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A key unknown limiting assessment of risk posed by inducing anomalous seismicity during hydraulic fracturing is the potential maximum magnitude of an event. To provide insights into the variation in maximum magnitude that can be induced by a hydraulic fracturing stage, worst-case scenarios were simulated in 2D using coupled hydro-geomechanical models. The sensitivity of the magnitude to the hydro-geomechanical properties of the fault and matrix rock were quantitatively compared through parametric analysis. Our base model predicts a maximum event with moment magnitude (
*M _{w}*) 4.31 and

*M*values range from 3.97 to 4.56 for the series of simulations. The highest magnitude is predicted for the model with a longer fault and the lowest magnitude for the model with a smaller Young’s modulus. For our models, the magnitude is most sensitive to changes in the Young’s modulus and length of the fault and least sensitive to changes in the initial reservoir pressure (

_{w}*i.e.*pore pressure) and the Poisson’s ratio.

The potential risk to the environment and public health and safety resulting from anomalous seismicity induced by hydraulic fracturing has become an increasing concern since the first reported occurrence in 2011 from Blackpool, England [

In an attempt to better understand maximum magnitude, a parametric analysis was performed to quantify the sensitivity of the magnitude to variations in the hydro-geomechanical properties of the fault and matrix rock. In this study, the fluid injection from a hydraulic fracturing stage is simulated for a series of numerical models with a critically stressed fault within a fractured shale reservoir using the 2D discontinuum based distinct element model, UDEC [

In order to simulate the interaction between natural and hydraulic fractures in combination with fault reactivation during a hydraulic fracturing stage, a coupled hydro-geomechanical approach is necessary. The two-dimensional (2D) distinct element model, UDEC version 5.0 (UDEC5, first presented by [

In UDEC, Newton’s equations of motion are directly solved using explicit time-stepping. The 2D model space is discretized into mutually interacting blocks (i.e. discrete elements) to simulate a discontinuous system with deformable boundaries representing planes for possible failure (i.e. fractures/joints/bedding planes/faults). Both shear and normal displacements are allowed along the boundaries according to the Mohr-Coulomb slip model with residual strength. The blocks are deformable and subdivided into a mesh of finite difference elements controlled by the basic Mohr-Coulomb slip criterion. UDEC5 performs a coupled hydro-geomechanical analysis with fluid flow through the discontinuities, while the blocks are impermeable. The program enables quantification of shear slip and dilation along pre-specified failure planes caused by disturbance of the initial stress field resulting from fluid injection and the generation of hydraulic fractures. Therefore, the response of the modeled system to fluid injection includes the mechanical effects, due to the changing stress field, coupled with the flow effects, due to changes in fluid pressure.

In this study, the pore pressure build-up and diffusion along a fault, near the injection source, within jointed shale, were simulated and the resulting slip along the fault was interpreted as a seismic event. The moment magnitude (M_{w}), calculated from the magnitude and extent of the slip, was then quantitatively compared for a series of simulations. The input parameters that were investigated during the parametric analysis include: the injection duration and flow rate; the length of the fault and its distance from the injection source; the magnitudes of the maximum and minimum principal stresses and the pore pressure; and the Young’s modulus and Poisson’s ratio of the shale matrix. Each parameter was systematically varied from the average value in the base model to the maximum and minimum end-member values shown in

The input parameter values for our simulation were chosen to represent a possible worst-case scenario where the injected fluid is transported through the newly created hydraulic fractures and opened fracture network to a nearby, critically stressed fault. A 2D numerical model was built, 3 × 3 km in size, containing an orthogonal incipient fracture network, oriented to the principal stress directions, with a 50 m spacing and a fault oriented 30˚ from the maximum principal stress. The 2D model, which is shown in

For the base model, simulated with the average parameter values, a maximum principal stress of 30 MPa, a minimum principal stress of 20 MPa, and a pore pressure of 10 MPa were applied. The effective principal stresses (green circle) and the failure envelopes for the incipient fractures and the fault are plotted on a Mohr diagram in

Parameter | Fractures | Fault | Block |
---|---|---|---|

Friction angle (˚) | 30 | 20 | |

Residual Friction angle (˚) | 25 | ||

Permeability (md) | 1 | ||

Residual perm (md) | 0.1 | ||

Cohesion (MPa) | 1 | ||

Residual cohesion (MPa) | 0 | ||

Tensile strength (MPa) | 0.5 | ||

Residual tensile strength (MPa) | 0 | ||

Normal stiffness (MPa) | 1E+04 | ||

Shear stiffness (MPa) | 1E+03 | ||

Spacing (m) | 50 | ||

Length (m) | 1000 (500, 1500, 5000) | ||

Distance to injector (m) | 100 (50, 200, 300) | ||

Density (g/cc) | 2.5 | ||

Young’s modulus (GPa) | 30 (10, 50) | ||

Poisson’s ratio | 0.25 (0.20, 0.30) | ||

Pore pressure (MPa) | 10 (5, 15) | ||

Max principal stress (MPa) | 30 (25, 35) | ||

Min principal stress (MPa) | 20 (15, 25) | ||

Injection rate (m^{2}/sec) | 0.1 (0.05, 0.15) | ||

Injection time (min) | 50 (25, 75) |

The model is first constructed with the orthogonal fracture network and fault, then is compressed to achieve the internal principal stresses, following which fluid is injected. In the base model, fluid is injected from a source 100 m from the center of a 1 km long fault at a rate of 0.1 m^{2}/s for 50 minutes (note that flow rates are in area per time due to the 2D model). Following shut in, the models were simulated for a total of 200 minutes, in order to investigate the post-injection response. The average rock mechanical properties of the matrix blocks for the base model were modeled as 30 GPa for the Young’s modulus and 0.25 for the Poisson ratio. The parameters input for the base model are summarized in

The magnitude earthquake induced by the fluid injection was calculated for each model at 5-minute intervals during the injection period and 10-minute intervals after shut-in by assuming all the shear slip along the fault, since the start of injection, was accommodated instantaneously at that time. At each time interval, the length of the fault that slipped > 1 cm and the average of the slips along the patches of that fault length (average slip) were determined to calculate a moment magnitude, M_{w}, using:

M w = 2 3 log M 0 − 6 [

where M_{0}, the scalar seismic moment in Nm, is the product of the shear modulus of the host rock, µ, the area of the fault that slip, A, and the slip along the fault, s:

M 0 = μ A s [

The fault area was calculated assuming a circular fault with a diameter equal to the modeled rupture length, L:

A = π ( L 2 ) 2 .

The modeled slip and length of fault slip and the calculated M_{w} were compared for the series of simulations providing insights into the relative importance of the hydro-geomechanical parameters on the maximum possible magnitude earthquake induced by a hydraulic fracturing stage.

While faults within shales are often argued to be impermeable (ex. [

The main uncertainty in the modelling is the 2D simplification, which results in difficulties estimating a representative injection rate and fault plane area. In addition, the fluid flow in UDEC5 is restricted to the discontinuities between blocks and the reservoir is assumed to be fully water saturated with no gas, which also provides limitations to the modelling. Therefore, the goal of this study is not to provide absolute magnitudes, but a comparison of the change in magnitude with hydro-geomechanical parameters.

The simulation of a hydraulic fracturing stage near a critically-stressed fault for the base case model predicts an average of 3.90 cm of slip (solid curve in _{w} 3.59 event (_{w} 4.31 event. The length of fault rupture remains constant following shut-in, while the average slip, and hence the magnitude of event, steadily decrease as the increased pore pressures diffuse into the surrounding fracture network. At the end of the 200-minute simulation, the results predict 18.5 cm slip and a M_{w} 4.16 event.

The magnitude versus time plot for the base case is compared with the simulation results from the parametric analysis in

Varying the rock mechanics properties of the shale reservoir has very little impact on the amount of slip or the rupture length of the fault (

over slightly shorter fault lengths than stronger shales. The Young’s modulus; however, has a large impact on the shear modulus input into the calculation of the moment magnitude. The difference in the shear modulus results in the greatest difference in peak magnitude between end-member values for the parameters tested (_{w} 4.45 peak induced event (solid red curve in _{w} 3.98 peak event predicted by the model with a Young’s modulus of 10 MPa (dotted red curve in

Three models were simulated with fault lengths of 500, 1500, and 5000 m for comparison with the base model with a fault length of 1000 m. The model with the 500 m long fault predicts the largest slip (solid blue curve in _{w} 4.10 (dotted red curve in _{w} 4.56 (solid red curve in _{w} 4.46 (dashed red curve in

Increasing the distance from the injection source to the center of the fault from 100 m in the base model to 200 m and 300 m predicts smaller slips (red and green versus black solid curves in

green versus black dotted curves in _{w} 4.16 and 4.04 (solid and dashed blue curves in _{w} 4.27 than for the base model (dotted blue versus solid black curves in

The model with a 50 m distance between injector and fault is the only model in the study where the average slip, and hence magnitude, continues to increase post-injection. The greatest magnitude event predicted for the model with a 50 m distance is a M_{w} 4.30 event, 50 minutes after shut-in.

The fluid injection rate of 0.1 m^{2}/s over 50 minutes for the base model results in 300 m^{2} of injected fluid during the simulation. Increasing the amount of injected fluid to 450 m^{2}, by increasing the injection duration to 75 min, delays and increases the peak magnitude of an event from 4.31 to 4.41 (solid blue curve in ^{2}, by decreasing the injection duration to 25 min, results in an earlier, lower magnitude peak event of M_{w} 4.10 (dotted blue curve in ^{2} to 150 m^{2}, by changing the injection rate from 0.15 m^{2}/s to 0.05 m^{2}/s results in peak magnitudes of 4.45 (solid red curve in ^{2} of injected fluid (dotted, blue and light blue curves in

As a result of the initial critical stress state of the fault in the models, varying the effective principal stresses by 5 MPa has a lower impact on the predicted magnitude of induced event, in comparison to the other model parameters tested. The

results show that the peak magnitude is least sensitive to the pore pressure of all parameters tested (

on the magnitude of induced event.

Increasing the differential stress, by increasing the maximum principal stress to 35 MPa from 30 MPa in the base model, predicts a lower peak magnitude event of M_{w} 4.29 (solid blue curve in _{w} 4.35 (dotted blue curve in _{w} 4.36 (solid red curve in F

The models with critically stressed fractures resulting from the effective principal stresses (the model with a pore pressure of 15 MPa, the model with a minimum principal stress of 15 MPa, and the model with a maximum principal stress of 35 MPa) predict greater pore pressure diffusion following shut-in, resulting in a more gradual decrease in the slip (solid red curve in

A series of 2D hydro-geomechanical models, representing potential worst-case scenarios where fluid is injected by a hydraulic fracturing stage nearby a permeable, brittle, critically-stressed fault, were simulated and compared to provide insights into the sensitivity of the magnitude of seismicity induced by hydraulic fracturing. The sensitivity of the magnitude to fluid injection rate and duration, fault length and its distance to the injector, effective stress state, and shale geo-mechanics were quantitatively compared through a parametric analysis.

The base model for the parametric analysis, with fluid injected at a rate of 0.1 m^{2}/s for 50 min, 100 m from the centre of a 1 km long fault predicts a maximum event with M_{w} 4.31. A quantitative comparison of the simulation results show that the magnitude of earthquake induced by a hydraulic fracturing stage ranges from 3.97 to 4.56. The model with a longer fault of 1.5 km, predicts the greatest magnitude and the model with a smaller Young’s modulus (10 versus 30 MPa) predicts the lowest magnitude. The differences in magnitude predicted for end-member parameter values indicate that the Young’s modulus (difference of 0.48) and the length of the fault (difference of 0.47) have the greatest impact on the magnitude of the parameters tested. The tested parameter with the next greatest impact on the magnitude is the rate of injection (difference of 0.4) followed by the duration of injection (difference of 0.30) and then the distance from the fault to the injection source (difference 0.24). In comparison, the pore pressure (difference of 0.016), Poisson’s ratio (difference of 0.021), maximum principal stress (difference of 0.063), and minimum principal stress (difference of 0.052) have little impact on the magnitude of induced event.

Understanding the maximum possible magnitude of seismicity induced by hydraulic fracturing and the sensitivity of the magnitude to geologic structure, rock mechanical properties, and completions parameters will aid in developing protocols for reducing the probability of inducing felt events and mitigation procedures to prevent larger magnitude induced events, as well as help to understand the variations in the magnitude of induced seismicity between regions.

The authors declare no conflicts of interest regarding the publication of this paper.

Bustin, A.M.M. and Bustin, R.M. (2020) Maximum Magnitude of Seismicity Induced by a Hydraulic Fracturing Stage in a Shale Reservoir: Insights from Numerical Simulations. Engineering, 12, 516-533. https://doi.org/10.4236/eng.2020.127036