**3. Geomechanical model**

A geomechanical model includes a description of in-situ stresses and of rock mechanical and structural properties. The key components include three principal stresses (vertical stress (Sv), maximum horizontal stress (SHmax) and minimum horizontal stress (Shmin)), pore pressure (Pp) and rock mechanical properties, such as elastic properties, uniaxial compressive strength (UCS) and internal friction. The relative magnitude of the three principal stresses and the consequent orientation of the most likely slipping fault or fracture define the stress regime to be normal faulting (Sv>SHmax>Shmin), strike-slip faulting (SHmax>Sv>Shmin) or reverse faulting (SHmax>Shmin>Sv). The horizontal stresses are highest relative to the vertical stress in a reverse faulting regime and lowest relative to the vertical stress in a normal faulting regime. Hydraulic fractures are vertical and propagate in the direction of the greatest horizontal stress in a strikeslip or normal faulting regime. In a reverse faulting stress regime in which Sv is the minimum stress, hydrofractures are horizontal. These different stress regimes also have consequences for the pressure that is required to open a network of orthogonal hydrofractures by stimulation. In places where the horizontal stresses are low and nearly equal, a relatively small excess pressure above the least stress may be required to open orthogonal fractures. Where the horizontal stress difference is larger, a larger excess pressure is required to open orthogonal fractures. Where the least stress is only slightly less than the vertical stress, weak horizontal bed boundaries and mechanical properties contrasts between layers may allow opening during stimulation of horizontal bedding ("T-fractures").

**Figure 2.** Structural map showing the offset well locations

wells with disappointing results. One fault block (see Figure 2) was chosen as the target of a pilot study that included building a geomechanical model, optimizing hydraulic fracturing design, assessing the stability of faults near the target well, and (although it is not discussed here) analyzing wellbore stability for drilling horizontal wells. Three vertical wells were drilled. D2 and D3 are near the crest of the structure and D1 is ~ 2.5-3 km to the west. The main target is Cretaceous tight sandstone occurring at ~5300m to ~6000m depth. Reservoir rock is composed of fine sandstone and siltstones interlayered with thin shales. Average reservoir porosity is ~7% and average permeability is ~0.07 mD. The gross reservoir thickness is ~180-220m in this fault block. Wells D1 and D2 were completed by acidizing and gel fracturing;

**Figure 1.** Workflow for predicting the complex fracture network developed by stimulating fractured reservoirs using

fracturing design for Well D3 based on the geomechanical analysis and investigate whether it is better to conduct slickwater treatment in the D3 well to stimulate and create a complex

Comprehensive datasets were available for all three wells including drilling experiences, wireline logs, image data, mini-fracs and well tests. Laboratory tests were also conducted on

A geomechanical model includes a description of in-situ stresses and of rock mechanical and structural properties. The key components include three principal stresses (vertical stress (Sv), maximum horizontal stress (SHmax) and minimum horizontal stress (Shmin)), pore pressure (Pp) and rock mechanical properties, such as elastic properties, uniaxial compressive strength (UCS) and internal friction. The relative magnitude of the three principal stresses and the consequent orientation of the most likely slipping fault or fracture define the stress regime to be normal faulting (Sv>SHmax>Shmin), strike-slip faulting (SHmax>Sv>Shmin) or reverse faulting (SHmax>Shmin>Sv). The horizontal stresses are highest relative to the vertical stress in a reverse faulting regime and lowest relative to the vertical stress in a normal faulting regime. Hydraulic fractures are vertical and propagate in the direction of the greatest horizontal stress in a strike-

cores from well D2 to estimate the rock mechanical properties of reservoir rocks.

/d. The objective of this project was to optimize hydraulic

test production was ~15-27 ×104

1018 Effective and Sustainable Hydraulic Fracturing

low-viscosity fluid.

**3. Geomechanical model**

m3

fracture network or utilize conventional two-wing gel fracturing.

Except for the magnitude of SHmax, other components of the geomechanical model can be determined using borehole data by reviewing a few representative wells in the field. Vertical stress is calculated by integrating formation density, which is obtained from wireline logs. The magnitude of Sv across this fault block is in a similar range. Pore pressure was constrained, mainly by referencing direct measurement data and drilling experiences. This is due to the complex tectonic history. Conventional under-compaction approaches for pore pressure estimation may not apply in the study area. Evidence for this is the over-compacted density profile. In addition, due to the complex lithology changes the log response with depth may reflect lithology changes rather than pressure variation. Well test data from D1 and D2 showed that the reservoir pressure is ~88-90 MPa, an equivalent pressure gradient of ~1.6-1.7 SG, which is abnormally over-pressured.

Rock mechanical laboratory tests were conducted on cores from the sandstone reservoirs and the interlayered shales in the D2 well, and the results were used to constrain a log-calibrated range of UCS and other rock mechanical parameters. Figure 3 shows the match between logderived rock strength profiles and laboratory test results in D2. Dynamic Young's modulus was calculated from compressional and shear velocities and density and calibrated to static values using laboratory test results. The relationship between dynamic and static Poisson's Ratio was not obvious; the dynamic Poisson's Ratio computed from Vp/Vs matched reasonably well with the laboratory results, so it was used directly in the modeling. Young's Modulusbased empirical relationships were used to estimate the UCS for both sandstone and interlayered shales.

Minimum horizontal stress (Shmin) at depth can be directly estimated from extended leakoff tests (XLOT), leak-off tests (LOT) or mini-frac tests. No extended leak-off tests were conducted in the field. LOTs and leak-off points from two reliable LOTs were used to constrain the upper limit of Shmin (~2.09 SG EMW at ~4000 m TVD). One mini-frac test was conducted in the sandstone reservoir in D2, with the interpreted fracture closure pres‐ sure (closest estimation to Shmin) ~2.064 ppg EMW at ~5400 m TVD. Because LOTs are usually conducted in shaly formations while mini-frac tests are usually carried out in sandstone reservoirs, the LOTs and mini-frac tests are used to construct separate Shmin profiles in shales and sandstones, respectively using the effective stress ratio method (Shmin-Pp/Sv-Pp). The effective stress ratio from LOT is ~0.725 and from mini-frac test is ~0.48, which indicates there is a dramatic stress difference between sandstones and shales (stress contrast). The contrast between different lithology significantly influences hydraulic fracturing design. The relative lower stress in sandstones indicates that a hydraulic fracture should be easily created in the tight sandstone, however, the interlayered shales which have higher stress act as frac barriers and pinch points, thereby complicating fracture propagation and the final fracture geometry and conductivity.

The azimuth and magnitude of maximum horizontal stress (SHmax) can be constrained through the analysis of wellbore failures such as breakouts and tensile cracks observed on wellbore images or multi-arm caliper data. Wellbore failure analysis allows constraining of the orien‐ tation and magnitude of the SHmax because stress-induced wellbore failures occur due to the stress concentration acting around the wellbore once is drilled. The presence, orientation, and severity of failure are a function of the in-situ stress fields, wellbore orientation, wellbore and formation pressures and rock strength [12]. High-resolution electrical wireline image logs were available in all three study wells. Both breakouts and drilling-induced tensile fractures (DITFs) were observed in the reservoir sections in D2 and D3 wells. Only DITFs were observed in well D1, which could be due to the higher mud weights used during drilling and the poor quality of the image data in lower part of the reservoir.

faults are close to or at the stage of being critically stressed. This has important implica‐ tions for the stress state in the area and the likelihood of stimulating fractures by injec‐ tion. Breakouts usually develop at the orientation of Shmin and DITFs in the direction of SHmax in vertical and near-vertical wells. In the left plot of Figure 4, DITFs can also be observed in the same interval as the breakouts with an orientation that is ~90 degrees from the breakout directions, consistent with this expectation. DITFs are seen more often in sandstone than in shale. Based on wellbore breakouts and DITFs interpreted from the image data in D3, the azimuth of SHmax is inferred to be ~143° ±10 °. This is similar to the azimuth of SHmax inferred from wellbore failures observed in the other two wells. It is also

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**Figure 3.** Comparison of laboratory (black squares) and log derived rock mechanical properties in D2 well

The magnitude of SHmax is constrained by forward-modeling the stress conditions that are consistent with observations of wellbore failures observed on image logs, given the data on rock strength, pore pressure, minimum horizontal stress, vertical stress, and mud weight used to drill the well. Figure 5 is a crossplot of the magnitude of Shmin and the magni‐ tude of SHmax, which summarizes the results of SHmax modeling in D3. The magnitude of Sv (~2.49 SG) is indicated by the open circle. The modeling was conducted in both sand‐ stone and shale. The rectangles in different colors are the possible Shmin and SHmax ranges at every modeling depth. Modeling shows slightly different results for the SHmax and Shmin

consistent with the regional stress orientation from the World Stress Map [13].

Figure 4 shows examples of the breakouts seen in the D3 well. The example shows the typical appearance of breakouts observed on images. Here, the average apparent break‐ out width is ~30-40 degree. The breakouts mostly occur in shales and more breakouts are observed in the lower part of reservoir where the formations become more shaly. The orientation of breakouts is quite consistent with depth and across the block. However, small fluctuations of breakout orientation can be observed locally while intercepting small faults (an example can be seen in the right plot in Figure 4). This may indicate that some of these Optimizing Hydraulic Fracturing Treatment Integrating Geomechanical Analysis and Reservoir Simulation for… http://dx.doi.org/10.5772/56384 1021

range of UCS and other rock mechanical parameters. Figure 3 shows the match between logderived rock strength profiles and laboratory test results in D2. Dynamic Young's modulus was calculated from compressional and shear velocities and density and calibrated to static values using laboratory test results. The relationship between dynamic and static Poisson's Ratio was not obvious; the dynamic Poisson's Ratio computed from Vp/Vs matched reasonably well with the laboratory results, so it was used directly in the modeling. Young's Modulusbased empirical relationships were used to estimate the UCS for both sandstone and inter-

Minimum horizontal stress (Shmin) at depth can be directly estimated from extended leakoff tests (XLOT), leak-off tests (LOT) or mini-frac tests. No extended leak-off tests were conducted in the field. LOTs and leak-off points from two reliable LOTs were used to constrain the upper limit of Shmin (~2.09 SG EMW at ~4000 m TVD). One mini-frac test was conducted in the sandstone reservoir in D2, with the interpreted fracture closure pres‐ sure (closest estimation to Shmin) ~2.064 ppg EMW at ~5400 m TVD. Because LOTs are usually conducted in shaly formations while mini-frac tests are usually carried out in sandstone reservoirs, the LOTs and mini-frac tests are used to construct separate Shmin profiles in shales and sandstones, respectively using the effective stress ratio method (Shmin-Pp/Sv-Pp). The effective stress ratio from LOT is ~0.725 and from mini-frac test is ~0.48, which indicates there is a dramatic stress difference between sandstones and shales (stress contrast). The contrast between different lithology significantly influences hydraulic fracturing design. The relative lower stress in sandstones indicates that a hydraulic fracture should be easily created in the tight sandstone, however, the interlayered shales which have higher stress act as frac barriers and pinch points, thereby complicating fracture

The azimuth and magnitude of maximum horizontal stress (SHmax) can be constrained through the analysis of wellbore failures such as breakouts and tensile cracks observed on wellbore images or multi-arm caliper data. Wellbore failure analysis allows constraining of the orien‐ tation and magnitude of the SHmax because stress-induced wellbore failures occur due to the stress concentration acting around the wellbore once is drilled. The presence, orientation, and severity of failure are a function of the in-situ stress fields, wellbore orientation, wellbore and formation pressures and rock strength [12]. High-resolution electrical wireline image logs were available in all three study wells. Both breakouts and drilling-induced tensile fractures (DITFs) were observed in the reservoir sections in D2 and D3 wells. Only DITFs were observed in well D1, which could be due to the higher mud weights used during drilling and the poor quality

Figure 4 shows examples of the breakouts seen in the D3 well. The example shows the typical appearance of breakouts observed on images. Here, the average apparent break‐ out width is ~30-40 degree. The breakouts mostly occur in shales and more breakouts are observed in the lower part of reservoir where the formations become more shaly. The orientation of breakouts is quite consistent with depth and across the block. However, small fluctuations of breakout orientation can be observed locally while intercepting small faults (an example can be seen in the right plot in Figure 4). This may indicate that some of these

propagation and the final fracture geometry and conductivity.

of the image data in lower part of the reservoir.

layered shales.

1020 Effective and Sustainable Hydraulic Fracturing

**Figure 3.** Comparison of laboratory (black squares) and log derived rock mechanical properties in D2 well

faults are close to or at the stage of being critically stressed. This has important implica‐ tions for the stress state in the area and the likelihood of stimulating fractures by injec‐ tion. Breakouts usually develop at the orientation of Shmin and DITFs in the direction of SHmax in vertical and near-vertical wells. In the left plot of Figure 4, DITFs can also be observed in the same interval as the breakouts with an orientation that is ~90 degrees from the breakout directions, consistent with this expectation. DITFs are seen more often in sandstone than in shale. Based on wellbore breakouts and DITFs interpreted from the image data in D3, the azimuth of SHmax is inferred to be ~143° ±10 °. This is similar to the azimuth of SHmax inferred from wellbore failures observed in the other two wells. It is also consistent with the regional stress orientation from the World Stress Map [13].

The magnitude of SHmax is constrained by forward-modeling the stress conditions that are consistent with observations of wellbore failures observed on image logs, given the data on rock strength, pore pressure, minimum horizontal stress, vertical stress, and mud weight used to drill the well. Figure 5 is a crossplot of the magnitude of Shmin and the magni‐ tude of SHmax, which summarizes the results of SHmax modeling in D3. The magnitude of Sv (~2.49 SG) is indicated by the open circle. The modeling was conducted in both sand‐ stone and shale. The rectangles in different colors are the possible Shmin and SHmax ranges at every modeling depth. Modeling shows slightly different results for the SHmax and Shmin

**Figure 4.** Drilling induced wellbore failures (breakouts & tensile fractures) observed on electrical image in D3 well.

 magnitudes in the different lithologies. However, both results are consistent with the magnitudes of Shmin inferred from LOTs and mini-fracs. Figure 5 shows that the magni‐ tude of maximum horizontal stress is higher than the vertical stress in both cases, and higher in the shale than in the sand. Thus, the study area is in a strike-slip faulting stress regime (Shmin < Sv < SHmax). The difference between the magnitudes of SHmax and Shmin is ~0.8 SG in the reservoir section, suggesting high horizontal stress anisotropy. In such a condition, it is unlikely to open the natural fractures by tensile mode. However, the natural fractures might dilate in shear mode depending on their orientations and stress condi‐ tions. The final geomechanical model was verified by matching the predicted wellbore failure in these wells with that observed from image data and drilling experiences.

**Figure 5.** Stress modeling results in well D3. The range of horizontal stress magnitudes are consistent with the occur‐

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Natural fractures were interpreted and classified using high-resolution electrical images in all three wells. Based on the appearance on image data, the natural fractures are classified as

**•** Drilling Enhanced: discontinuous and fracture traces are 180 degrees apart and in the

rence of wellbore failures (breakouts and DITFs) observed on wellbore images.

**•** Conductive: dark highly dipping planes on image logs

**•** Resistive: white dipping planes on image log

**•** Critically Stressed: related to local failure rotation

**•** Fault: features discontinued across the dipping planes

below:

direction in tension

#### **4. Natural fractures characterization and stimulation modeling**

Natural fractures have been observed on cores and image logs in the study area. The fluid losses during drilling not only suggest the existence of natural fractures but also that some at least of these fractures are permeable in-situ. Based on the core photos shown in Figure 6, open high-angle tectonic fractures can be seen on cores from D2 and D3 wells near the crest of the structure. A fracture network consisting of a group of fractures with different orientations can be seen on the cores from the D1 well, and these fractures appear to have less apertures than high-angle fractures observed in D2 and D3.

**Figure 5.** Stress modeling results in well D3. The range of horizontal stress magnitudes are consistent with the occur‐ rence of wellbore failures (breakouts and DITFs) observed on wellbore images.

Natural fractures were interpreted and classified using high-resolution electrical images in all three wells. Based on the appearance on image data, the natural fractures are classified as below:


 magnitudes in the different lithologies. However, both results are consistent with the magnitudes of Shmin inferred from LOTs and mini-fracs. Figure 5 shows that the magni‐ tude of maximum horizontal stress is higher than the vertical stress in both cases, and higher in the shale than in the sand. Thus, the study area is in a strike-slip faulting stress regime (Shmin < Sv < SHmax). The difference between the magnitudes of SHmax and Shmin is ~0.8 SG in the reservoir section, suggesting high horizontal stress anisotropy. In such a condition, it is unlikely to open the natural fractures by tensile mode. However, the natural fractures might dilate in shear mode depending on their orientations and stress condi‐ tions. The final geomechanical model was verified by matching the predicted wellbore failure in these wells with that observed from image data and drilling experiences.

**Figure 4.** Drilling induced wellbore failures (breakouts & tensile fractures) observed on electrical image in D3 well.

**4. Natural fractures characterization and stimulation modeling**

high-angle fractures observed in D2 and D3.

1022 Effective and Sustainable Hydraulic Fracturing

Natural fractures have been observed on cores and image logs in the study area. The fluid losses during drilling not only suggest the existence of natural fractures but also that some at least of these fractures are permeable in-situ. Based on the core photos shown in Figure 6, open high-angle tectonic fractures can be seen on cores from D2 and D3 wells near the crest of the structure. A fracture network consisting of a group of fractures with different orientations can be seen on the cores from the D1 well, and these fractures appear to have less apertures than


**Figure 6.** Core photos showing the natural fractures observed in three offset wells

Figure 7 shows a few examples of natural fractures observed on the electrical images. The plot on the left shows some examples of high-angle and low-angle conductive fractures that appear to be continuous dark lines on the images. Flexible sinusoids can be fit to the fracture traces and fracture orientation can be determined. The plot on the right shows an example of drilling enhanced natural fractures for which the fracture trace is discontinuous. The fact that parts of these fractures can be detected on the electrical image is due to fluid penetration into the fracture at the orientation around where the rock at the borehole wall is in tension during drilling. The classification of the natural fractures indicates the relative strength of the fractures. For example, the resistive fractures are closed and mineralized. Active faults or critically stressed natural fractures might be open and conductive, even under the original conditions. During stimulation, these fractures are the most easily stimulated. However, it is important to note that the classification of natural fractures is purely based on their appearance on the electrical images, and cannot be used directly to quantify permeability or other flow properties.

**Figure 7.** Examples of natural fractures observed on electrical image in D1 and D3 wells.

Effective stresses in the earth are always compressive, and natural processes tend to "heal" fractures through vein filling and other processes. Therefore, the intrinsic fracture aperture of most fractures is likely to be very small or even zero (cases where dissolution creates voids that prevent full closure are a notable exception). Thus, it is increasingly recognized that active processes are necessary to maintain fracture permeability. One such process is periodic slip along fractures that are critically stressed (i.e., those that are at or near the limiting ratio of shear to normal stress to slip). This process, and the influence of effective normal stresses on fracture aperture, can be modeled using a simple equation that describes the variation in aperture as a function of normal stress for a pure Mode I fracture. The same equation with different parameters can also be used to model the same fracture after slip has occurred [9-11].

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*<sup>a</sup>* <sup>=</sup> *<sup>A</sup>* <sup>∙</sup> *<sup>a</sup>*<sup>0</sup> (1 + 9*σ*'

minor amounts of rubble at the fracture face.

Equation 1 is one example that describes aperture in terms of an initial aperture (*A*∙*a*0) and an effective normal stress at which the aperture is only 10% as large (B). A and B both increase due to slip, resulting in a larger "unstressed" aperture and a stiffer fracture caused by "selfpropping" due to generation during slip of a mismatch in the fracture faces and/or creation of

The contribution of fractures to the relative productivity of a well of any orientation can be computed by summing the contributions of all fractures, weighted by the product of their relative transmissivity (which is a function of aperture) and the likelihood of the well inter‐

*<sup>n</sup>* / *<sup>B</sup>*) (1)

Figure 8 shows the fractures orientations on a crossplot of the strike and dip angles of all fractures observed in the three wells. The natural fractures observed can be divided into three groups. The first group is low-angle fractures (dip<20 °), which could be related to beddings. The second group is the major fractures seen in this block that have intermediate dip angles (~25-55°) and strike at an azimuth of ~155°N. The third group consists of fractures with strikes of ~355°N and ~100°N and dip angles ~ 35°-65° and 25°-35°, respectively. Because of their wide range of orientations and cross-cutting relationship, these three groups of fractures could be stimulated to form a well-connected grid with a major fracture azimuth (~155°N) aligned with the direction of maximum horizontal stress (~143°N). This direction is nearly perpendicular to the faults, defining the shape of fault block (see Figure 2). Because the structural trends and the stresses are aligned, it enabled us to create a reservoir model with a grid that is consistent with both.

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**Figure 7.** Examples of natural fractures observed on electrical image in D1 and D3 wells.

D1 D3 D2

Figure 7 shows a few examples of natural fractures observed on the electrical images. The plot on the left shows some examples of high-angle and low-angle conductive fractures that appear to be continuous dark lines on the images. Flexible sinusoids can be fit to the fracture traces and fracture orientation can be determined. The plot on the right shows an example of drilling enhanced natural fractures for which the fracture trace is discontinuous. The fact that parts of these fractures can be detected on the electrical image is due to fluid penetration into the fracture at the orientation around where the rock at the borehole wall is in tension during drilling. The classification of the natural fractures indicates the relative strength of the fractures. For example, the resistive fractures are closed and mineralized. Active faults or critically stressed natural fractures might be open and conductive, even under the original conditions. During stimulation, these fractures are the most easily stimulated. However, it is important to note that the classification of natural fractures is purely based on their appearance on the electrical images, and cannot be used directly to quantify permeability or other flow

Figure 8 shows the fractures orientations on a crossplot of the strike and dip angles of all fractures observed in the three wells. The natural fractures observed can be divided into three groups. The first group is low-angle fractures (dip<20 °), which could be related to beddings. The second group is the major fractures seen in this block that have intermediate dip angles (~25-55°) and strike at an azimuth of ~155°N. The third group consists of fractures with strikes of ~355°N and ~100°N and dip angles ~ 35°-65° and 25°-35°, respectively. Because of their wide range of orientations and cross-cutting relationship, these three groups of fractures could be stimulated to form a well-connected grid with a major fracture azimuth (~155°N) aligned with the direction of maximum horizontal stress (~143°N). This direction is nearly perpendicular to the faults, defining the shape of fault block (see Figure 2). Because the structural trends and the stresses are aligned, it enabled us to create a reservoir model with a grid that is consistent

**Figure 6.** Core photos showing the natural fractures observed in three offset wells

1024 Effective and Sustainable Hydraulic Fracturing

properties.

with both.

Effective stresses in the earth are always compressive, and natural processes tend to "heal" fractures through vein filling and other processes. Therefore, the intrinsic fracture aperture of most fractures is likely to be very small or even zero (cases where dissolution creates voids that prevent full closure are a notable exception). Thus, it is increasingly recognized that active processes are necessary to maintain fracture permeability. One such process is periodic slip along fractures that are critically stressed (i.e., those that are at or near the limiting ratio of shear to normal stress to slip). This process, and the influence of effective normal stresses on fracture aperture, can be modeled using a simple equation that describes the variation in aperture as a function of normal stress for a pure Mode I fracture. The same equation with different parameters can also be used to model the same fracture after slip has occurred [9-11].

$$a = \frac{A \bullet a\_0}{\left(1 + 9\sigma\right)\_n / \left(B\right)\_0} \tag{1}$$

Equation 1 is one example that describes aperture in terms of an initial aperture (*A*∙*a*0) and an effective normal stress at which the aperture is only 10% as large (B). A and B both increase due to slip, resulting in a larger "unstressed" aperture and a stiffer fracture caused by "selfpropping" due to generation during slip of a mismatch in the fracture faces and/or creation of minor amounts of rubble at the fracture face.

The contribution of fractures to the relative productivity of a well of any orientation can be computed by summing the contributions of all fractures, weighted by the product of their relative transmissivity (which is a function of aperture) and the likelihood of the well inter‐

**Figure 8.** Cross-plot between the strike and dip angles of all the fractures observed in three offset wells.

secting the fracture (which is a function of the difference between the fracture and the well orientation). This relative productivity can be written as [10]

$$P\_{\text{well}} = \sum\_{\text{faces}} \left\{ \max \left( \left| \stackrel{\Lambda}{w} \bullet \stackrel{\Lambda}{n\_i} \right|, \, a \right) \times P\_i \right\} \tag{2}$$

Figure 9 shows relative productivity for wells of all orientations based on the fractures observed in all three wells. Natural fractures are shown as poles to the fracture surfaces (black dots). Different apertures and strengths were assumed for the different types of fractures based on their classifications described above (Table 1). The plot on the left shows the relative productivity under pre-stimulation conditions, while the plot on the right shows the relative productivity calculated using equation 2 after the fractures were stimulated with a pressure 20 MPa above the original reservoir pressure. It can be seen that the maximum productivity increases by a factor of 5 if all fractures see the same 20-MPa pressure increase, which is obviously not the case during real stimulation. Superimposed on Figure 9 are the computed optimal orientations of wells based on the fracture and stress analysis (green circles). If none of the fractures is critically stressed, then the best orientation to drill a well is perpendicular to the largest population of natural fractures. If some fractures have enhanced permeability because they are critically stressed, the optimal orientation shifts in the direction of the greatest concentration of critically stressed fractures. Figure 9 shows there are some fractures already near or being critically stressed, even under ambient condition (left plot), and the maximum productivity is achieved by drilling highly deviated wells with ~20 °N hole azimuth. The optimum wellbore orientation after ~ 20-MPa stimulation is nearly horizontal and in the

Optimizing Hydraulic Fracturing Treatment Integrating Geomechanical Analysis and Reservoir Simulation for…

direction of ~228 °N.

**Fracture cohesion (MPa)**

**Sliding Friction** *a***<sup>0</sup>**

**Table 1.** Model parameters to calculate relative productivities for different types of natural fractures

Conductive 5 0.6 10 0.18 0.18 10 100 Resistive 5 0.6 10 0.1 0.18 1 100 Faults 0 0.6 30 0.18 0.18 100 100 Drilling enhanced 0 0.6 10 0.1 0.18 10 100 Critically Stressed 1 0.2 10 0.1 0.2 10 100

Figure 10 shows the general effect of reservoir flow properties changes due to the natural fracture stimulation for studied fault block. Again, all the fractures interpreted from image logs in the three wells are used for modeling. Cross-plots between relative productivity (flow rate/pressure) vs. reservoir pressure are shown for three different cases: under original conditions, after 30-MPa and after 50-MPa stimulation. The blue curves show productivity changes during stimulation when the pressure is increasing, the green curves show the productivity changes during flowback and production. Modeling ends at ~20-MPa depletion. The relative productivity at ~20-MPa depletion increases five-fold after the 30-MPa stimulation (productivity increases from ~4 to ~20). There is no obvious improvement in the relative productivity of natural fractures for 50-MPa stimulation (bottom left) compared to 30-MPa stimulation. The bottom-right plot shows the number of stimulated natural fractures under different pressure conditions. It is clear that nearly all of the natural fractures are stimulated while the pressure increases to ~130 MPa (40-Ma stimulation), which explains why there is

**A B (MPa) Un-stimulated Stimulated Un-stimulated Stimulated**

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**Fracture classification**

where *w* ^ and *ni* ^ are unit vectors along the axis of the well and normal to the ith fracture, *a* is a number representing the likelihood of a well intersecting a fracture if it lies in the plane of the fracture, and *Pi* is the relative permeability of the fracture.

The fractures interpreted from image data are only those that intersect the logged wells that are a function of their orientations, and there is no information about the fracture distribution between the wells. To ensure the most meaningful representation of the fractures in the reservoir, the fractures interpreted from all three wells were combined and the distribution was corrected to account for the likelihood of each fracture intersecting the well at the point where it was observed. This combined fracture data set was then used to model the produc‐ tivities of wells in their natural condition and the change in productivity due to the shear-slip of natural fractures.

Figure 9 shows relative productivity for wells of all orientations based on the fractures observed in all three wells. Natural fractures are shown as poles to the fracture surfaces (black dots). Different apertures and strengths were assumed for the different types of fractures based on their classifications described above (Table 1). The plot on the left shows the relative productivity under pre-stimulation conditions, while the plot on the right shows the relative productivity calculated using equation 2 after the fractures were stimulated with a pressure 20 MPa above the original reservoir pressure. It can be seen that the maximum productivity increases by a factor of 5 if all fractures see the same 20-MPa pressure increase, which is obviously not the case during real stimulation. Superimposed on Figure 9 are the computed optimal orientations of wells based on the fracture and stress analysis (green circles). If none of the fractures is critically stressed, then the best orientation to drill a well is perpendicular to the largest population of natural fractures. If some fractures have enhanced permeability because they are critically stressed, the optimal orientation shifts in the direction of the greatest concentration of critically stressed fractures. Figure 9 shows there are some fractures already near or being critically stressed, even under ambient condition (left plot), and the maximum productivity is achieved by drilling highly deviated wells with ~20 °N hole azimuth. The optimum wellbore orientation after ~ 20-MPa stimulation is nearly horizontal and in the direction of ~228 °N.


**Table 1.** Model parameters to calculate relative productivities for different types of natural fractures

secting the fracture (which is a function of the difference between the fracture and the well

**Figure 8.** Cross-plot between the strike and dip angles of all the fractures observed in three offset wells.

^ <sup>∙</sup>*ni*

number representing the likelihood of a well intersecting a fracture if it lies in the plane of the

The fractures interpreted from image data are only those that intersect the logged wells that are a function of their orientations, and there is no information about the fracture distribution between the wells. To ensure the most meaningful representation of the fractures in the reservoir, the fractures interpreted from all three wells were combined and the distribution was corrected to account for the likelihood of each fracture intersecting the well at the point where it was observed. This combined fracture data set was then used to model the produc‐ tivities of wells in their natural condition and the change in productivity due to the shear-slip

^ |, *<sup>a</sup>*) <sup>×</sup>*Pi*

^ are unit vectors along the axis of the well and normal to the ith fracture, *a* is a

} (2)

orientation). This relative productivity can be written as [10]

where *w*

fracture, and *Pi*

of natural fractures.

^ and *ni*

1026 Effective and Sustainable Hydraulic Fracturing

*Pwell* =∑ *fracs* {max (|*w*

is the relative permeability of the fracture.

Figure 10 shows the general effect of reservoir flow properties changes due to the natural fracture stimulation for studied fault block. Again, all the fractures interpreted from image logs in the three wells are used for modeling. Cross-plots between relative productivity (flow rate/pressure) vs. reservoir pressure are shown for three different cases: under original conditions, after 30-MPa and after 50-MPa stimulation. The blue curves show productivity changes during stimulation when the pressure is increasing, the green curves show the productivity changes during flowback and production. Modeling ends at ~20-MPa depletion. The relative productivity at ~20-MPa depletion increases five-fold after the 30-MPa stimulation (productivity increases from ~4 to ~20). There is no obvious improvement in the relative productivity of natural fractures for 50-MPa stimulation (bottom left) compared to 30-MPa stimulation. The bottom-right plot shows the number of stimulated natural fractures under different pressure conditions. It is clear that nearly all of the natural fractures are stimulated while the pressure increases to ~130 MPa (40-Ma stimulation), which explains why there is

The above relative productivity modeling of natural fractures shows the conductivity of natural fractures increases significantly if the stimulation pressure is at or above the minimum horizontal stress. This is because many of the natural fractures are non-optimally oriented. Assuming a connected fracture network exists, the conductivity increase could be a factor of five for the stimulated fracture network while stimulation pressure is ~130MPa or higher

Optimizing Hydraulic Fracturing Treatment Integrating Geomechanical Analysis and Reservoir Simulation for…

http://dx.doi.org/10.5772/56384

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Fracture stimulation modeling showed that the shear slip of natural fractures could be effective in improving reservoir properties. Next, we need to reproduce the affected productive volume in the reservoir using the "shear stimulation" concept to enable more accurate production prediction. At the present no commercial simulator can fully model this process in 3D, although some research simulators have been developed. It was decided to use two different commercial models to simulate both fracture network stimulation created by low-viscosity frac fluid and the growth of the main hydraulic fracture. A commercial dual-porosity, dualpermeability simulator is used to simulate the flow property changes of natural fractures due to the shear slip. A commercial hydraulic fracturing design and evaluation simulator is used to model the geometry and conductivity of the principal hydraulic fracture filled with proppant. The modeling in two separate simulators is coupled by the fluid volume used for stimulation. The fluid volume leaked off in the shear-dilated natural fracture network was estimated in the dual-permeability, dual-porosity flow simulator. By adjusting the pressuredependent leak-off coefficient, the fluid volume leaked off in the hydraulic fracturing simu‐ lator was matched with the fluid volume leaked into natural fractures networks estimated by the flow simulator. The prediction of the stimulated reservoir volume is discussed in the rest

of this section and the hydraulic fracturing design will be discussed in next section.

To predict the extent and properties of the stimulated volume by a dual-permeability, dualporosity simulator, a finely gridded model (Model A) was created based on the original reservoir model. The main function of this model is to simulate the change in flow properties in every single frac stage during and immediately after injection. The model is initialized with average known reservoir characteristics such as matrix porosity and permeability, fracture permeability and initial pressure, characterized from core and log analysis. Although different cases have been tested in the study, only one of the most realistic cases will be discussed here: the average matrix porosity used in the initial model is ~7.4%, matrix permeability is 0.07 mD in all directions, and the initial fracture permeability is ~ 0.2 mD. The initial fracture permea‐ bility is set close to the lower bound of fracture permeability based on core and log analysis. The orientations of the principal flow directions were chosen to correspond to the principal directions of the fracture sets and of bedding, which also approximately corresponded to the

The relative magnitudes of the permeability enhancements in different directions were constrained by the geomechanical analysis. A set of permeability-pressure tables for different directions were then used to describe the hysteretic rock behavior that results from shear fracture activation. Although the fracture properties during stimulation can be estimated as

**5. Predicting the shape of the stimulated reservoir volume**

(assuming the pressure reaches all fractures).

principal stress directions.

**Figure 9.** Relative well productivity for wells of all orientations based on the fractures observed in all three wells. (a) Ambient condition. (b) After 20-MPa stimulation. Natural fractures are shown as poles to the fracture surfaces (black dots). Green circles are computed optimal orientations of wells with highest productivity from natural fractures based on the fracture and stress analysis.

little improvement with further stimulation. It is important to note that this result does not take into account the possibility of injecting proppant to maintain the conductivity of fractures which open at pressures above 40 MPa.

**Figure 10.** Reservoir flow properties changes with time due to natural fracture stimulation for studied fault block. The blue curves are showing the productivity changes when pressure increases during stimulation, the green curves are showing productivity changes during flowback and production. (a) no stimulation (b) 30-MPa stimulation (c) 50-MPa stimulation (d) number of stimulated (shear slip) natural fractures. Fracture properties: cohesion=0, sliding fric‐ tion=0.6.

The above relative productivity modeling of natural fractures shows the conductivity of natural fractures increases significantly if the stimulation pressure is at or above the minimum horizontal stress. This is because many of the natural fractures are non-optimally oriented. Assuming a connected fracture network exists, the conductivity increase could be a factor of five for the stimulated fracture network while stimulation pressure is ~130MPa or higher (assuming the pressure reaches all fractures).
