**5. History matching of field injection pressure — Coupled geomechanical injection models**

In coupled geomechanical simulation, because stresses are continuously computed, *Pfoc* in Equation (3) is updated at each time step and grid block in reservoir simulator by taking as an input effective stress from geomechanical part of the simulator. Therefore there is no need to modify stress data to correct for poroelastic effects. To run a fully coupled geomechanical simulation the original in-situ stress is used to calculate transmissibility and permeability multipliers, which are a function of effective stresses. Run times for coupled simulation are generally very large and consequently a detailed study for each parameter was not possible due to time constraints. The sensitivity study and calculations shown here are performed for well A. Only conclusions and end results are then applied to well B to get a history match.

Note that for fracture initiation (and propagation) minimum effective stress must be negative; in other words injection pressure should be higher than minimum horizontal total stress. Biot's constant of 1.0 was initially used for effective stress calculation, but it was found that fracture initiation could not be achieved because the poroelastic stress component caused by injection pressure was too high and the total stress increased above the injection pressure limit (set at 10,000 psia). The smaller the Biot's constant the slower is the increase in total stress and it is less difficult to fracture the rock. It was therefore concluded that Biot's constant should be significantly less than 1.0.

#### **5.1. Effects of limiting length of fracture propagation**

Few simulation cases are run using different values of permeability reduction factor and confining length of fracture propagation. For this purpose, it was assumed that rock behaves as a perfectly elastic material which does not exhibit hysteresis during loading and unloading. A base case here (Case-1) was therefore set up allowing unlimited fracture propagation in ydirection and modifying Biot's constant value in the geomechanical simulator to 0.65 (initial guess). Summary of history matching parameters are presented in Table 1. Simulation results for all these cases for well A and history matched case for Well B are presented in Figure 3 and 4 respectively.


**Table 1.** Parameters varied in coupled injection Cases 1 – 4 – Well A

Results of all uncoupled cases are not shown here except best matched case (see Figure 3 and 4) as history matching was not achieved. Only their effects are discussed here (detailed description of the results is provided in reference [2]). Results show that decreasing the *Rfa* factor pushes the injection pressure upward. Smaller reduction factor means smaller trans‐ missbility mutlipliers and hence larger pressure drop down in the fracture. However, fracture propagation confinement did not improve the rising trend of injection pressure in uncoupled

**5. History matching of field injection pressure — Coupled geomechanical**

In coupled geomechanical simulation, because stresses are continuously computed, *Pfoc* in Equation (3) is updated at each time step and grid block in reservoir simulator by taking as an input effective stress from geomechanical part of the simulator. Therefore there is no need to modify stress data to correct for poroelastic effects. To run a fully coupled geomechanical simulation the original in-situ stress is used to calculate transmissibility and permeability multipliers, which are a function of effective stresses. Run times for coupled simulation are generally very large and consequently a detailed study for each parameter was not possible due to time constraints. The sensitivity study and calculations shown here are performed for well A. Only conclusions and end results are then applied to well B to get a history match.

Note that for fracture initiation (and propagation) minimum effective stress must be negative; in other words injection pressure should be higher than minimum horizontal total stress. Biot's constant of 1.0 was initially used for effective stress calculation, but it was found that fracture initiation could not be achieved because the poroelastic stress component caused by injection pressure was too high and the total stress increased above the injection pressure limit (set at 10,000 psia). The smaller the Biot's constant the slower is the increase in total stress and it is less difficult to fracture the rock. It was therefore concluded that Biot's constant should be

Few simulation cases are run using different values of permeability reduction factor and confining length of fracture propagation. For this purpose, it was assumed that rock behaves as a perfectly elastic material which does not exhibit hysteresis during loading and unloading. A base case here (Case-1) was therefore set up allowing unlimited fracture propagation in ydirection and modifying Biot's constant value in the geomechanical simulator to 0.65 (initial guess). Summary of history matching parameters are presented in Table 1. Simulation results for all these cases for well A and history matched case for Well B are presented in Figure 3 and

simulation.

**injection models**

316 Effective and Sustainable Hydraulic Fracturing

significantly less than 1.0.

4 respectively.

**5.1. Effects of limiting length of fracture propagation**

**Figure 3.** Comparison of simulation results and field BHIP - Well A

The effect of fracture permeability reduction was discussed in detail in uncoupled simulation section; decreasing its value shifts pressure injection curve upward which can be observed in Figure 3. Although simulation results of Case – 4 of well A do not exactly match field injection pressure, it represents a reasonable history match. It is concluded that injection history match requires some mechanism to constrain fracture propagation at a late stage. This issue was not pursued further; however, the coupled cases show much improvement compared to the uncoupled simulations as shown in Figures 3 and 4.

injection pressure except at late time when the pressures are lower with higher S value (see Figure5). We observed similar difference in results for injection pressures when the exercise was repeated for well B. It is therefore concluded that effect of leak off on injection pressures in low permeability formations is not considerable, although it affects fracture length and the

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match with microseismic (MS) data.

**Figure 5.** Effects of Stress Factor (S) on BHIP - Well A

present section.

**6. Failure predictions — Tensile and shear failure**

The simulations of the injection process presented in this work showed that one must assume a substantial stress-dependent enhancement of permeability around the primary single plane fracture (SPF) to history match the injection pressures. Often it is postulated that the creation of this SRV is due to shear fracturing, i.e., creating shear failure. Coupled modeling provides us with the tool to investigate under what conditions shear fracturing occurs and what would be the extent of the SRV if it was caused purely by shear failure. This aspect is examined in the

**Figure 4.** Comparison of simulation results and field BHIP - Well B

#### *5.1.1. Discussion on the late time history matching (Well A)*

It is important to point out that history matching of field injection pressure after 190 minutes of injection for well A cannot be achieved through our simulation results (See Figure 3). It was observed in field treatment report (See Figure 1) that the injected proppant concentration was increased after 190 minutes to approximately three times of the overall average concentration. Our simulation study does not include coupling of fracture propagation simulation with proppant transport, modeling of fracture propagation based on downhole variable proppant concentration is not possible here and beyond the scope of this study. Fracture modeling in this work was performed based on total downhole amount of slurry injected. Late time history matching for well B is more acceptable.

#### **5.2. Effects of stress factor (***S***)**

Stress factor (S) defines shape of pressure/ effective stress dependent permeability curves and controls the permeability dependence on effective stress [1, 2]. The larger the value of S, the higher is the permeability dependence on stress. Permeability multipliers are applied in the whole reservoir except in fractured blocks. Increasing S value from 6 to 16 results in increase of permeability multipliers to several orders of magnitude but there is little difference in injection pressure except at late time when the pressures are lower with higher S value (see Figure5). We observed similar difference in results for injection pressures when the exercise was repeated for well B. It is therefore concluded that effect of leak off on injection pressures in low permeability formations is not considerable, although it affects fracture length and the match with microseismic (MS) data.

**Figure 5.** Effects of Stress Factor (S) on BHIP - Well A

*5.1.1. Discussion on the late time history matching (Well A)*

**Figure 4.** Comparison of simulation results and field BHIP - Well B

matching for well B is more acceptable.

**5.2. Effects of stress factor (***S***)**

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It is important to point out that history matching of field injection pressure after 190 minutes of injection for well A cannot be achieved through our simulation results (See Figure 3). It was observed in field treatment report (See Figure 1) that the injected proppant concentration was increased after 190 minutes to approximately three times of the overall average concentration. Our simulation study does not include coupling of fracture propagation simulation with proppant transport, modeling of fracture propagation based on downhole variable proppant concentration is not possible here and beyond the scope of this study. Fracture modeling in this work was performed based on total downhole amount of slurry injected. Late time history

Stress factor (S) defines shape of pressure/ effective stress dependent permeability curves and controls the permeability dependence on effective stress [1, 2]. The larger the value of S, the higher is the permeability dependence on stress. Permeability multipliers are applied in the whole reservoir except in fractured blocks. Increasing S value from 6 to 16 results in increase of permeability multipliers to several orders of magnitude but there is little difference in

### **6. Failure predictions — Tensile and shear failure**

The simulations of the injection process presented in this work showed that one must assume a substantial stress-dependent enhancement of permeability around the primary single plane fracture (SPF) to history match the injection pressures. Often it is postulated that the creation of this SRV is due to shear fracturing, i.e., creating shear failure. Coupled modeling provides us with the tool to investigate under what conditions shear fracturing occurs and what would be the extent of the SRV if it was caused purely by shear failure. This aspect is examined in the present section.

When tensile stress across a plane exceeds critical limit then tensile failure occurs. This critical limit is called the tensile strength or ultimate tensile strength (UTS). The tensile failure criterion is applied to determine the propagation of the main fracture (SPF) through grid blocks. In some rare instances, tensile failure can also occur in the reservoir around the SPF (e.g. due to thermal effects [11]).

When shear stresses along a plane in a specimen exceed shear strength of material, shear failure occurs. The shear strength of material / rock indirectly depends on the normal stress acting on the failure plane. There are different shear failure criterions available in literature such as Tresca, Mohr-Coulomb and Griffith. For this study Mohr-Coulomb criterion is used to predict failure mechanism during injection.

To investigate if tensile or shear failure will occur; time-history of pressure and stresses was extracted for specific grid blocks from a coupled simulation run. By plotting the Mohr circles in MATLAB® we can make failure prediction of these grid blocks in graphical form. For this purpose, the history matched case, i.e., Case – 4 of well A was used. All the fractures behave the same way and pressure propagation is also approximately the same for all fractures. Therefore only one fracture is selected for this analysis which is fracture # 4 (4th fracture from the line of symmetry) and conclusions drawn from this analysis will apply to all sets of fractures. Two grid blocks were selected and marked as shown in Figure 8, which represents cross section of the model in y-z plane of the fracture. The well is completed in x-direction and block 1 represents the perforation location.

#### **6.1. Base case — High cohesion**

The Mohr-Coulomb failure envelope was based on rock geomechanical data given in referen‐ ces [1, 2]. The base case used friction angle of 300 and Uniaxial compressive strength of 321 Mpa (intact rock). Mohr – Coulomb circle progression is presented in Figure 6 for well A, where Circles 1 - 5 are for block 1 and circles 6 - 10 for block 2. Similar envelope can be constructed from coupled simulations output for well B. In Figure 6 there is no shear failure during injection because Mohr's circles are much below the failure line. It is obvious that the dominant failure mechanism in these blocks is tensile because the SPF penetrated them. We also repeated the same exercise for all blocks/time steps and confirmed that no shear failure occurred.

#### **6.2. Case with low cohesion**

More realistic case was run by reducing the uniaxial compressive strength by 10 times to a base value while keeping other parameters such as friction angle, elastic modulus and Poisson's ratio the same as in the previous case. Mohr-Coulomb circles for this case are shown in Figure 7.

the fracture plane. It should be noted that our simulations were not carried out using elastoplastic modeling, but only linear elastic treatment, and therefore *SL* can exceed 1. The modeling is not rigorous past shear failure, but it still provides useful picture of the possible extent of


Effective Normal Stress (psi)


Mohr Coulomb Failure Envelope

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Effective Normal Stress (psi)

Mohr Coulomb Failure Envelope

Shear Stress (psi)

Shear Stress (psi)

Block1 - 45 mins Block1 - 60 mins Block1 - 100 mins Block1 - 140 mins Block1 - 237 mins Block2 - 45 mins Block2 - 60 mins Block2 - 100 mins Block2 - 140 mins Block2 - 237 mins

**Figure 6.** Mohr – Coulomb failure envelope for Co= 46570psi – Well A

**Figure 7.** Mohr – Coulomb failure envelope for Co= 4657psi – Well A

Block1 - 45 mins Block1 - 60 mins Block1 - 100 mins Block1 - 140 mins Block1 - 237 mins Block2 - 45 mins Block2 - 60 mins Block2 - 100 mins Block2 - 140 mins Block2 - 237 mins x 10<sup>4</sup>

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From above simulation runs (which required increase of matrix permeability during injection), and knowledge of presence of micro cracks and heterogeneities in tight sands [2] as recorded by microseismic, it is concluded that the high original value of uniaxial compressive strength (which does not allow any shear events) is unlikely. Reducing the C0 to account for weak planes

failure. In this case, failure is also predicted for planes adjacent to fracture plane.

Complete spatial map of the failure can be obtained by plotting "stress level" *SL*, a feature offered in GeoSim® (Geomechanical Simulator) which represents the ratio of the size of the Mohr circle at any point to the circle at critical state, i.e., when the circle touches the failure line. Stress level therefore ranges between 0 and 1. When *SL* < 1 there is no shear failure, and when shear failure is reached, *SL* remains theoretically at 1. Stress level for fracture # 4 after 237 minutes of injection (end of injection) is shown in Figure 8 for the y-z cross section through

**Figure 6.** Mohr – Coulomb failure envelope for Co= 46570psi – Well A

When tensile stress across a plane exceeds critical limit then tensile failure occurs. This critical limit is called the tensile strength or ultimate tensile strength (UTS). The tensile failure criterion is applied to determine the propagation of the main fracture (SPF) through grid blocks. In some rare instances, tensile failure can also occur in the reservoir around the SPF (e.g. due to thermal

When shear stresses along a plane in a specimen exceed shear strength of material, shear failure occurs. The shear strength of material / rock indirectly depends on the normal stress acting on the failure plane. There are different shear failure criterions available in literature such as Tresca, Mohr-Coulomb and Griffith. For this study Mohr-Coulomb criterion is used to predict

To investigate if tensile or shear failure will occur; time-history of pressure and stresses was extracted for specific grid blocks from a coupled simulation run. By plotting the Mohr circles in MATLAB® we can make failure prediction of these grid blocks in graphical form. For this purpose, the history matched case, i.e., Case – 4 of well A was used. All the fractures behave the same way and pressure propagation is also approximately the same for all fractures. Therefore only one fracture is selected for this analysis which is fracture # 4 (4th fracture from the line of symmetry) and conclusions drawn from this analysis will apply to all sets of fractures. Two grid blocks were selected and marked as shown in Figure 8, which represents cross section of the model in y-z plane of the fracture. The well is completed in x-direction and

The Mohr-Coulomb failure envelope was based on rock geomechanical data given in referen‐

Mpa (intact rock). Mohr – Coulomb circle progression is presented in Figure 6 for well A, where Circles 1 - 5 are for block 1 and circles 6 - 10 for block 2. Similar envelope can be constructed from coupled simulations output for well B. In Figure 6 there is no shear failure during injection because Mohr's circles are much below the failure line. It is obvious that the dominant failure mechanism in these blocks is tensile because the SPF penetrated them. We also repeated the

More realistic case was run by reducing the uniaxial compressive strength by 10 times to a base value while keeping other parameters such as friction angle, elastic modulus and Poisson's ratio the same as in the previous case. Mohr-Coulomb circles for this case are shown

Complete spatial map of the failure can be obtained by plotting "stress level" *SL*, a feature offered in GeoSim® (Geomechanical Simulator) which represents the ratio of the size of the Mohr circle at any point to the circle at critical state, i.e., when the circle touches the failure line. Stress level therefore ranges between 0 and 1. When *SL* < 1 there is no shear failure, and when shear failure is reached, *SL* remains theoretically at 1. Stress level for fracture # 4 after 237 minutes of injection (end of injection) is shown in Figure 8 for the y-z cross section through

same exercise for all blocks/time steps and confirmed that no shear failure occurred.

and Uniaxial compressive strength of 321

effects [11]).

failure mechanism during injection.

320 Effective and Sustainable Hydraulic Fracturing

block 1 represents the perforation location.

ces [1, 2]. The base case used friction angle of 300

**6.1. Base case — High cohesion**

**6.2. Case with low cohesion**

in Figure 7.

**Figure 7.** Mohr – Coulomb failure envelope for Co= 4657psi – Well A

the fracture plane. It should be noted that our simulations were not carried out using elastoplastic modeling, but only linear elastic treatment, and therefore *SL* can exceed 1. The modeling is not rigorous past shear failure, but it still provides useful picture of the possible extent of failure. In this case, failure is also predicted for planes adjacent to fracture plane.

From above simulation runs (which required increase of matrix permeability during injection), and knowledge of presence of micro cracks and heterogeneities in tight sands [2] as recorded by microseismic, it is concluded that the high original value of uniaxial compressive strength (which does not allow any shear events) is unlikely. Reducing the C0 to account for weak planes and natural fractures then will predict possibility of shear fracturing and shear-generated SRV creation. However, the SRV based on shear failure is still very narrow and therefore one has to conclude that the majority of the matrix permeability enhancement should be contributed to matrix and micro-fractures. These results are preliminary and further work should be done using finer gridding and elasto-plastic modeling.

**•** Preliminary work on the modeling of shear failure region (SRV) shows that no shear events are detected when a high value of uniaxial compressive strength (UCS) of the rock is assumed, representative of intact rock. A narrow shear region is predicted when the UCS

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This work demonstrates the need for coupled geomechanical modeling in injection to capture

is lowered to represent media with pre-existing fractures or planes of weakness.

poroelastic effects and stress alterations during stimulation.

**Nomenclature**

*E*= Elastic modulus, psi

*H <sup>f</sup>* = Fracture half height, ft

*L <sup>f</sup>* = Fracture half length, ft

*P <sup>f</sup>* = Fluid (fluid) pressure, psi

SPF = Single planer fracture

*Tr*= Transmissibility multiplier

*W <sup>f</sup>* = Fracture width, ft

UTS = Ultimate tensile strength, psi *W* = Grid block size in x-direction, ft

SRV = Stimulated reservoir volume, ft3

MS = Microseismic

*S*= Stress factor

*SL=* Stress level

*K <sup>f</sup>* = Fracture permeability, mD

*Km*= Matrix block permeability, mD

*Af* = Fracture cross sectional area, ft2

*Am*= Matrix block cross sectional area, ft2

BHIP = Bottomhole injection pressure, psi

*Co* =Uniaxial compressive strength (UCS), psi

*Rfa*= Permeability enhancement/reduction factor

*P foc*= Fracture opening or closing pressure, psi
