SPE 167801

Modeling Multiple Hydraulic Fractures Interacting with Natural Fractures Using the Material Point Method Yamina E. Aimene, John A. Nairn, Oregon State University, USA

Copyright 2014, Society of Petroleum Engineers This paper was prepared for presentation at the SPE/EAGE European Unconventional Conference and Exhibition held Vienna, Austria, 25–27 February 2014. 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

This paper describes use of the Material Point Method (MPM) for modeling the propagation and interaction of multiple hydraulic fractures (HF) with natural fractures (NF). First the method is used on a laboratory experiment involving one HF and one NF positioned at different angles from the maximum horizontal stress. Various geomechanical simulations are performed by varying the stress anisotropy and the angle of the NF to study the remote impact of the HF on the NF. The results show the various levels of influence a HF has on a NF with a general trend being a higher influence for lower anisotropy ratio and lower NF angles. For an anisotropy equal to 1 and a NF with angle of 90 degrees, the detailed NF opening mechanism before, during and after the HF crosses a NF is studied in detail. The MPM simulations show that under the influence of the HF, the NF opening starts before the HF reaches it and even before the HF propagation. This result could help better understand the microseismic events recorded farther from the HF tip. Finally, a new workflow that integrates geophysics, geology, geomechanical simulations using MPM and completion engineering is described and validated with a real and complex Marcellus gas shale well. The workflow uses a seismically derived fault attribute map as input into the Continuous Fracture Modeling (CFM) approach to generate an Equivalent Fracture Model (EFM). The MPM geomechanical simulation of multiple hydraulic fractures propagating in the input EFM model leads to estimation of a strain field and J integral at each frac stage with a computation time not exceeding a few hours. The application of this workflow to an anomalous Marcellus gas well, shows that the estimated strain model has many striking similarities with the interpreted microseismic. The shape and the extent of the geobodies seen in the simulated strain field are very similar to those seen in the microseismic. Furthermore, the predicted J integral at each frac stage is correlated well with the density of the microseismic events at the same frac stage. The entire workflow takes only few hours thus making it suitable for any completion engineer designing his well. The new workflow brings improved and realistic geomechanics into the G&G world by providing new insights into the complex behavior of multiple hydraulic fractures propagating in a naturally fractured reservoir. This new insight will provide an additional powerful tool for an integrated approach that combines G&G, geomechanics and engineering for the imaging of sweet spots and reliable estimates of well performance thus allowing improved and economical fracing and development of shale reservoirs.

Introduction

The ongoing shale revolution in the North American continent has dramatically changed the worldwide energy landscape.

Until recently, the USA was importing more crude oil than it was producing but with the development of shale basins such as the Eagle Ford in Texas and Bakken in North Dakota, the US oil production is continuously increasing while its imports are decreasing. The situation with gas production is more dramatic since the new shale gas produced in the Marcellus, Haynesville, and other shale gas basins is responsible for a glut that is keeping gas prices in North America very low as long as LNG terminals and adequate infrastructure is not allowing the export of these large gas reserves. This dramatic shift in energy production is occurring as a result of improved fracing technologies that are unlocking the hydrocarbons found in these shale basins. Producing these shale hydrocarbons is achieved by primarily pumping water and proppant to break the rock and create a complex network of induced and natural fractures. Unfortunately, the actual process that is creating this complex fracture network resulting from the interaction between the hydraulic fracture and the natural fracture system is still poorly understood.

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Many authors1-3 have pointed to the important role played by the natural fractures in the overall performance of the shale

wells as a result of their interaction with the hydraulic fractures. However, the actual modeling of these interactions and the imaging of the final fracture network is very challenging and results are progressing slowly. For many years, hydraulic fracturing was modeled with ideal bi-wing planar fractures. The bi-wing models evolved from simple 2D models4-6 to pseudo 3D models7 where the reservoir rock properties are assumed homogeneous across the reservoir or in each geologic layer. Unfortunately, field and laboratory experiments8-13 are showing a more complex fracture geometry where the hydraulic fracture is interacting with natural fractures thus creating a complex fracture network that depends on the nature and orientation of the natural fractures, the variable rock mechanical properties where the hydraulic fracture is developed and the differential stress present in the subsurface. Among the multiple deficiencies14 of current bi-wing hydraulic fracture simulations technologies is their inability to correctly account for fluid leakoff caused by the natural fractures interacting with the hydraulic fracture. To address these shortcomings, various approaches were developed to model the complex interaction between the induced and natural fractures.

Modeling the Interaction Between Hydraulic and Natural Fractures

The modeling of the natural fractures is a challenging task. As a result, including them in a reservoir volume that is crossed by a hydraulic fracture took different forms that vary in the ways the natural fractures are represented and in the computation time required to simulate hydraulic fracture propagation. Among the computationally-intensive approaches we find the use of full fledge 3D finite elements15 (FEM) or the extended finite elements16 (XFEM) geomechanical simulators to model the interaction between the hydraulic and natural fractures. Another computationally intensive approach use the Discrete Element Method17 (DEM) where shear failure is used as a means to simulate microseismic events. The authors17 focused on the importance of fluid viscosity but no actual field measurements or real data was shown to illustrate these findings. These computationally-intensive approaches are not suitable for the completion and drilling engineers who have to design their completion strategies with a turn-around measured in hours not days. Another approach18,19 developed with the concern of computation time is an enrichment of the pseudo 3D models described earlier with analytical rules that drive the interaction between hydraulic and natural fractures represented by a Discrete Fracture Network (DFN).

Most of these modeling approaches rely on hydraulic-natural fracture intersection rules derived from observations made

in laboratory and mineback experiments9 where the interaction between the hydraulic and natural fracture is restricted to a limited number of scenarios19. The current modeling scenarios consider either a hydraulic fracture (HF) stopped by a natural fracture (NF) or crossing it. When stopped, the HF could cause the dilation of the NF and turn to propagate along that weakness plane. On the other hand, when the HF crosses the NF, it could either continue its propagation with the NF remaining closed or it could cause dilation of the NF. From the published literature it appears that most of the focus in the HF-NF interaction is on the intersection and the ensuing consequences (stopping, crossing, bifurcation) and not much effort was spent on investigating the critical time prior to the intersection where the NF is affected by the stress field20 created by the HF. This stress field is discussed mainly in the context of "stress shadow effect" which deals with the effect of an initial frac stage on the subsequent ones occurring in the altered stress field caused by the first one. This stress shadow effect is important on the new HF and its surroundings but is also extremely important on the existing NF network. The behavior of the NF in the presence of an altered stress field created by a propagating HF is an important issue because the NF could dilate BEFORE the HF reaches its position and as a consequence a microseismic event could potentially emanate from that NF. In other words, understanding this critical mechanism of NF reacting to HF stress fields before the actual front arrives, will help us better understand the difference between the Microseismic Stimulated Reservoir Volume (MSRV) and the Actual Stimulated Reservoir Volume (ASRV) where the proppant was placed in the dilated natural fractures.

To better understand this effect this paper addresses the following topics. First this paper describes the use of the Material

Method Point (MPM) to model the interaction of multiple hydraulic fractures in the presence of natural fractures. To the best of our knowledge, MPM was never used in this area so we will describe its benefits and strengths both from the physical modeling point of view but also from a computational time point of view. Second, this paper examines the behavior of a NF in the presence of a HF created in a laboratory experiment9 used by many authors working in this area. Emphasis will be given to the overlooked period of time where the NF is under the influence of the stress field created by the approaching HF. Third, this paper describes a new workflow validated with real field data (microseismic and production logs) from the Marcellus to better understand anomalous microseismic responses using the MPM geomechanical simulations of multiple hydraulic fractures in the presence of a complex and realistic natural fracture network derived from seismic data.

Modeling Hydraulic and Natural Fractures with the Material Point Method (MPM)

The Material Point Method (MPM) is a meshless method, developed as a potential tool for numerical modeling of dynamic solid problems21-28. It represents an alternate approach, with alternate characteristics, for solving problems

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traditionally studied by dynamic Finite Element Methods. In MPM, a solid body is discretized into points, called particles, much as a computer image is represented by pixels (Figure 1). A background grid is associated with the particles, it is composed of elements, (like Finite Elements found in 3D geomechanical software used in the oil and gas industry or Finite Difference found in 3D reservoir simulation software), and boundary conditions are specified on the grid. The background grid is only used as a calculation tool space. At each time step, the particle information is extrapolated to the background grid, to solve the equations of motion. Once the equations are solved, the grid-based solution is used to update all particle properties such as position, velocity, acceleration and stress state, etc. This combination of Lagrangian (particles) and Eulerian (grid) methods has proven useful for solving solid mechanics problems including those with large strains or rotations and involving materials with history-dependent properties such as plasticity or viscoelasticity effects21.

MPM has been extended to handle explicit fractures by using the Crack in the Material Point (CRAMP) algorithm25 and cohesive zones27. Both the particle nature and the meshless nature of MPM makes CRAMP well suited to the analysis of fracture mechanics problems. In MPM, fractures are represented by a series of line segments. For compatibility with MPM data structures, the endpoints of the line segments are massless material points. By translating the fracture segments along with the solution, it is possible to track fractures in moving bodies. The fracture particles track fracture-opening displacement that allows for calculation of fracture surfaces. The fracture particles influence the velocity fields on nodes in the background grid. In addition, CRAMP fully accounts for fracture surface contact, is able to model fractures with frictional contact, can use fractures to model imperfect interfaces27, and can insert traction laws to model cohesive zones, or input pressure

The CRAMP algorithm models explicit fractures by allowing each node near the fracture to have two velocity fields representing particles above and below the fracture (Figure 1). Since the original development25, the method has been extended to explicitly handle two interacting fractures, even when they are in the same background cell, by allowing each node to have up to four velocity fields representing each combination of particles above and below each fracture. An MPM model can include any number of fractures as long as no background cell contains more than two fractures at a time. The modeling of three interacting fractures in one cell is not possible at this time in MPM.

MPM is a computational tool adapted to dynamic fracture modeling29-32. In this paper, we use the extended CRAMP to account for the interaction of multiple hydraulic and natural fractures. The extended CRAMP uses elastic fracture mechanics to model material failure and fracture propagation. In MPM, simulations that include fracture propagation require three steps. First, the stress state and fracture-tip parameters are evaluated and used to determine whether or not the stress state is critical for fracture growth and propagation. If the stress state is such that the fracture should propagate, the fracture-tip stress field is then analyzed to evaluate the direction of propagation. Finally, a new fracture particle is added in the selected direction of propagation. A variety of criteria for fracture propagation and growth direction are implemented. Unlike finite element methods15 where fractures must follow mesh lines or there must be time-consuming re-meshing, a fracture in CRAMP can proceed in any arbitrary direction. The problem of re-meshing is reduced with the development of extended finite elements methods16 (XFEM) when applied to a SINGLE hydraulic fracture but have not worked well when dealing with the propagation of MULTIPLE hydraulic fractures such as the ones commonly found in shale wells.

In fracture mechanics, the main problem is the analysis of stress field in the fractured media. To characterize the stress singularity around the fracture tip, and to predict fracture propagation, we consider the global approach based on the balance of energies involved in the process of fracture growth, mainly the energy release rate G. The fractures grows33 when the energy release rate, G, exceeds a critical toughness Gc. In MPM, the knowledge of the local stresses and the fracture plane is sufficient for calculating G using J integral calculation. The two stress intensity factors in mode I and II (KI and KII) in 2D problems are calculated from J and fracture opening displacememts. The energy release rate G is given as:

G =1E '

KI2 +KII

2( )

with E’ = E for plane stress and E ' = E / 1−υ 2( ) for plane strain analysis, where E is the Elastic modulus.

The fracture propagation angle for the hydraulic fracture is assumed to be in the direction of the maximum hoop stress. This assumption is based on the observation that materials resist fracture in shear and always turn to the direction that promotes mode I fracture. With this criterion, the fracture direction is at an angle θ relative to the horizontal axis and follows the equation34, which gives the same propagation angle as ones used in many geomechanical models35:

θ = arccos 3R2 + 1+8R2

1+ 9R2!

"##

$

%&&

with R = KII

KI

For the natural fractures, we assumed a self-similar propagation criterion36 specified at the two extremities of the natural fracture. This choice was dictated by the fact that a natural fracture is a weakness plane, and propagation would be first along

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this weakness plane.

This approach is implemented in the software OSParticulas36 and will be used to analyze both laboratory and field experiments. The implementation of CRAMP in OSParticulas36 is accomplished through efficient C++ coding and parallelization which makes it extremely fast while retaining all the complex physics of multiple fracture propagation. The time required for solving different multiple fracture problems is given in the next sections.

Understanding the Remote Effect of a Hydraulic Fracture on a Natural Fracture

A laboratory experiment9 conducted in the early 80's at Sandia National Laboratory on a Coconino sandstone sample helped many authors refine their modeling of the interaction between hydraulic and natural fractures. In this work, we examined the same experiment but focused on two overlooked issues: 1) the period prior to the intersection between the hydraulic and natural fracture and 2) the detailed variation of the NF opening before and after the HF reaches it. The motivation behind this focus is related to current interpretation of microseismic events and the difference between the Microseismic Stimulated Reservoir Volume (MSRV) and the Actual Stimulated Reservoir Volume (ASRV). Increasing evidence37 is showing that a large number of microseismic events are most likely reactivated natural fractures. In other words, the stress field created by the hydraulic fractures is causing this reactivation, which is a phenomenon that has not been extensively studied. These reactivated natural fractures could contribute to the MSRV but not necessarily to the ASRV thus the importance to deriving a good understanding of the basic mechanisms responsible for this reactivation.

The MPM method described in the previous section was used to model the Coconino sandstone experiment9. The rock sample dimensions, boundary conditions and the elastic properties of the studied rock were input in the OSParticulas software. Two time phases were used to reproduce the stress conditions applied to the rock sample. In the first phase, we loaded the sample with compressive stress boundary conditions at a constant, quasi-static load rate. This phase created subsurface stress conditions prior to any hydraulic fracturing. In the next phase a linearly increasing pressure was applied in the HF by using MPM pressure law. The pressure reached a maximum value of 10 MPa at a rate of 47.62 MPa/msec. In the last phase, we monitored propagation of the HF and focused especially on the behavior of the NF before the HF reaches it. The maximum horizontal stress σHmax is along the X-axis, which is also the direction of the HF. The values of σHmax vary according to the experimental set-up. In the Y direction, the minimum horizontal stress σHmin exerts on the rock sample a constant pressure thus creating a stress anisotropy that could vary. The anisotropy is defined as the ratio of the maximum horizontal stress by the minimum horizontal stress and could take 3 possible values: 1, 2 and 3. The NF could take 3 possible orientations: 30, 60 and 90 degrees angles. The 90 degree angle will have the NF perpendicular to the HF while the 30 degree angle will make the NF almost an extension of the HF.

Prior to any hydraulic fracturing by imposing a large pressure in the HF, the application of the stress boundary conditions to the existing HF and NF shows noticeable effects of stress anisotropy (Figure 2). When the anisotropy is equal to 1, the stress in the X direction σxx, shows that the variation of the NF angle from 90 to 30 degrees does not affect the stress field. This observation holds also for a 90 degrees NF with an anisotropy equal to 2. However, for an angle of 60 or 30 degrees, the stress field around the NF and its extremities is disturbed going from tension to compression from one side to the other side of the NF. For the anisotropy 3, the stress field shows high stress concentration around the NF especially for 30 degrees angle of the NF.

Once the pressure is ramped up to 10 MPa in the HF, we start noticing the major effects on the NF (Figure 3) for all the possible anisotropy values and for different NF orientations. Figure 3 shows that the effects and the influence of the HF on the NF is greater as the NF angles goes from 90 to 30 which is intuitively understood. In addition, stress concentration around the NF tips, increased as the NF orientation decreased, and it decreased as anisotropy increased. For anisotropy 2, the stress field shows more compression on the edges of the sample that is too close to the extremities of the NF especially for 90 degrees. This compression would stop any propagation of its tips. However, for an angle of 60 or 30 degrees, a differential stress field around the NF is observed and the NF tips show tensile stress (blue colors in Figure 3) that could promote propagation. At an angle of 30 degrees, the HF wants to join the NF and this tendency is exaggerated for higher anisotropy. For anisotropy 3, the stress field shows high stress concentration around the NF especially for 30 degrees. The high in-situ compressive stress may not allow the opening of the the HF with the applied pressure for NF at 90 and 60 degrees, however shearing in the sample will most likely occur for 30 degrees. Again this explains the behavior of the frac jobs occurring near faults where there is high anisotropy. The question arises — how does relative position of the HF compared to the NF affect the interactions? Figure 4 shows the case for anisotropy 1 where we varied position of the HF along the Y axis which is similar to selecting the frac stage at different locations along the wellbore. From Figure 4, it appears that any NF in the vicinity of the HF will feel its stress field especially the NF extremity closest to the HF. This effect is exaggerated when the NF angle drops down from 90 to 30. If the NF is farther in the X direction (Figure 5), the effect of the HF is still present and in the limiting case of infinitely long vertical fractures the distance of this effect was estimated analytically9,20 to be around

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one fracture height. Numerically, we see that the effect could be felt for a much longer distance.

To better see the effects of the HF on the NF, we examined the stress field in the Y direction σyy (Figure 6), which shows the tensile stress concentration around the tips (blue colors in Figure 6) of the NF which results in the "pulling" of the NF causing its opening. For anisotropy 1, when changing the relative position of the HF compared to the NF, the stress concentrations are still causing the pull effect along the entire length of the NF even when the HF is not directly facing the NF (Figure 7). The same observations are made when the NF is moved along the X direction farther away from the HF (Figure 8).

A more visual way to see the effect of the HF on the NF is to plot the displacement in the X direction (Figure 9). The area of the NF affected by the HF is clearly visible for the various angles and anisotropries. The applied pressure tends to open the HF, which is augmented with the presence of the NF especially for low anisotropy and high angles (red colors, displacement in –X direction in Figure 9). For NF angles of 60 and 30 degrees, the HF pulls only on one part of the length of the NF, at the same time, the NF is trying to close the HF by compressing it with the other part of its length. As the anisotropy increases, the X displacement decreases to very low values for the 60 and 90 degrees. This is due to the pre-existing high compressive stress existing in the subsurface. For anisotropy 1, when moving the HF along the wellbore (Figure 10), the intensity of the HF pulling on NF (negative displacement, in –X direction) is reduced. The same observation is made when moving the NF away from the HF along the X direction (Figure 11). Moreover, all these figures illustrate HF-NF interactions and show a favorable path going from the HF to NF for the different relative positions of the HF and NF. Based on these observations that highlight the influence of the HF under the considered conditions, it is expected to see, in many situations, the NF reacts by opening or dilating. In the experiment9, out of the 9 cases listed, six of them clearly showed dilation or shear slippage. The next section, describes the magnitude of these openings and their timing before, during and after crossing of the NF.

Quantifying the Opening of the Natural Fracture

We next investigated the behavior of the NF as it reacts to the stress field created by the HF. We divided the time in three phases. During the first phase, the HF is not propagating but its stress field is already acting remotely on the NF as seen in the previous section. We will consider in this section the case of anisotropy 1, an angle of 90 degrees for the NF and we are dealing with the time after the pressure in the HF is ramped up to 50% of its target of 10 MPa. The relative length of NF is equal to 0.6. Figure 12 shows the displacement X at different times before the HF propagates. One can notice that at time t=0.163342 the NF starts to open and continues to do so until time t=0.182006 which corresponds to the time where the HF started propagating. During this phase, the NF length grows slowly in a symmetric fasion relative to its center, as illustrated in Figure 12 plot showing the fracture opening versus the dimensionless fracture length. Its final relative opening is about 0.3 representing around 50% of its length.

Phase 2 behavior is described in Figure 13 where the displacement in the X direction shows a rapid increase from t=0.184339 to t=0.193671 when the HF reaches the NF. During this phase, propagation of the HF that did not reach yet the NF, we notice an increase in the NF length opening until its full relative length 0.6. In the last phase (Figure 14), the HF grows toward the NF, parallel to maximum horizontal stress. This promotes the propagation of the NF symmetrically at its tips, the NF length opening is growing also (Figure 14). At the end of the simulation, the HF intersects and crosses the NF.

The critical time occurring when the HF approaches the NF and the resulting behavior is better understood when examining Figure 15 where a zoom on the intersection zone will help us better understand the resulting mechanism. At time t=0.186672, the HF did not reach the NF but is still able to cause its opening as shown in the plot of crack-opening versus NF dimensionless length. At time t=0.193671, the remote opening of the NF continues and at time t=0.20067 the HF intersects the NF and causing a jump in the NF opening that indicates its propagation. At time t=0.226364, the HF and the NF are opening and at time t= 0.233363 the HF crosses the NF which continues its opening with a lower rate. This close look at what is happening before, during and after a HF crosses a NF shows the complexity of the events and the interaction between the HF and NF.

In this example we have only described results for anisotropy 1 and an angle of 90 degrees for the NF. The other cases with different anisotropies and angles show other very interesting features that will be described in future publications. The computation time required for the simulations described in the two previous sections on a laptop with a dual (2.3 GHz) Intel two-core i7 processors (Mac) is around 5 minutes. This computation speed is the result of a very efficient coding of the MPM method in OSParticulas36 and its parallelization although in this example, parallelization was not used.

Armed with this computationally efficient tool and a better understanding of the basic mechanisms involved in the HF-NF interaction, one could address actual field scale engineering problems and use the derived knowledge to improve the decision

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process by providing a new workflow that is able to integrate multiple disciplines with the geomechanical tools described in the previous sections.

A New Integrated Workflow that Combines Geomechanics, Completion Engineering and G&G

E&P companies developing shale plays are devoting large budgets for microseismic acquisition with the hope that the microseismic events could help show the Stimulated Reservoir Volume (SRV). Unfortunately, these microseismic campaigns sometimes raise more questions than provide answers. The goal of the proposed workflow is to answer some of these questions and bring the support of realistic and fast geomechanical simulations to enrich an integrated approach that includes the use of geophysical, geologic and engineering data. In this section we describe a new workflow that could be used by completion engineers working on their desktops designing optimal completion strategies, and predicting microseismicity. The new workflow is illustrated with a Marcellus real field data where the behavior of an anomalous well could be better understood when adding the geomechanical component to the integrated approach.

Microseismic38 data acquired in the Marcellus gas shale has been helping many operators optimize their well spacing and estimate their Stimulated Reservoir Volume. Microseismic has also revealed unpleasant surprises where sometimes half the frac stages along a wellbore have no microseismicity39. In other words, half the completion budget for that wellbore could have been saved if the completion engineer had a tool that would allow him to predict the poorly performing frac stages. In fact, with such a predictive tool, the wellbore length could have been reduced or the well not drilled at all in that location where many frac stages perform poorly. The illustration of the newly developed workflow will address one of these situations39,40 where a pad of three wells shows a very anomalous microseismic behavior at well 4H (Figure 16). The goal of the new integrated workflow is to explain similar situations but ultimately to allow drilling and completion engineers to avoid drilling and fracing in such locations.

Figure 16 shows that wellbore 4H is crossing 3 faults which seems to have dramatically affected the microseismic response shown in blue in Figure 16. As indicated by the authors39,40, it is very likely that the faults are playing a major role in driving this microseismic response which has resulted in poor production in the first five frac stages as shown in Figure 16-17. Could geomechanical simulations of the complex fracture network created by these faults help explain this anomalous wellbore? To answer this question we will describe the steps involved in the new workflow.

We will focus on the area east of the wellbore and assume a 2D quasi-static plane strain problem in the horizontal plane. The rock is modeled as an elastic model where the behavior of the rock is assumed linear isotropic. Rock elastic properties and current horizontal stresses are taken from various publications.

The first step in the workflow is to characterize the distribution of the natural fractures in the considered area. Most of the geomechanical modeling17,18 uses a Discrete Fracture Network (DFN) representation. The use of DFN for natural fracture modeling has been shown41 to be time consuming and may not be appropriate for a rapid deployment of a geomechanical solution. A more efficient approach to natural fracture modeling is the Continuous Fracture Modeling42,43 (CFM) which seems more adapted to our workflow. This approach provides an Equivalent Fracture Model (EFM), which gives in each elementary representative volume or gridblock of the reservoir a fracture density. The 2D or 3D distribution of this fracture density is the result of the integration of geophysical and geologic information with any fracture indicator derived at the wells. In other words, if image logs or cores are not available, one can still get a 2D or 3D natural fracture model using any other fracture indicator available at the wells. Furthermore, this approach could be used directly on any seismic attribute that could represent or be considered a good proxy for the fracture density. Using the CFM approach42 one can turn, for example, a curvature or fault attribute map derived from seismic data into an EFM model, which is exactly what we did in this example.

Figure 17 (left) shows a fault attribute derived directly from the seismic. Although natural fractures depend on many factors and not only faults, in shale plays, the use of curvature and other structural attributes44,45 as a proxy for natural fractures is a reasonable first order approximation during the early stages of completion designs. The fault attribute shown in Figure 17 was digitized and used as input in FracPredictor46, which generated the Equivalent Fracture Model (EFM) shown in Figure 18. In each reservoir gridblock, the EFM model has a fracture that has an angle and a length calculated from the CFM approach42.

The second step of the workflow is to export the derived EFM fracture length and angles to OSParticulas, which will create an MPM discretized model (Figure 19). This data export process is very simple and consists of exporting a file from FracPredictor that provides at each location the length and angle of the fractures. This information is then converted to positions of start-tip and end-tip of the fractures. In fact, the MPM model doesn’t need any specific discretization into elements around fractures as needed in Finite Element Methods with explicit fractures. In MPM, all that is needed are the

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fracture positions. For each fracture, we specify the "start" (x1,y1) and "end" tip (x2,y2) positions and define series of massless material points tracing the fracture path on top of the background grid. For a collection of any number of NF and HF fractures, a table of their positions can be directly input to the MPM software to model all explicit fractures. When including both NF and HF fractures, each fracture tip is assigned appropriate propagation criterion for that type of fracture.

The third step consists of running OSParticulas to simulate first the in-situ pre-stress, then the simultaneous increase of pressure in the hydraulic fractures. This simulation could be done in a sequential manner according to the actual or planned field operations or could be run on all the hydraulic fractures simultaneously to speed-up the completion design process. The results of this simulation are multiple but we will focus on two major ones (Figure 19). The first one will be the strain in the Y direction (Figure 20) and the second one will be the J integral estimation at the frac stages (Figure 21).

When applying these three steps to the Marcellus data set and limiting the geomechanical simulation to only the frac stages where microseismicity has been observed (frac stages 5 to 12), we are able to get several results like a strain map (Figure 20) and the J integral at each frac stage (Figure 21), within 3 hours when using a dual Xeon 5600 six-core processors (Dell PowerEdge T610) and OpenMP parallel code. In other words, any completion engineer working on his desktop could get realistic geomechanical simulations added to his analysis in about the same time frame it takes him today when using pseudo 3D models frac design software. Furthermore, these MPM simulations combined with the EFM natural fracture models derived using the CFM approach will be dramatically faster than any solution that involves a DFN model to describe the distribution of the natural fractures.

When examining the resulting strain map (Figure 20), we can easily recognize the three distinct regions or geobodies interpreted from the microseismic. The first geobody in the strain map (white color in Figure 20) between frac stage 9 and 10 has the same shape and volume as the one seen in the microseismic interpretation. The second geobody (red rectangle in Figure 20) at frac stage 8 shows clearly a long rectangular zone that has very low strain where there was no microseismicity recorded due most likely to the presence of the interpreted fault. Finally, the third geobody (Yellow color in Figure 20) between frac stages 8 and 6 show a similar shape as the one interpreted with the microseismic data.

In addition to capturing the shapes and the lateral extent of the microseismic geobodies, the geomechanical simulation provides valuable output: the J integral estimation at each frac stage (Figure 21). The J integral results show the highest energy at frac stage 10 where the highest number of microseismic events was recorded and the lowest J integral value at frac stage 8 where no microseismic events were recorded. This could be explained by the relative position of the NF associated with the fault and HF and their interaction as discussed above. The J integral results confirm and explain the strain results and allows the direct link between microseismic and geomechanics as demonstrated on this real and complex well. In other words, with this new workflow the completion engineer could predict during his frac design which frac stage will show the highest and lowest microseismicity.

With this complex Marcellus gas well, we confirm that shear faillure when modeled with MPM using multiple hydraulic fractures propagating in an Equivalent Fracture Model derived with the CFM approach, does reproduce closely actual microseismic interpretations but is it really what matters the most ? Figures 20 and 21 show the production logs along the 4H wellbore where it is very clear that high microseismicity does not necessarily translate into high production. Knowing where shear failure occurs (information that could be acquired with actual microseismic field measurements or estimated numerically using the proposed new workflow) does not translate into a correct evaluation of the estimated ultimate recovery (EUR), the corresponding Actual Stimulated Reservoir Volume and most importantly the well performance. In other words, other factors related to rock properties, proppant behavior during the fracing and many other issues need to be accounted for when estimating the EUR and well performances. Whatever these additional factors are, we strongly believe that the geomechanical results derived from the proposed workflow could add tremondeous value to the ultimate goal of estimating the well performance and EUR in an integrated approach that combines geophysics, geology, geomechanics and engineering.

Conclusions

The application of the material point method to the study of multiple hydraulic fractures propagating into a naturally fractured reservoir has led to many results. The application of MPM to laboratory experiments revealed the complex interaction that exists between a HF and a NF. This influence could be responsible for the opening of the NF even when the HF is still far from it. The rate of fracture opening depends on the proximity of the NF to the HF and appears to be a complex phenomenon. The improved understanding derived from these laboratory experiments led to the development of a new workflow that was validated on a Marcellus gas well. The new workflow confirms the possible use of seismically derived structural maps as a reasonable proxy for natural fracture mapping. The combination of these seismically derived structural data with the use of the continuous fracture modeling approach to generate Effective Fracture Models (EFM) provides the necessary input for the MPM geomechanical simulations. When using the new workflow on a Marcellus gas well, the derived

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strain maps show striking similarities with the interpreted microseismic recorded at the same well. The shape and extent of the geobodies seen in the strain maps appear to be the same as the ones found on the interpreted microseismic events. More interestingly the J integral computed at each frac stage correlates very well with the density of the microseismic events recorded at the same frac stage. The results of this field validation confirms the fact that microseismic events are most likely related to the opening and shearing of natural fractures and provides a useful design and analysis tool to any completion engineer. This workflow could be easily used on desktops because it includes multiple levels of optimization that provides a practical turn-around of few hours similar to the existing time frame used by completion engineers using pseudo 3D frac design software. Unfortunately, geomechanical results are not sufficient to explain the well performance along the different frac stages but they could be a valuable input to an integrated approach that combines geophysics, geology, geomechanics and engineering

Acknowledgements

The authors would like to thank Go Geoengineering (GoGeo) for their financial support, for the stimulating discussions regarding the new developed workflow and for providing the Marcellus Equivalent Fracture Model (EFM) derived in FracPredictorTM. References

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behavior with continuous fracture models:" AAPG Bulletin, v.,. 93/11, 2009, p. 1597-1608. 44. Refunjol, X., E., Marfurt, K., J., Le Calvez, J.H., " Inversion and attribute-assisted hydraulically induced

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46. FracPredictorTM: http://gogeo.biz/FracPredictor.html

Figure 1. Sample view of digitization used in MPM and CRAMP. In MPM, the body is digitized into a collection of material points. Boundary conditions may be applied to the grid or directly to particles.

Figure 2. Variation of the stress in the x direction when the angle of the NF and the anisotropy varies and when the stress boundary conditions are applied without any pressure applied in the HF.

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Figure 3. Variation of the stress in the x direction when the angle of the NF and the anisotropy vary and when the pressure in the HF is ramped up to 10 MPa.

Figure 4. For the anisotropy equal to 1 and pressure of 10 MPa applied to the HF, variation of the stress in the x direction when the angle of the NF and the position of the HF vary.

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Figure 5. For the anisotropy equal to 1 and pressure of 10 MPa applied to the HF, variation of the stress in the x direction when the angle of the NF and its position compared to the HF vary.

Figure 6. Variation of the stress in the y direction when the angle of the NF and the anisotropy vary and when the pressure in the HF is ramped up to 10 MPa.

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Figure 7. For the anisotropy equal to 1 and pressure of 10 MPa applied to the HF, variation of the stress in the y direction when the angle of the NF and the position of the HF vary.

Figure 8. For the anisotropy equal to 1 and pressure of 10 MPa applied to the HF, variation of the stress in the y direction when the angle of the NF and the position of the NF vary.

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Figure 9. Variation of the displacement in the x direction when the angle of the NF and the anisotropy vary and when the pressure in the HF is ramped up to 10 MPa.

Figure 10. For the anisotropy equal to 1 and pressure of 10 MPa applied to the HF, variation of the displacement in the x direction when the angle of the NF and the position of the HF vary.

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Figure 11. For the anisotropy equal to 1 and pressure of 10 MPa applied to the HF, variation of the displacement in the x direction when the angle of the NF and the position of the NF vary.

Figure 12. For the anisotropy equal to 1 and just after the pressure in the HF reaches 10 MPa, variation of the displacement in the x direction as a function of time and the resulting opening of the NF while the HF is still not propagating.

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Figure 13. For the anisotropy equal to 1 and just after the HF start propagating, variation of the displacement in the x direction as a function of time and the resulting opening of the NF while the HF did not reach the NF yet.

Figure 14. For the anisotropy equal to 1 and just after the HF start propagating, variation of the displacement in the x direction as a function of time and the resulting opening of the NF after the HF reach the NF and NF start propagating.

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Figure 15. For the anisotropy equal to 1 and just after the HF start propagating, zoom around the intersection point between the HF and the NF. The opening of the NF starts before the HF reaches the NF and continues after intersection and crossing as shown in the fracture opening plot on the lower right corner.

Figure 16: Microseismic events and interpreted seismic lineaments (left) shown with production logs (right). Notice that the wellbore 4H has no microseismicity in half of its frac stages. (from paper40 UrTec 1577009)

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Figure 17: Fault attribute in gray color (left) shown under the wells along with their corresponding frac stages and their resulting production logs (right) (from paper39 URTeC 1575448)

Figure 18: Equivalent Fracture Model (EFM) derived in FracPredictor46 from the fault attribute shown in Figure 17 and the corresponding frac stages with their production logs

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Figure 19: The new workflow that transforms a geologic or geophysical attribute that relates to natural fractures into an Equivalent Fracture Model which provides to the MPM grid the necessary natural fracture information for the geomechanical simulation which will lead to a strain distribution and a J integral estimation at each frac stage

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Figure 20: Strain in the y direction resulting from the MPM calculations (right). Notice the ability of the MPM model to reproduce all 3 major anomalous microseismic responses at well 4H between frac stages 5 and 10.

Figure 21: Strain in the y direction resulting from the MPM calculations (right) along with the J integral at each frac stage (left). Notice the ability of the MPM model to predict the highest J integral at frac stage 10 where the highest microseismicity is observed (white geobody) as well as the lowest J integral at frac stage 8 where no microseismicity is observed at all (red rectangle).