integration of fracture, reservoir and geomechanic Modeling for shale gas reservoir development

These models predict that principal stresses are influenced far beyond the drainage area of a horizontal well and hence can play a critical role in fracture orientation and performance o

SPE 164018

Integration of Fracture, Reservoir, and Geomechanics Modeling for Shale Gas Reservoir Development

Jugal K Gupta, Richard A Albert, Matias G Zielonka, Yao Yao, Elizabeth Templeton-Barrett, Shalawn K Jackson, Wadood El-Rabaa, ExxonMobil Upstream Research Company, Heather A Burnham, Nancy H Choi, XTO Energy

Copyright 2013, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Middle East Unconventional Gas Conference and Exhibition held in Muscat, Oman, 28–30 January 2013

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

Fracture nucleation and propagation are controlled by in-situ stresses, fracture treatment design, presence of existing fractures (natural or induced), and geological history In addition, production-driven depletion and offset completions may alter stresses and hence the nature of fracture growth For unconventional oil and gas assets the complexity resulting from the interplay of fracture characteristics, pressure depletion, and stress distribution on well performance remains one of the foremost hurdles in their optimal development, impacting infill well and refracturing programs

ExxonMobil has undertaken a multi-disciplinary approach that integrates fracture characteristics, reservoir production, and stress field evolution to design and optimize the development of unconventional assets In this approach, fracture modeling and advanced rate transient techniques are employed to constrain fracture geometry and depletion characteristics of existing wells This knowledge is used in finite element geomechanical modeling (coupling stresses and fluid flow) to predict fracture orientation in nearby wells

In this paper, an integrated methodology is described and applied to a shale gas pad as a case study The work reveals a strong connection between reservoir depletion and the spatial and temporal distribution of stresses These models predict that principal stresses are influenced far beyond the drainage area of a horizontal well and hence can play a critical role in fracture orientation and performance of neighboring wells Strategies for manipulating stresses were evaluated to control fracture propagation by injecting, shutting-in, and producing offset wells In addition, we present diagnostic data obtained from the pad that demonstrates inter-well connectivity and hydraulic communication within the pad The workflow presented herein can be used to develop strategies for (1) optimal infill design, (2) controlling propagation of fractures in new neighboring wells, and (3) refracturing of existing wells

Introduction

The spatial and temporal evolution of stresses due to reservoir depletion and mechanical opening of fractures has received widespread attention over the past two decades due to the richness of the associated physical phenomena as well as its technological importance in governing fracture propagation and geometry (Detournay and Cheng, 1988; Bruno and Nakagawa, 1991; Elbel and Mack, 1993; Berchenko and Detournay, 1997) Recently, the concepts have been extended to ultra low permeability unconventional reservoirs such as tight gas and shale gas reservoirs, where the phenomenon of stress

reorientation has shed light on refracturing of wells (Zhai and Sharm., 2007) and led to the development of new completion strategies for improving well productivity (Soliman et al., 2010) Stress reorientation around vertical wells and fractured vertical wells has been studied extensively in the past (Siebrits et al., 1998) Experimental (Bruno and Nakagawa, 1991; El-Rabaa, 1987) and field observations (Dozier et al., 2003; Wright et al., 1995) have been pivotal in providing fundamental

insights into the mechanisms by which stresses reorient

Although it is generally accepted that geomechanical stresses are important for understanding fracture propagation in shales

with low contrast in principal compressive stresses, the absence of precise knowledge of input parameters needed for reliable

predictions has limited the broad use and applicability of geomechanical models (Dozier et al., 2003) Parameters such as

permeability, fracture half length, number of propagated fractures and geological heterogeneity still carry much uncertainty for

shales and can have a significant impact on model predictions In this paper, ExxonMobil presents a methodology (Figure 1) to

address some of these limitations by integrating knowledge derived from production and fracturing data to reduce the

uncertainty in key parameters and enable realistic predictions We have employed advanced rate transient techniques in

conjunction with numerical history matching of production data and fracture modeling to deconvolve the complex interplay of

parameters impacting well productivity Recent geomechanical studies of multistage horizontal shale gas wells (Roussel and

Sharma, 2010) have quantified the impact of key reservoir and mechanical parameters on the extent and degree of stress

reorientation However, most of these studies have been limited to investigation of stresses near a single fracture and have used

periodic boundary conditions to extend predictions to a multi-fractured horizontal well This paper moves beyond past studies

(Mahrer et al., 1999) of near fracture stress reorientation effects by describing a set of 2D and 3D simulations that take into

account far field, i.e, thousands of feet away from the drainage area, deformation-driven stress reorientation

Figure 1: Multidisciplinary approach that integrates fracture, reservoir and geomechanical analyses to achieve an integrated

solution for optimizing the development of unconventional oil and gas resources

We have investigated the spatial and temporal evolution of stresses for multiple horizontal fractured shale gas wells on a pad

by explicitly modeling each of the hydraulic fracture extending from the wellbore The models are contructed using

simplifying assumptions of planar bi-wing fractures Both 2D plane strain and full 3D formulations are used Our results

reveal significant reorientation of principal stresses thousands of feet away from a producing well in addition to the anticipated

near fracture stress changes The reorientation of stresses far from a producing well can have a significant impact on hydraulic

fracture propagation during stimulation of new infill or neighboring wells This is especially relevant for maturing shale gas

plays where operators are actively engaged in refracturing and infill drilling In this paper, we present a case study of a shale

gas pad to illustrate: (1) evolution of stresses far beyond the drainage area of a hydraulically fractured shale gas well, (2) the

potential for propagating tilted or longitudinal fractures instead of the expected transverse fractures, and (3) communication

between infill wells during fracturing operations The workflow that we have developed has been employed in a number of

published (Gupta et al 2012) and unpublished scenarios such as refracturing of declining wells, infill drilling in maturing

regions and steering of fractures away from water producers

Methodology

A multidisciplinary approach integrating aspects related to completion, reservoir production, and geomechanics was utilized to optimize development of unconventional gas assets The available well, reservoir, production, and geologic data were incorporated to better constrain the problem and to enable prediction of fracture characteristics, drainage areas, and spatial and temporal changes in stress with reasonable accuracy A high level overview of the integration of the different aspects is shown

in Figure 1 It illustrates the three main components of this approach: fracture, reservoir, and geomechanics analysis and modeling Fracture pressure analysis and fracture modeling were conducted to estimate the number of propagating fractures in

a stage and to predict fracture length and height Reservoir modeling and production data analysis were employed to use available production data and obtain estimates for drainage area, gas-in-place, permeability, and estimated ultimate recovery (EUR) Geomechanical modeling was utilized to determine the evolution of stress state for existing and infill wells and to predict new fracture orientation

Figure 2: Flow chart illustrating an integrated methodology that employs fracture modeling, production data analysis,

numerical history matching and finite element geomechanics analysis to predict spatial and temporal evolution of stresses and strategies to manipulate them for potential application in refracturing, steering of fractures and optimizing infills

A detailed workflow showing the interaction among all three disciplines is highlighted in Figure 2 The main inputs for this process are reservoir, geological, and mechanical properties of the formation, which are used in hydraulic fracture modeling and analysis, production data analysis (diagnostic plots), flowing material balance, numerical history matching and finite element geomechanics analysis The production analysis determines the dominant flow regimes in the well to infer fracture-to-fracture and well-to-well interference Using information from production data analysis and fracture-to-fracture height, EUR, and drainage area are calculated from type curves and numerical simulations Finite element analysis (FEA) is conducted to determine evolution of stresses due to production, shut-in, injection, and offset well completion These geomechanical models utilize reservoir properties, number of fractures per stage, drainage widths and reservoir pressures to predict the stresses

Input: Reservoir, Geological, and Mechanical Properties

Output: Strategies for infill, refracturing, new field development

Predict Hydraulic Fracture Orientation

Collect Field Data for Model Validation

Numerical History Matching of Production Data

Spatial and Temporal Evolution

of Stresses

Input Reservoi Completio Geomechanic Output

Output: Improved performance prediction based

on new fracture geometries

Hydraulic Fracture Modeling and Analysis

Production Data Analysis & Flowing Material Balance

Finite Element Geomechanics Analysis (FEA)

Obtain initial estimates of permeability, drainage area, fracture height and length to reasonably constrain geomechanics models

surrounding single or multiple wells If an offset well comes on line, then fractures are explicitly added to the wellbore along

the maximum horizontal compressive stress direction as predicted by FEA Numerical history matching, incorporating new

predicted fracture geometries and any additional field data, can be performed to better constrain permeability and fracture

half-lengths This process is repeated for each well on the pad Additional details of the workflow, including the modeling

assumptions and limitations that define the framework for this paper, will be discussed in the case study that follows

This workflow is ultimately used to develop strategies that optimize: (1) the timing, well placement and fracture strategy of

infill wells, (2) the timing and fracture strategy for refracture candidates, or (3) the timing, well placement, and fracture

strategy for new field developments In the following sections, we will discuss the application of this methodology to an infill

well scenario in a shale gas reservoir

Case Study

The shale gas pad shown in Figure 3A consists of two primary wells (drilled and fractured at different times) and four infill

wells that had been drilled but not fractured This type of development strategy, which has been employed by several operators

in the US, involves initially drilling wells at a sparse spacing to hold acreage followed later by infill drilling to optimize

resource development Such a strategy allows the lease retention constraints to be honored and assists with identifying

production performance "sweet spots" for further drilling The objectives of this case study were twofold: (1) to assess the

potential for interference between the primary (Well 1 and 2) and infill wells due to fracturing of infill wells (Wells 3-6) and

(2) to identify a completion strategy to minimize interference By utilizing the available data, our integrated methodology

employing reservoir, fracture, and geomechanics modeling was used to make reasonable predictions and develop practical

operational recommendations Below we describe each component of the workflow in detail and summarize the lessons

learned

Figure 3: (A) Layout of primary and infill wells for the pad and (B) production data for Well 1

Figure 3B shows the production data from Well 1, a top performer in the region Two key observations were made by closely

inspecting the production data from Wells 1 and 2 First, we observed significantly different productivity between Wells 1 and

2, despite the two wells being in close proximity to each other Normalizing the initial production by lateral length (IP/lateral

length) showed that Well 1 had twice the productivity of Well 2, despite more sand being pumped into the latter Similar

observations have also been made in the past for shale gas wells where it has been difficult to discern the role of geology and

completion practices to substantiate the performances of the wells Second, we observed well-to-well connectivity induced by

nearby fracturing operations In Figure 3B, several spikes in the production rates of Well 1 were observed (some indicated by

arrows) We were able to associate most of these spikes in gas rate with a fracturing event taking place in the close vicinity of

the pad These observations suggest well-to-well connectivity during a fracturing operation when the reservoir is dilated with

millions of gallons of fracturing fluid However, whether these reservoir connections persist long after the flowback of fluids is

still unknown We will revisit some of these observations in light of results obtained from modeling and analysis of the pad

Fracture Modeling

We first sought to take advantage of the available fracture treatment and pumping pressure data to constrain fracture length,

height, and the number of fractures per stage With regards to completion and fracture design in a horizontal well, several

perforation clusters (~3-8) are typically placed along one fracture stage to generate multiple fractures It is unlikely that

fractures propagate from every perforation cluster in the plug-and-perf approach for fracturing shales A recent study by

Schlumberger on more than 100 horizontal shale gas wells concluded that 30-40% of perforations do not contribute to the flow

(Miller et al., 2011) However, an estimate of the number of fractures propagating per stage is important to reduce uncertainty

in fracture character and to make reasonable predictions This is accomplished by calculating perforation friction from fracturing treatment pressures and determining the number of perforation clusters taking fluid The perforation friction as a

function of number of open perforations (McClain, 1963) can be calculated by:

) 5187 1 exp(

459 0

2369

2

p p perf

D C

C D n

q p





(1)

where pperf (psi) is the total perforation friction, q (bpm) is the total flow rate,  (ppg) is the fluid density, n is the number of open perforations, D p (in.) is the perforation diameter, and C is the discharge coefficient For wells that were investigated,

perforation friction was estimated to be 400-700 psi Based on the Equation (1), two to three propagating fractures were assumed for each stage

Figure 4: (A) Wattenbarger diagnostic plot to identify dominant flow regimes in Well 1 (B) Flowing material balance to

calculate volume of the depleted reservoir and (C) fracture models to calculate height of propped fractures When combined, these analyses provide an estimate of the drainage area of Well 1 (D) The red and green dotted boxes correspond to the best and the conservative estimate of the drainage area, respectively

Fracture modeling was also conducted to estimate fracture height (Figure 4C) Mechanical properties (Young’s Modulus, Poisson’s ratio, fracture toughness, and critical stress) of shales were derived from sonic logs and correlations using conventional analysis Mechanical properties along with wellbore and treatment designs were added to a fracture simulator to estimate fracture heights and lengths Note that these simulations are based on a pseudo-3D model with inherent assumptions

of elasticity, symmetry, no natural fractures, bi-wing fractures, and layer homogeneity in lateral directions For the given mechanical properties and treatment size we calculated a fracture height of ~150 ft and a length of ~400 ft as a reasonable estimate of fracture dimensions

Reservoir Modeling

To further constrain the reservoir and fracture characteristics, we employed advanced rate transient analysis developed

recently for unconventional gas resources, e.g Wattenbarger diagnostic plot (Wattenbarger et al., 1998) Figure 4 shows the

step-by-step methodology to estimate the drainage area of Well 1 First, a diagnostic Wattenbarger plot was made to identify

the dominant flow regimes experienced by Well 1 As shown in Figure 4A, a half slope signature was observed for an initial

linear or transient flow (also confirmed by a square root time plot) followed by a slope of unity, indicating possible boundary

effects As suggested by others (Anderson et al., 2010; Song et al., 2011; Houze et al., 2011) and in the absence of nearby

wells and known geological features, we interpreted the observation of boundary effects as interference between fractures on

the same horizontal lateral This evidence for fracture-to-fracture interference is independent of the fracture character –

bi-wing or complex fracture network Similar observations of fracture-to-fracture interference have also been reported for other

shale gas wells (Warpinski et al., 2008) Collectively these observations suggested that although we would anticipate the

transient linear flow to last for a dominat part of a well’s life due to ultra low permeabilities, production data suggested an

early transition to a boundary dominated flow depending on fracture character Next, we performed a flowing material balance

to estimate the stimulated rock volume (SRV) assuming minimum contribution of gas from the unstimulated rock (Anderson

et al., 2010) This stimulated rock volume along with the estimate of fracture height from fracture model provided an estimate

for the drainage area of Well 1 of 130 acres It is important to note that the methodology to calculate this drainage area did not

involve making any assumptions about the permeability, a parameter that has a high degree of uncertainty

The estimated drainage area of 130 acres for Well 1 based on production, reservoir properties, and fracture height is shown in

Figure 4D by the red dotted box The green dotted box shows a conservative estimate of the drainage area (65 acres) based on

a fracture height extending through the entire pay zone With these calculations and including uncertainties, we estimated the

drainage area of Well 1 to be between 65-130 acres We associated this unusually high number for drainage area (as compared

to drainage areas typically used for shale gas wells) for Well 1 due to its extraordinary production performance Based on this

result, the already-drilled infill wells, Wells 3 and 4, have a very high likelihood of laying within the drainage area of Well 1,

making it very likely that these wells would communicate during fracturing operations (Figure 4D)

Figure 5: History matching of the Well 1 production data (A) and normalized pressure derivative (B) to estimate permeability

and number of propagated fractures

To obtain an estimate for permeability, history matching of the production data was performed using a numerical model with

fine gridding to capture sharp pressure gradients near the fractures The history matching assumed bi-wing fractures uniformly

spaced over the lateral length The extent of the fractures or the fracture half length was already estimated from the drainage

area calculations discussed above The history matching variables were the permeability and the number of fractures The

history match of the production data of Well 1 is shown in Figure 5A Due to occasional spikes in the gas rate (resulting from

fracturing in neighboring wells) a perfect history match could not be obtained at those times For the same reason, many

history matches could be obtained that appeared very similar to the one shown in Figure 5A To reduce this non-uniqueness,

we plotted the derivative of the integral of normalized pressure (Figure 5B) of the history-matched data to uniquely identify

the flow regimes noted in Figure 4A This additional constraint significantly reduced the non-uniqueness, and the best history

match yielded a permeability of 400 nD and an average of 2.4 fractures per stage totaling to 12 fractures for 5 stages The

estimated number of fractures from the production data was consistent with 2-3 open perforations per stage as estimated from

pumping pressures For Well 2, diagnostic plots similar to Well 1 indicated the presence of linear flow Due to the short

production history of Well 2 relative to Well 1, diagnostic signatures for boundary effects were not observed In the presence

of linear or transient flow any history match of the production data yields non-unique results, i.e., several combinations of permeability and fracture half length will be obtained that match the production data However, the uncertainty is reduced

from the square root time plot, which demonstrates that,

2 / 1 ) (

K x

where, n f is the number of fractures, x f is the fracture half length and K m is the matrix permeability Since it is impossible to

determine n f and K m uniquely, we obtain one of the realizations by assuming permeability for Well 2 to be similar to that

n f to be 15 As we will see, Well 1 predominantly dictated the evolution of stresses due to its better performance and longer time of production as compared to Well 2, hence discounting for the higher degree of uncertainty around the parameters

estimated for Well 2

Geomechanical Modeling

Based on the fracture and reservoir analyses, we anticipated interference between primary and infill wells during fracturing of the infill wells Such interference can potentially lead to proppant or fracturing fluid production in primary wells which could severely impact their performance In order to gauge the magnitude of this interference and to develop effective strategies to minimize well interference we ran geomechanical models using a commercial finite element code to (1) predict the propagation of fractures in the infill wells and (2) evaluate strategies based on injection, shut-in and production in primary or infill wells to steer the propagation of fractures in the infill wells (Wells 3 and 6) away from the highly productive primary wells

It is important to note that we do not model the creation and propagation of hydraulic fractures Instead, all fractures are pre-defined in the mesh prior to their activation according to the production schedule from the wells The fractures are linear features that are loci of production or injection of pore fluid, but do not explicitly open Our finite element analyses for this case study were conducted in 2D plane strain, but we did run models to address the importance of 3D effects The fracture geometry was assumed to be planar bi-wing The stresses portrayed in the following figures are effective stresses with a Biot coefficient close to unity

Figure 6: Plan view layout for Well 1 with pore pressures (A, C, E) as a function of time and trajectories of maximum

horizontal compressive stress (B, D, F), with arrows added to emphasize reorientation of stresses versus time Note that the

pressures respectively

As shown in Figure 2, our finite element analyses followed an iterative process in which we simulated the completion and production schedule for an initial well in a pad (Well 1 in this case) and noted the orientations of the most compressive horizontal principal stresses ( ) in the vicinity of the next well at the time it was to be fractured (Well 2) The fractures

originating from the newly activated Well 2 were oriented parallel to the most compressive stress field at this well assuming

that the fracture propagation direction in this 2D analysis is predominantly governed by maximum horizontal compressive

stresses It has been noted that the propagation of fractures is also controlled by pre-existing discontinuities or planes of

weaknesses (Olson et al., 2009), the net pressure used for fracturing and configuration and alignment of perforations (Olson et

al., 1995); however, we have ignored the impact of these parameters in this study The spacing between fractures on the lateral

as estimated from the fracture and reservoir models is large enough to ignore stress shadow effects (Bai and Pollard, 2000) In

the manner described above, the fracture orientations for each well were determined by the evolution of the stress field based

on production from all nearby wells that were active prior to the addition of the following well Fracture lengths, permeability

and the number of fractures used to construct geomechanical models were reasonably constrained by the fracture and reservoir

models described earlier

We created a geomechanical finite element model for the pad with the considerations described above The direction of in situ

principal maximum horizontal compressive stress is shown in Figure 6A In the model, we first simulated the evolution of

stresses due to production in Well 1 until Well 2 was fractured To set up the model, a permeability of 400 nD and 12 fractures

of 400 ft half length each aligned with the direction of maximum principal stress (almost transverse) were used for Well 1

Figure 6 shows the spatial and temporal evolution of stresses on Pad A Figure 6A and B shows the pore pressure distribution

and stress configuration, respectively, soon after Well 1 started producing We note that soon after production initiation in

Well 1 the high pore pressure gradients are confined near the fractures (consistent with the early timed linear flow exhibited by

Well 1 as seen in Figure 4A), and the stress orientation had not shifted appreciably from the initial state Figures 6C and D

shows the distribution of pore pressure and stresses right before Well 2 was fractured We observed that with production in

Well 1, the drainage area confining the pore pressure gradients had expanded but was still in the vicinity of the fractured rock

The maximum compressive stress orientation at this time had altered over an area that extended beyond Well 2 and the

magnitude (as noted by the red arrows) of this change in stress direction was also significant It is interesting to note that the

predicted fracture geometry for Well 2 was tilted fractures with the tilt varying along the wellbore as illustrated in Figure 6D

To predict the evolution of stresses after Well 2 was fractured, a new mesh was generated to include Well 2 in the model A

permeability of 400 nD and 15 fractures with 400 ft half length aligned according to the stress configuration illustrated in

Figure 6D were used to simulate the effect of production of both Wells 1 and 2 Figure 6E and F shows the impact of

production from both wells on pore pressure and stress distribution immediately prior to fracturing the infill wells

Figure 7: Predicted hydraulic fracture geometry based on the assumption of simple bi-wing planar fractures (A) Plan view

layout (as per Figure 6F) showing overall maximum compressive stress orientation Stress orientation (thin lines defining the

vector field) near the top of Well 1 (B) and Well 2 (C) showing the tendency for producers to protect fractures (Zhai and

Sharma, 2007, Singh et al., 2008) by orienting the stress parallel to the pre-existing fractures (D) The compressive stress in

the vicinity of infill Wells 4 and 5 runs parallel to their borehole paths, suggesting longitudinal fractures (E) Simple schematic

of the fracture orientation for assuming bi-wing planar fractures with the cracks from Well 1 intersecting infill 3 and the

fractures at Well 2 in close proximity to infill 6 PR and PW on the scale refer to reservoir and well bottom-hole pressures

respectively

Figure 7 shows the overlay of Figure 6E and F and zooms of regions to illustrate the orientation of maximum stresses Close

inspection of Figure 7D suggested that the orientation of maximum stress in a region between Well 1 and 2 had almost

reversed with respect to its original direction and was now almost longitudinal to the infill drilled wells Assuming that the

propagation of fractures was predominantly governed by existing stresses as mentioned earlier, we anticipated propagating longitudinal fractures in the infill wells (Well 4 and 5) A schematic of the expected fracture pattern, based on the previously discussed assumptions, is shown in Figure 7E In summary, geomechanical simulations predict stresses which suggest propagation of tilted fractures in Well 2 and longitudinal fractures for Wells 4 and 5, fracture geometries that are otherwise not obvious In light of this predicted fracture pattern we revisit the question regarding the differences in the performance of wells closely spaced as noted earlier Potential reasons for the lower performance of Well 2 as compared to Well 1 despite their close proximity could be (1) the difference in the fracture character (transverse vs tilted fractures) as predicted by our models and (2) the large skin damage observed for Well 2 as compared to Well 1 as noted in the y-intercept of the square-root time

plot (Anderson et al., 2010) Other potential reasons include geological complexity and completion differences which are not

discussed in this paper

Prior studies that have reported stress reorientation in fractured horizontal wells either in the context of refracturing (Roussel et

al., 2009) or stress shadow effects (Soliman et al., 2010) have primarily focused on stress effects very near to the fractures

The case study presented in this paper aimed at investigating far field impact of depletion-driven stress reorientation and its implication in understanding well interference and optimizing resource developments Figure 8 illustrates the impact of depletion-driven stress reorientation at two different length scales for Well 1: effects near the fractures as vastly studied and reported in the past and far field effects at distances of the order of infill well spacings After one year of production in Well 1, the stress field between the individual fractures had remained parallel to the initial most compressive horizontal stress component, essentially transverse to the path of Well 1 However, very near to the fractures themselves the stress was reoriented and almost orthogonal to the fracture orientation (Figure 8A and B) Previous work (El-Rabaa, 1989; Elbel and

Mack, 1993; Berchenko and Detournay, 1997; Seibrits et al., 1998; Roussel and Sharma, 2009) has shown that this orientation

is to be expected, and that the extent of the re-orientation zone around the individual fractures is a function of time This time-dependent stress re-orientation is essentially a poroelastic phenomenon, but that inclusion of the mechanical effects of fracture opening adds to the maximum spatial extent of stress re-orientation (Roussel and Sharma, 2010) They show that this expansion and contraction of the reorientation zone creates the prospect of an optimum time for refracturing Within this study,

we also note that after a year of production in Well 1 the stresses far from it (at Well 2 in Figures 8A and C) have also dramatically changed relative to the initial stress orientation At Well 2 stresses are both parallel to the borehole path (lower half of the well in Figure 6C) as well as transverse to the path (upper section of the well in Figure 6C)

Figure 8: (A) Plan view showing stress orientations [running left to right: Well 1 (with transverse fractures), infills 4 and 5,

and Well 2] (B) Detail of the maximum compressive stress field near the transverse fractures of Well 1 showing reorientation

of stresses very near to the fractures (C) Far-field stress field shows the reorientation of stress along the borehole path of Well

2 PR and PW on the scale refer to reservoir and well bottom-hole pressures respectively

A 3D finite element model of a single well was developed to verify the assumption of 2D plane strain in the FEA models used

in the integrated modeling approach Figure 9 shows the 3D finite element model for Well 1 Pore pressures were prescribed

as a function of time and the reservoir depletion history, perforation spacing and fracture length are the same as that used in the 2D modeling Figure 10 shows a comparison between the stress orientations predicted using the 2D finite element and 3D finite element model with a fracture height of 200 ft at three different times The stress field and orientation predictions of 2D and 3D models are comparable at late times Although the drainage area is similar to the fractured area, both the 2D and 3D models show that the stress field is altered well beyond the fractured region Compared with the 3D model, 2D plain strain model shows a more severe stress reorientation and predicts that a larger zone is affected by depletion A parametric study was performed for perforation spacing, magnitude of stress contrast and fracture height using the 3D model The parametric study showed that higher stress contrast constrains the fracture reorientation Both the stress reorientation and stress shadowing

effects are highly dependent upon the perforation spacing with tighter perforation spacing leading to stronger stress shadowing

stress reorientation occurs increases with increasing fracture height Generally, 3D modeling provides a more accurate

prediction for the stress field and stress orientation surrounding a hydraulically fractured well, particularly for fractures with

confined height However, in this case a 2D model can be used to produce comparable results to the 3D at production times

of interest and can provide a good estimate to stress reorientation with reasonable accuracy with minimal computational

expense

Figure 9 3D finite element model for of Well 1

Figure 10 Comparison between stress orientations predicted using 2D plain strain finite element model and a 3D finite

element models with fracture height of 30 m at three different times

Next, we sought to extend our observation of depletion-driven far field stress reorientation for a range of permeability and

stress anisotropy relevant to shale resources and develop quantitative trends as shown in Figure 11A and B We selected the

distance to the far field isotropic point from the well midpoint, L, as a measure of the extent of stress changes due to reservoir

depletion and explored the relationship between L and the reservoir permeability (Figure 11A) The normalized distance (L/x f)

increases as the permeability increases when comparing results at identical times Essentially this occurred because the effects

of pore pressure reduction in the field from production at the well are experienced over a greater distance when the

permeability is higher This is a poroelastic effect, with the stress change due to porous flow being proportional to the pressure

gradient in the reservoir That is, with a very low permeability, the significant pressure gradients are very close to the fractures

and the mechanical ‘pulling’ of material toward the sink is concentrated near the fractures For a higher permeability, the pore

pressure gradients are more distributed and the ‘pulling’ of the rock toward the sink occurs over a larger spatial extent The

isotropic point is at least twice the fracture half-length for the most unfavorable stress ratio and 400 nDpermeability