method for extended fractures for oy along the y-axis, ox along the y-axis, and oy along the y-axis respectively. x. Figure 5.1 transposes oy / p (y-axis) with respect to the normalized distance to the fracture (x-axis) using 2D DDM and Flac3D methods. Figure 5.2 transposes ox / p (y-axis) to the normalized distance from fracture (x-axis) using 2D DDM and Flac3D methods. Figure 5.3 transposes oy / p (y-axis) to the normalized distance to the fracture (x-axis) using the 2D DDM and Flac3D methods. Location L_f of the tip of the fracture is illustrated along the line x / h.

[89] As shown in Figures 5.1-5.3, the simulated efforts from the improved 2D DDM approach with the 3D correction factor match quite well with those from the full 3D simulator results, indicating that the correction factor allows the 3D effect to be captured from fracture height on the stress field.

Comparison with the CSIRO model [90] The UFM model incorporating the enhanced 2D DDM approach can be validated against the 2D DDM simulator by CSIRO (see, for example, Zhang, X, Jeffrey, RG, and Thiercelin, M. 2007. Deflection and Propagation of Fiuid-Driven Fracturas at Frictional Bedding Interfaces: A Numerical! Investigation Journal of Structural Geology, 29: 396-410, (hereafter "Zhang 2007") whose entire content is incorporated herein by

<img file="RO131506A2_D0026.tif" />

^ - 2 0 1 6 - 0 0 3 2 3 0 6 Mon- 20H

<img file="RO131506A2_D0027.tif" />

citation). This approach can be used, for example, in the case of the very high fracture height where the 2D DDM approaches do not consider the 3D effects of the fracture height.

[91] Comparison of the influence of two closely propagating fractures on the propagation paths of the other can be used. Propagation of two hydraulic fractures initiated parallel to each other (propagating along the direction of maximum local effort) can be simulated for configurations, such as: 1) starting points one above the other and offset from each other for the isotropic, and 2) highly anisotropic stress fields The fracture propagation path and the pressure within each fracture can be compared for the UFM model and the CSIRO code for the input data given in Table 1.

<td>Injection rate</td><td>0,106m³/ s</td><td>40 bbl / min</td>

<td>Anisotropy effort</td><td>0.9 MPa</td><td>130 psi</td>

<td>Young's module</td><td>3x 10^A10Pa</td><td>4.35e + 6 psi</td>

<td>Poisson's report</td><td> 0,35</td><td> 0,35</td>

<td>Fluid viscosity</td><td>0.001 pa-s</td><td>1 cp</td>

<td>Specific fluid weight</td><td> 1,0</td><td> 1,0</td>

<td>Minimal horizontal effort</td><td>46,7MPa</td><td>6773 psi</td>

<td>Maximum horizontal effort</td><td>47,6MPa</td><td>6903 psi</td>

<td>Fracture toughness</td><td>1MPa-m^Ub</td><td>1000 psi / in^{And b}</td>

<td>fracture height</td><td>120m</td><td>394 ft</td>

Table 1 Input data for validation with respect to the CSIRO model [92] When two fractures are initiated parallel to each other with starting points separated by dx = O, dy = 33 ft (10.1 m) (the maximum horizontal stress field is oriented in the x direction, they can turn to each other due to the effort tracking effect.

[93] The propagation paths for the isotropic and anisotropic stress fields are shown in Figures 6.1 and 6.2. These figures are graphs 600.1, 600.2 illustrating the propagation paths for two initially parallel fractures 609.1, 609.2 in isotropic and anisotropic stress fields respectively. Fractures 609.1 and 609.2 are initially parallel to each other

<img file="RO131506A2_D0028.tif" />

Cț- 2 Ο 1 6 - - 003230 8 -π- 201 (

<img file="RO131506A2_D0029.tif" />

injection points 615.1, 615.2, but they diverge as they move away from them. Comparing the isotropic case, the fracture curves in the case of stress anisotropy are illustrated as being smaller. This may be due to the competition between the effort tracking effect that tends to return fractures away from each other, and the distant effort fields, which push the fractures to propagate in the direction of maximum horizontal effort (x direction). The influence of the effort in the far field becomes dominant as the distance between fractures increases, in which case the fractures may tend to propagate parallel to the direction of the maximum horizontal effort.

[94] Figures 7.1 and 7.2 illustrate graphs 700.1, 700.2 showing a pair of fractures initiated from two different injection points 711.1, 711.2, respectively. These figures show a comparison for the case when the fractures are initiated from points separated by a distance dx = dy- (10.1 m) for the isotropic and anisotropic stress fields respectively. In these figures, fractures 709.1, 709.2 tend to spread to each other. Similar examples of behavior have been observed in laboratory experiments (see, for example, Zhang 2007).

[95] As indicated above, the enhanced 2D DDM approach implemented in the UFM model may be able to capture the 3D effects of finite fracture height on the interaction of fractures and propagation model, while ensuring computational efficiency. A good estimation of the stress field for a network of vertical hydraulic fractures and the direction (pattern) of fracture propagation can be ensured.

Examples of cases

Bath # 1 Parallel fractures in horizontal wells [96] Figure 8 is a schematic graph 800 of parallel transverse fractures

811.1, 811.2, 811.3 that propagate simultaneously from several drill groups 815.1,

815.2, 815.3, respectively, around a horizontal borehole 804. Each of the fractures

811.1,811.2,811.3 provides a different flow rate qi, q₂, q3 which is part of the total flow q_t at a pressure po.

[97] When the state of the formation and the perforations are the same for all fractures, the fractures may have approximately the same size if the friction pressure in the borehole between the perforations group is small proportionally. This can be considered if the fractures are sufficiently separated and the effects of

<img file="RO131506A2_D0030.tif" />

Ο 1 6 - - 0 0 3 2 3 ⁰ 6 -11- 2014 efforts tracking are negligible. When the distance between the fractures is within the region of influence of the pursuit of efforts, the fractures can be affected in width, and in another dimension of the fracture. To illustrate this, a simple example of five parallel fractures can be considered.

[98] In this example, fractures are considered to have a constant height of 100 ft (30.5 m). The spacing between the fractures is 65 ft (19.8m). Other input parameters are given in Table 2.

<td>Young's module</td><td>6,6x10⁶ psi = 4.55 + 10Pa</td>

<td>Poisson's report</td><td> 0,35</td>

<td>Flow</td><td>12.2 bbl / min = 0.032m3 / s</td>

<td>Viscosity</td><td>300 hp = 0.3Pa-s</td>

<td>height</td><td>100 ft = 30.5m</td>

<td>Drain coefficient</td><td>3,9x10 '² THX^1/2</td>

<td>Anisotropy effort</td><td>200 psi = 1.4Mpa</td>

<td>Fracture spacing</td><td>65 ft = 19.8m</td>

<td>Nr. of perforations per fracture</td><td> 100</td>

Table 2 Input parameters for Case # 1

For this simple case, a conventional Perkins-Kern-Nordgren (PKN) model (see, for example, Mack, MG and Warpinski, NR, Mechanics of Hydraulic Fracturing. Chapter 6, Reservoir Stimulation, 3rd Ed, eds. Economides, MJ and Nolte, KG. John Wiiey &amp; Sons (2000)) for several fractures can be modified by incorporating the effort tracking calculation, as given in Eq. 6. The increase of the closing effort can be approximated by weighting the calculated effort from Eq. 6 throughout the fracture. It should be noted that this simplistic PKN model may not simulate fracture return due to the effort tracking effect. The results from this simple model can be compared with the results from the UFM model, which incorporates the calculation of the point-to-point efforts along the complete fracture paths, as well as the fracture return.

[99] Figure 9 shows the results of the simulation of the fracture lengths for five fractures, calculated from both models. Fig. 9 is a graph 900 illustrating the length (axis

<img file="RO131506A2_D0031.tif" />

OV- 2 Ο 1 6 - - 003230 6 -Π- 2014

y) versus time (t) for five parallel fractures during injection. Lines 917.1-917.5 are generated from the UFM model. Lines 919.1-919.5 are generated from the simplistic PKN model.

[100] Fracture geometry and width contour of the UFM model for the five fractures in Figure 9 are shown in Figure 10. Figure 10 is a schematic diagram 1000 illustrating fractures 1021.1-1021.5 around a borehole 1004.

[101] Fracture 1021.3 is the middle one of the five fractures, and the fractures

1021.1 and 1021.5 are the outer ones. Because the fractures 1021.2, 1021.3, and 1021.4 have a smaller width than the external ones due to the effort tracking effect, they have a higher flow resistance, receive a lower flow rate and have a shorter length. Therefore, the effects of effort tracking can be the width of the fracture and also the length of the fracture under dynamic conditions.

[102] The effect of stress tracking on fracture geometry can be influenced by many parameters. To illustrate the effect of some of these parameters, fracture lengths calculated for the cases with variable fracture spacing, perforation friction and stress anisotropy are presented in Table 3.

[103] Figures 11.1 and 11.2 show the fracture geometry predicted by the UFM model for the case of large perforation friction and the case of large fracture spacing (for example, approximately 120 ft (36.6 m)). Figures 11.1 and 11.2 are schematic diagrams

1100.1 and 1100.2 illustrating five fractures 1123.1-1123.5 around a borehole 1104. When the perforation friction is large, a large deflection force can be provided that uniformly distributes the flow rate across all drill groups. consequently, the effort tracking effect can be exceeded and the resulting fracture lengths can become approximately equal, as shown in Figure 11.1. When the distance between fractures is large, the effort tracking effect can be dissipated, and the fractures can have approximately the same dimensions as those shown in Figure 11.2.

<td>tails</td><td>Case of the base</td><td>120 ft spacer (36.6 m)</td><td>Nr. of perforations = 2</td><td>Anisotropy = 50 psi (345000Pa)</td>

<td> 1</td><td> 133</td><td> 113</td><td> 105</td><td> 111</td>

<td> 2</td><td> 93</td><td> 104</td><td> 104</td><td> 95</td>

<img file="RO131506A2_D0032.tif" />

oil 2 Ο 1 6 - - 0 0 3 2 3 0 6 -11- 2014

<td> 3</td><td> 83</td><td> 96</td><td> 104</td><td> 99</td>

<td> 4</td><td> 93</td><td> 104</td><td> 100</td><td> 95</td>

<td> 5</td><td> 123</td><td> 113</td><td> 109</td><td> 102</td>

<td>Tabe</td><td colspan="2">ul 3 The influence of the various parame</td><td colspan="2">tri on fracture geometry</td>

Case # 2 Complex Fractures [104] In an example of Figure 12, the UFM model can be used to simulate a treatment of 4-stage hydraulic fractures in a horizontal shaft of a shale formation. See, for example, Cipoiia, C., Weng, X, Mack, M., Ganguiy, U., Kresse, O., Gu, H, Cohen, C. and Wu, P., integrating Microseismic Mapping and Complex Fracture Modeiing to Characterize Fracture Compiexity. Paper SPE 140185 presented at the SPE Hydraulic Fracturing Conference and Exhibition, Woodiands, Texas, USA, January 2426, 2011, (hereinafter referred to as "Cipoiia 2011"), the entire content of which is incorporated herein by citation. The well can be piped and cemented, and each stage pumped through three or four drilling groups. Each of the four stages can consist of approximately 25,000 bbls (4000 m³) of fluid and 440,000 Ibs (2e + 6kg) of support agent. Extensive data may be available at the well level, including advanced sonic charts that provide minimal and maximum horizontal effort estimation. Micro-seismic mapping data may be available for all stages. See, for example, Daniels, J., Waters, G., LeCa / vez, J., Lassek, J., and Bent / ey, D., Contacting More of the Barnett Shaie Through an integration of Reai-Time Microseismic Monitoring , Petrophysics, and Hydraulic Fracture Design. Paper SPE 110562 presented at the 2007 SPE Annuat Technicat Conference and Exhibition, Anaheim, California, USA, October 12-14, 2007. This example is shown in Figure 12. Fig. 12 is a graph illustrating microseismic mapping of microseismic events 1223 in the various stages around a borehole 1204.

[105] Effort anisotropy from the advanced sonic diagraph, indicates a higher effort anisotropy in the downstream section of the well compared to the upstream part. An advanced 3D seismic interpretation may indicate that the trend of the dominant natural fracture changes from NE-SV in the downstream section to NV-SE in the upstream section on the side. See, for example, Rich, JP and Ammerman, M., Unconventionai Geophysics for Unconventionai Piays. Paper SPE 131779 presented at the Unconventional Gas Conference,

<img file="RO131506A2_D0033.tif" />

A -1 O 1 6 - - 003230 6 -11- 20U%

Pittsburgh, Pennsy / vania, USA, February 23-25, 2010, the entire content of which is incorporated herein by citation.

[106] The simulation results can be based on the UFM model without incorporating the entire calculation of the effort tracking (see, for example, Cipolla 2011), including shear stress and fracture return (see, for example, 2011). The simulation can be updated with the full model of efforts as provided here. Figures 13.1-13.4 show a plan view of a simulated fracture network 1306 around a borehole 1304 for all four stages, respectively, and their comparison with microseismic measurements 1323.1-1323.4, respectively.

[107] From the simulation results in Figures 13.1-13.4 it can be seen that for Steps 1 and 2, the close fractures do not differ significantly. This may be due to the high anisotropy of the efforts in the downstream section of the borehole. For Phases 3 and 4, when the anisotropy of the efforts is lower, a large divergence of the fractures can be seen as a result of the effect of the effort tracking.

Case # 3 Examples mu / ti-steps [108] Case # 3 is an example showing how tracking efforts from previous stages can influence the propagation pattern of hydraulic fracturing networks for subsequent treatment steps, resulting in the modification of the overall network image. of hydraulic fractures generated for the four-stage treatment case.

[109] This case includes four stages of treatment of hydraulic fractures. The well is tubed and cement. Steps 1 and 2 are pumped through three perforated groups, and Steps 3 and 4 are pumped through four perforated groups. The canvas is isotropic. The input parameters are listed in Table 4 below. The top view of the network of total hydraulic fractures without and taking into account the follow-up of the efforts from the previous stages are presented in Figures 13.1-13.4.

<img file="RO131506A2_D0034.tif" />

<img file="RO131506A2_D0035.tif" />

Ο 1 6 - - D03230 6 -11- 20Η

<td>Young's module</td><td>4,5x10⁶psi = 3,1e + 10Pa</td>

<td>His report Poisson</td><td> 0,35</td>

<td>Flow</td><td>30.9 bpm = 0.082m '^and/ s</td>

<td>Viscosity</td><td>0.5 cp = 0.0005pa-s</td>

<td>height</td><td>330 ft = 101m</td>

<td>Pumping time</td><td>70 min</td>

Table 4 Input Parameters for Case # 3 [110] Figures 14.1-14.4 are schematic diagrams 1400.1-1400.4 illustrating a network of fractures 1429 at various stages during the fracture operation. Figure 14.1 shows a discrete fracture network (DFN) 1429 before treatment. Figure 14.2 illustrates a simulated DFN 1429 after a first treatment step. DFN 1429 has propagated hydraulic fractures (HFN) 1431 extending from it due to the first treatment step. Figure 14.3 shows the DFN illustrating a simulated HFN 1431.1-1431.4 propagated during four stages, respectively, but without considering the effects of the previous step. Figure 14.4 shows the DFN network illustrating the HFN invoices 1431.1, 1431.2'1431.4 'propagated during the four stages, but taking into account the fractures, the traces of the forts and the HFN fractures from the previous stages.

[111] When the stages are generated separately, they may not be visible to each other, as shown in Figure 14.3. When tracking the stresses and fractures of the HFN from the previous stages are taken into account, as in Figure 14.4, the propagation pattern can be modified. The hydraulic fractures 1431.1 generated for the first stage are the same for both scenarios, as shown in Figures 14.3 and 14.4. The propagation model of the second stage 1431.2 can be influenced by the first stage by tracking the efforts, as well as by the new DFN network (including the HFN 1431.1 fractures in Step 1), resulting in the modification of the propagation models to the HFN 1431.2 'fractures. HFN 1431.1 'may begin to follow the HFN 1431.1 fractures created in step 1, taking this into account. The third step 1431.3 may follow a hydraulic fracture created during the second treatment step 1431.2, 1431.2 ', and may not propagate too far due to the effort tracking effect of Step 2, as indicated by

<img file="RO131506A2_D0036.tif" />

fl 1 6 - - 0 0 3 2 3 fl 6 -π- 20H M

1431.3 from 1431.3 '. Stage 4 (1431.4) may tend to return from step three when it can, but may follow the HFN 1431.3 'fracture from previous stages when it encounters them and may be illustrated as the HFN 1431.4' fracture in Figure 14.4.

[112] There is presented a method for calculating the efforts tracking in a network of complex hydraulic fractures. The method may involve an improved 2D or 3D displacement discontinuity method with correction for finite fracture height. The method can be used to approximate the interaction between the different fracture branches in a complex fracture network for the fundamental 3D fracture problem. This calculation of effort tracking can be incorporated into the UFM, a complex fracture network model. The results for the simple cases of two fractures show fractures that can be drawn or rejected one to another depending on their initial relative positions, and the favorable comparison with model non-planar hydraulic fractures 2D independently.

[113] Simulations of multiple parallel fractures with one horizontal well can be used to confirm the behavior of two more dominant external fractures, while the inner fractures have a reduced fracture length and width due to the tracing effect. . This behavior may also depend on other parameters, such as puncture rubbing and fracture spacing. When the fracture spacing is greater than the fracture height, the effort tracking effect may be diminished and there may be significant differences between multiple fractures. When the perforation friction is high, sufficient deviation may be provided for the distribution of equal flow between the drill groups, and the fracture dimensions may become approximately equal despite the effort tracking effect.

[114] When complex fractures are created, if the formation has a reduced anisotropy of the stresses, the interaction of the fractures can lead to a dramatic divergence of the fractures, when they tend to reject each other. On the other hand, for a large anisotropy of the efforts, there may be a limited divergence of the fractures in which the anisotropy of the stresses compensates for the effect of returning the fractures due to the pursuit of the efforts, and the fracture can be forced to go in a direction of maximum effort. Regardless of the value of the fracture divergence, the tracking of the efforts can have an effect on the width of the fractures, which can affect the distribution of the injection rate in the multiple perforation groups, and overall the imprint of the fracture network and the placement of the support agent.

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^ 2 0 1 6 - 0 0 3 2 3 0 6 -11- 2014 [115] Figure 15 is a block diagram illustrating a method 1500 for performing a fracture operation at a well location, such as well location 100 from Figure 1.1. The well location is positioned around an underground formation having a drill hole through it and a network of fractures in it. The fracture network has natural fractures, as shown in Figures 1.1 and 1.2. Method (1500) may involve (1580) performing an estimation operation by stimulating the location of the well by injecting an injection fluid with support agent into the fracture network to form a network of hydraulic fractures. In some cases, the stimulation may be performed at the well location or by simulation.

[116] The method involves obtaining data on the location of the well (1582) and a mechanical ground model of the underground formation. The well location data may include any well location data that may be useful for simulation, such as natural fracture parameters, fracture network images, etc. The parameters of natural fractures may include, for example, the orientation of densities, distribution and mechanical properties (for example, friction coefficients, cohesion, fracture toughness, etc.). The fracture parameters can be obtained from direct observations of the diagrams that form the images of the drill hole, estimated from the 3D seismic data, the ant colony algorithm, the sonic wave anisotropy, the curvature of the geological layers, microseismic events or images, etc. Examples of techniques for obtaining fracture parameters are provided in PCT / US2012 / 48871 and US2008 / 0183451, the entire contents of which are incorporated herein by citation.

[117] Images can be obtained. For example, by observing the diagrams with images of the borehole, estimating fracture dimensions from borehole measurements, obtaining micro-seismic images and / or the like. Fracture dimensions can be estimated by evaluating seismic measurements, track tracking, sonic measurements, geological measurements and / or the like. Other data about the location of the well can also be generated from various sources, such as measurements at the location of the well, historical data, presumptions, etc. This data may involve, for example, completion, geological, petrophysical, geomechanical, drilling measurements and other data. The mechanical earth model can be obtained using conventional techniques.

[118] The method (1500) also involves the generation (1584) of a model of hydraulic fracture development over time, such as during the stimulation operation.

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Figures 16.1-16.4 illustrate an example of generation (1584) of the hydraulic fracture development model. As shown in Figure 16.1, in its initial state, a network of fractures 1606.1 with natural fractures 1623 is positioned around an underground formation 1602 with a bore hole 1604 through it. As the supporting agent is injected into the underground formation 1602 from the borehole 1604, the pressure from the supporting agent creates the hydraulic fractures 1691 around the borehole 1604. The hydraulic fractures 1691 extend into the underground formation along Li and l_2. (Figure 16.2), and encounter other fractures in the fracture network 1606.1 over time, as shown in Figures 16.2-16.3. The contact points with the other fractures are the intersections of 1625.

[119] Generation (1584) may involve the extension (1586) of hydraulic fractures from the borehole and into the fracture network of the underground formation to form a network of hydraulic fractures including natural and hydraulic fractures, as shown in Figure 16.2. The fracture development model is based on the natural fracture parameters and a minimum effort and maximum effort on the underground formation. Generation may also involve determining (1588) the parameters of the hydraulic fractures (for example, the pressure p, the width w, the flow rate q, etc.), the determination (1590) of the transport parameters for the supporting agent passing through the network of hydraulic fractures and determining (1592) the dimensions of the fractures (for example, the height) of the hydraulic fractures, for example, from the determined parameters of the hydraulic fractures, the transport parameters determined and the mechanical ground model. The parameters of hydraulic fractures can be determined after enlargement. The determination (1592) can also be made from the transport parameters of the supporting agent, the well location parameters and other elements.

[120] Generation (1584) may involve modeling of rock properties based on a mechanical soil model, as described, for example, in Koutsabeloulis and Zhang, 3D Reservoir Geomechanics Modeiing in Oii / Gas Fieid Production, SPE Paper 126095, 2009 SPE Saudi Arabia Section Technicai Symposium and Exhibition held in Ai Khobar, Saudi Arabia, May 9-11, 2009. Generation may also involve modeling the fracture operation by using well location data, fracture parameters and / or images as inputs of modeling software, such as UFM, to generate successive images of hydraulically induced fractures in the fracture network. .

[121] The method (1500) also involves carrying out (1594) the pursuit of efforts

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on the hydraulic fractures to determine the interference of the efforts between the hydraulic fractures (or with other fractures), and the repetition (1598) of the generation (1584) based on the tracking of the efforts and / or the interference of the efforts determined between the hydraulic fractures. Repetition may be performed to take into account the interference of fractures that may affect the development of fractures. Effort tracking can involve, for example, 2D or 3D DDM for each of the hydraulic fractures and updating the fracture development model over time. The fracture development model can normally propagate in a direction of the main effort according to the efforts tracking. The fracture development model may involve influences of natural and hydraulic fractures on the fracture network (see Fig. 16.3).

[122] Effort tracking can be done for multiple drill holes of the well location. Tracing efforts from the various drill holes can be combined to determine the interaction of fractures as determined from each of the drill holes. Generation can be repeated for each of the efforts pursued for one or more of the multiple boreholes. Generation can also be repeated for tracking efforts where stimulation is provided by several drill holes. Multiple stimulations can also be performed on the same drill hole with various data combinations, and compared as desired. Historical or other data can also be entered in the generation to provide multiple sources of information to be considered in the final results.

[123] The method also involves determining (1596) the intersection behavior between hydraulic fractures and a fracture encountered, if the hydraulic fracture encounters another fracture, and the repetition (1598) of generation (1584) based on the intersecting behavior, if the hydraulic fracture encounters a fracture (see, for example, Figure 16.3). The intersection behavior can be determined using, for example, the techniques in PCT / US2012 / 059774, the entire content of which is incorporated herein by citation.

[124] Determining the intersection behavior may involve pursuing efforts. Depending on the conditions in the drilled hole, the fracture development model may be unchanged or modified when the hydraulic fracture encounters the fracture. When a fracture pressure is greater than an effort acting on the fracture encountered, the fracture development model may propagate along the fracture encountered. The fracture development model can continue its propagation throughout

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JLfO fracture encountered until the end of the natural fracture is reached. The fracture development model can change its direction at the end of the natural fracture, with the fracture development model extending in a normal direction with minimal effort at the end of the natural fracture, as shown in Figure 16.4. As shown in Figure 16.4, the hydraulic fracture extends on a new route 1627 according to local efforts σ_Ί and 02.

[125] Optionally, method (1500) may involve validation (1599) of fracture development model. Validation can be achieved by comparing the resulting development model with other data, such as micro-seismic images, as shown for example in Figures 7.1 and 7.2.

[126] The method can be performed in any order and repeated as desired. For example, generation (1584) - (1599) can be repeated over time, for example, by iterations when the fracture network changes. Generation (1584) can be performed to update the iterated simulation performed during generation to take into account the interaction and effects of multiple fractures, when the fracture network is stimulated over time.

[127] Method 1500 can be used for a variety of well location conditions having perforations and fractures, such as fractures 811.1-811.3, as illustrated in Figure 8. In the example in Figure 8, fractures 811.1-811.3 can be positioned approximately at the same depth in the formation. In some cases, the fractures may be different depths, as shown, for example, in Figures 18-20.

[128] Figures 18-20 show various examples of schematic transpositions 1800, 1900, 2000 of parallel transverse fractures 1811.1, 1811.2 that propagate simultaneously from several drill groups 1815.1, 1815.2, respectively, around a borehole inclined 1804 from formation 1802. Each of the fractures 1811.1, 1811.2 crosses layers 1817.1, 1817.2, 1817.3, 1817.4, 1817.5, 1817.6 at different depths D1-D6, respectively, along the 1802 formation. Formation 1802 may have one or more layers with various compositions, such as shale, sand, rock, etc. Formation 1802 has a total effort of and each of layers 1817.1-1817.6 has a corresponding effort of 1-of6, respectively.

[129] Figures 18 and 19 can be generated using effort tracking, as described above. In the example in Figure 18, fracture 1811.1 extends through the layers

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1817.2-1817.4 and the fracture 1811.2 extends through the layers 1817.3-1817.5. In the example in Figure 19, the fracture 1811.2 'extends through layers 1817.2-1817.5. As shown in Figure 19, fractures can have a given vertical length and can extend at a given distance through one or more layers and receive the effects of the corresponding efforts from them.

[130] in the example of Fig. 19, fractures 1811.1, 1811.2 'are taken without considering the effects of efforts tracking. In this case, the height increase of the fractures 1811.1 and 1811.2 'is influenced by the vertical distribution of the in-situ stresses of the stresses of the corresponding layers around the fractures. Fracture 1811.1 has a vertical length L1 above the perforation group 1815.1 and a vertical length L2 below the perforation group 1815.1. Fracture 1811.2 'has a vertical length L3 above the perforation group 1815.2 and a vertical length L4 below the perforation group 1815.2.

[131] Figure 20 can be generated from effort tracking using 3D DDM, as described above. In the example in Figure 20, fracture 1811.1 'extends through layers 1817.1-1817.4 and fracture 1811.2 extends through layers 1817.3-1817.6. Fig.

shows a cross section of the fractures in Figure 19 once the effect of tracking vertical efforts is considered. Fracture 1811.1 develops further upwards and fracture 1811.2 develops more downward, due to efforts tracking.

[132] In this case, the increase of the fracture height is influenced by the vertical distribution of the in-situ stresses plus the stress tracking of the adjacent fractures. Fracture 1811.1 'has an extended vertical length L1' above the perforation group 1815.1 and a reduced vertical length L2 'below the perforation group 1815.1. Fracture 1811.2 "has a reduced vertical length L3 'above the perforation group 1815.2 and an extended vertical length L4' below the perforation group 1815.2. The growth shown in Figure 20 reflects the divergent growth due to the interaction of fractures, as schematically represented by the arrows in Figure 18.

[133] As in Figures 19-20, where fractures are at different depths and are subjected to different stresses, the increase in fracture height may vary depending on the relative height of the fracture. Fractures are initiated from different formations, and the presence of the adjacent fracture can help prevent a fracture from developing in the geological formations occupied by another fracture due to the effect of tracking vertical efforts.

[134] The effect of the efforts tracking described in the present frame can be taken in ___, // \ jfe rominUei p OR ^ -2016-- 003230 6 -11-20

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consideration of the interaction between fractures at the same or different heights. For example, in Figure 8, the median fracture can be compressed by the fractures on each side of it and may become smaller and narrower, as described in connection with Figure 10. The UFM model provided herein can be used to describes this interaction. In another example, as shown in Figures 18-20, the two fractures can compress one another and tear the fractures apart. In this example, the 1811.1 fracture extends upward and the right fracture develops downward due to the bore of the drill hole.

[135] Figure 21 illustrates another version of method 2100 that may consider the effects of fractures at various depths. Method 2100 can take into account the interference of the efforts between the hydraulic fractures to evaluate the increase of height of each fracture, whether at the same or at different heights. Method 2100 can be used to perform a fracturing operation in a well location having a drill hole with a fracture network around it, as shown, for example, in Figures 18-20. In this version, method 2100 may be performed according to part or all of method 1500, as described in connection with Figure 15, except for further tracking of efforts 2195, modified determination 1596 'and modified repetition 1598'.

[136] Further tracking of efforts 2195 can be performed based on the vertical development of hydraulic fractures to take into account the effects of hydraulic fractures at different depths. Further tracking of efforts 2195 can be accomplished using the 3D DDM method when fractures are at different depths (see, for example, Fig. 18-20). Further tracking of efforts 2195 can be done after accomplishment 1594 and before modified determination 1596 '. In some cases, additional effort tracking 2195 may be performed concurrently with effort tracking 1594. For example, when achievement 1594 is performed using the 3D DDM method, depth may be considered without additional effort tracking 2195. In some cases, embodiment 1594 may be accomplished using another technique, such as the 2D DDM method, and fracture depth may be taken into consideration with further efforts tracking 2195 using the 3D DDM method. The 3D DDM method can take into account the influence of adjacent fractures and associated vertical stresses, and can generate adjusted vertical development and / or length.

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ίΧ2 Ο 1 6 - 003230 (- ||. 2014 [137] Determination 1596 'and repetition 1598' can be modified to take into account further tracking of efforts 2195, if performed. Modified determination 1596 'involves determining intersection behavior between the hydraulic fracture and the fracture encountered on the basis of the 1594 achievement and the further pursuit of the 2195 efforts. The modified repetition 1598 'implies the repetition of the fracture development model based on the determination of the interference of the efforts 1594, the additional pursuit of the efforts 2195 and the determination of the intersection behavior 1596'.

[138] An additional adjustment 2197 can be made based on the efforts tracking 1594 and / or 2195. For example, fracture development can be compensated by adjusting at least one stimulation parameter, such as pumping pressures, fluid viscosity, etc. during injection (or fracture). Fracture development can be simulated using the modified UFM model for the adjusted pumping parameters.

[139] One or more portions of the method, such as performing the stimulation operation 1580, may be repeated based on part or all of the operations 1594-1599. For example, based on the effort tracking 1594 and / or 2195 and / or the resulting fracture development, the stimulation can be adjusted to achieve the desired fracture development (see, for example, Figure 20). The stimulation can be modified, for example, by adjusting the pumping pressures, viscosities and / or other injection parameters to obtain the desired operation at the location of the well and / or the desired development of the fracture.

[140] Various combinations of part or all of the methods of Figures 15 and / or 21 can be carried out in various orders.

[14 |] Although the present invention has been described with reference to illustrative embodiments and embodiments thereof, the present invention is not limited by or to these illustrative embodiments and / or implementations. In contrast, the systems and methods of the present invention are subject to various modifications, variations and / or improvements without departing from the spirit or purpose of the present invention. Accordingly, the present invention expressly encompasses all such modifications, variations and improvements within its scope.

[142] It should be noted that in the development of any such current embodiment, or numerous implementations, specific decisions can be made to achieve developer-specific goals, such as correspondence with the associated system and business-related constraints, which will vary from from one implementation to the other. More,

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(Vί ο 16 - - 0 Ο 3 2 3 Ο 6 -11- 20Η it will be appreciated that such a development effort could be complex and time consuming but it will undoubtedly be a routine task performed by those with average training In the art which have benefited from this disclosure, in addition, the embodiments used / disclosed herein may also include some components, other than those mentioned herein.

[143] In the description, each numeric value must be read once as modified by the term "approximately" (if not already expressly modified as such), and then read again as not modified unless otherwise indicated in context. Also, in the description, it should be understood that any range listed or described as useful, appropriate, or similar, is intended for values ​​within the range, including end points, to be considered as mentioned. For example, "range 1 to 10" should be read as indicating continuously possible numbers between about 1 and about 10. Thus, even if specific data points within the range, or even no data points in the range, are explicitly identified or referred to as specific, it should be understood that inventors appreciate and understand that any and all data points within the range should be considered as specified, and that the inventors present knowledge of the entire range and all points within the range.

[144] The statements made herein provide only information relating to the present invention and cannot constitute the prior art, and may describe some embodiments illustrating the invention. All references cited here are incorporated by citation in the present application in their entirety.

[145] Although some illustrative embodiments have been described in detail, those skilled in the art will readily appreciate that many modifications are possible in illustrative embodiments without removing material from the system and method for performing drill hole stimulation operations. drilling. Accordingly, all of these modifications are intended to be included within the scope of this invention as defined in the following claims. In the claims, the middle plus function sentences are intended to cover the structures described herein as performing said function and a structural equivalent and equivalent structures. Thus, although a nail and a screw may not be structurally equivalent in that the nail uses a cylindrical surface for jointly securing the pieces of wood, while a screw uses

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or 2 Ο 1 6 - - 00323 »ί -) Ι- 2914 ο helical surface, in the environment of fixing the pieces of wood, a nail and a screw can be equivalent structures. The express intention of the applicant is not to invoke 35 USC § 112, paragraph 6 for any limitations of the claims herein, except for those in which the claim expressly uses the words "means for" together with an associated function.