Research Article  Open Access
D. A. Angus, J. P. Verdon, "Using Microseismicity to Estimate Formation Permeability for Geological Storage of CO_{2}", International Scholarly Research Notices, vol. 2013, Article ID 160758, 7 pages, 2013. https://doi.org/10.1155/2013/160758
Using Microseismicity to Estimate Formation Permeability for Geological Storage of CO_{2}
Abstract
We investigate two approaches for estimating formation permeability based on microseismic data. The two approaches differ in terms of the mechanism that triggers the seismicity: porepressure triggering mechanism and the socalled seepageforce (or effective stress) triggering mechanism. Based on microseismic data from a hydraulic fracture experiment using water and supercritical CO_{2} injection, we estimate permeability using the two different approaches. The microseismic data comes from two hydraulic stimulation treatments that were performed on two formation intervals having similar geological, geomechanical, and in situ stress conditions, yet different injection fluid was used. Both approaches (porepressure triggering, and the seepageforce triggering) provide estimates of permeability within the same order of magnitude. However, the seepageforce mechanism (i.e., effective stress perturbation) provides more consistent estimates of permeability between the two different injection fluids. The results show that permeability estimates using microseismic monitoring have strong potential to constrain formation permeability limitations for largescale CO_{2} injection.
1. Introduction
Fracture stimulation has been applied for the past 60 years to enhance recovery from hydrocarbon reservoirs, with an estimated 70% of wells being fracture stimulated, and hence is a key factor in the economic exploitation of unconventional reserves, such as tightgas and shalegas reservoirs [1]. Over the past 20 years, microseismic monitoring has developed into one of the most effective methods of monitoring fracture stimulation and hence is routinely applied to monitor fracture stimulation programs.
The spatial and temporal variations in microseismicity can be used to monitor changes in the stress field and hence potentially be used to monitor perturbations in fluid pathways as well as topseal and wellbore integrity. Furthermore, microseismicity has been used also to characterise spatial and temporal variations within the reservoir and surrounding rock mass by monitoring changes in seismic attributes between the source and receiver (e.g., shearwave splitting analysis to characterise fractureinduced anisotropy [2–4]). Additional information can be gained by evaluating microseismic failure mechanisms to characterise the rock mass at the source and provide a measure of the strength, orientation, and type of elastic failure to potentially quantify damage (e.g., [5–7]).
Although microseismicity can provide fairly accurate temporal and spatial locations of brittle failure, how the measured microseismicity relates to the evolution of the induced pressure front and effective stress field as well as creation and enhancement of cracks and fractures is still not well constrained. Examination of the distribution of microseismic events can help characterize the flow and mechanical properties of the stimulated reservoir. In particular, by assuming that seismicity is triggered by the diffusion of porepressure from the injection point, Shapiro [8] has shown that the permeability of a formation can be estimated from the rate of increase in distance between injection well and event hypocenter distance through time. This spatiotemporal behaviour is commonly visualized on the socalled  plot, (where is injectionwelltoevent distance and is time). This method has shown potential for predicting apparent formation permeability and hydrocarbon production for various fracture stimulation case studies (e.g., [9]).
Although this porepressure diffusion approach has shown some promise in estimating reservoir permeability, there are some nonphysical aspects to the theory, such as weak porepressure perturbation triggering seismicity [10]. As an alternative to the porepressure diffusion approach, Rozhko [11] introduces the concept of seepageforce triggering to predict the  response of seismicity, which considers diffusion of effective stress perturbations as the driving force of microseismicity.
In this paper we compare both methods, predicting formation permeability by modelling observed  behaviour during hydraulic fracturing, where water and supercritical CO_{2} have been used as the injected fluids. By estimating permeability using microseismic monitoring, we hope to explore the potential of using microseismic monitoring to constrain formation permeability limitations for largescale CO_{2} injection sites.
2. Models Describing Spatiotemporal Evolution of Seismicity
2.1. PorePressure Triggering
The  porepressure triggering approach is based on the concept that the spatial and temporal evolution of microseismicity is hydraulically induced and characterised in terms of a low frequency porepressure relaxation mechanism described by Biot [12]. The key assumption for application of this approach to hydraulic fractureinduced microseismic data is that the tectonic stress in the subsurface is close to the critical stress needed for brittle failure (e.g., [13]). As such, increasing fluid pressure (i.e., injecting fluid) within the reservoir results in a transient increase of the reservoir porepressure and a decrease in effective stress. If the decrease in effective stress is sufficient, it can lead to relaxation of normal stresses along preexisting fractures and hence slip along the fracture and associated microseismicity. The following derivations are from Shapiro [8] and so the reader is referred to this paper for a more detailed presentation of the approach.
Assuming a pointsource injector and a homogeneous and isotropic medium, the triggering front (i.e., the distance between outer enveloe of the microseismic “cloud” and the fluid injection point) is described by where is observation time, is injection start time, and is the scalar apparent hydraulic diffusivity. By plotting the microseismic events on a timedistance plot and matching the bestfitting  curve to the triggering front an estimate of the hydraulic diffusivity can be obtained. The calculated apparent diffusivity can then be used to estimate other reservoir and flow parameters, such as formation permeability.
Assuming that the injected fluid is incompressible, the fluid volume balance is such that the total injected fluid is equal to the sum of the fluid volume within the fracture and lost to the surrounding formation. Further, assuming that the induced fracture is straight and of fixed height (i.e., the PKN model; see [14]), then the fracture halflength is approximated by where is the average injection rate, is the fracture height (either estimated from perforation interval or vertical extent of microseismicity), is the fluidloss coefficient, and is the average fracture width. The fluidloss coefficient is given by Another surface, the back front, characterises the seismically quiet zone after injection stops and tracks the propagation of maximum porepressure perturbation. The back front is given by where is the dimension of the pressure diffusion (1D, 2D, or 3D) and is the injection shutoff time.
Neglecting induced fracture surface effects such as filter cake permeability damage and effects on pore space and fractures within the vicinity of the fracture treatment, the permeability of the reservoir can be estimated: where and are the compressibility and viscosity of the reservoir fluid, respectively, is the difference in the average injection pressure and the initial (or farfield) reservoir pressure, and is the reservoir porosity.
2.2. SeepageForce Triggering
The nonlinear diffusion approach of Shapiro [8] and the socalled Coulomb failure stress (CFS) criteria (e.g., [15]) applied to microseismicity make the assumption that seismicity is triggered by the propagation of a fluid pressure perturbation front. Based on the previous mechanism, it is implied that small changes in porepressure are sufficient to trigger seismicity, and this is often explained by assuming that most of the faults are critically stressed [13, 15]. Rozhko [11] argues that induced microseismicity is explained and predicted better by linear diffusion coupled to linear poroelastic deformation rather than the highly nonlinear fluid diffusion mechanism [8] or CFS and critically stressed faults [15].
In the Rozhko [11] approach, the seismicity is triggered by the propagation of an effective stress perturbation front. The role of fluid pressure in rock strength is significant, yet comes about through the Terzaghi [16] effective stress law where is the effective stress tensor, is the stress tensor, is pressure, and is the Kronecker delta function. Rozhko [11] refers to this as the socalled seepageforce and makes use of the Coulomb yielding criteria (CYS) written as where CYS is the Coulomb yielding stress and and are the maximum and minimum principal stresses (positive in tension). The parameters and are the friction angle and cohesion during dilatancy and can be determined from geomechanical triaxial laboratory measurements. Application of CYS stems from laboratory measurements, where observed acoustic emissions during loading have been shown to correlate with the onset of dilatancy. CYS not only describes the onset of dilatancy and hence microseismicity, but also incorporates the Kaiser effect [17]; during unloading deformation is elastic with no additional fracturing, and during reloading no additional fracturing and seismicity develop until overcoming the previous loading maximum.
The seismicitytriggering front (the CYS equivalent to (1)) is given by where is radial distance, is the poroelastic stress coefficient, , , and are nondimensional functions given by Rozhko [11, equations 7, 10, and 11], , and are the pressure perturbations for times and , and , and is the pressure diffusivity constant. The seismicitysuppression front (the CYS equivalent to (4)) is written as By fitting the seismicitytriggering and seismicitysuppression fronts to the induced seismicity, the formation diffusivity can be estimated. Apparent permeability can then be estimated from where is the pore volume compressibility.
3. Microseismic Data
Verdon et al. [20] compared the microseismicity produced when first water and then CO_{2} (in a supercritical state) were used as the injection fluids for hydraulic fracture of a tight gas reservoir, with the purpose of identifying any characteristic differences in event locations and/or magnitudes induced by the different fluids. A total of 9 injection stages were performed in a vertical well, with each stage at a slightly shallower depth than the previous stage (see Maxwell et al. [21]). The first 7 stages used water, while the final 2 used supercritical CO_{2}. No major lithologic differences have been identified between the stages. The fracture stimulations were monitored with a downhole array of 12 threecomponent geophones installed in a nearby vertical well. Verdon et al. [20] presented data from stages 4 (water) and 8 (CO_{2}). For both fluids, microseismic event locations indicated the formation of fracture networks parallel to the maximum horizontal stress (Figure 1). Event magnitudes showed a weak correlation with injection pressure, while the influence of the differing fluids was found to be minimal.
(a)
(b)
4. Permeability Estimates from PorePressure and SeepageForce Triggering
4.1. PorePressure Triggering
4.1.1. WaterGel Injection
Figure 1(a) displays a map view of the recorded microseismicity during the watergel fracture treatment. The microseismicity follows an approximately linear trend with an absolute correlation coefficient of 0.83 using simple linear regression. The length and width of the microseismic cloud are approximately 220 m and 70 m. In Figure 2, the microseismic events are plotted with respect to distance from injection well and injection time (i.e.,  space). The vertical error bars represent the estimated location errors based on the residuals between the predicted and observed travel times. The events were located using the inhouse location algorithm of Pinnacle Technologies (see Zimmer et al. [22]) using an isotropic onedimensional velocity model (see Figure 3). Also shown are horizontal error bars that serve as a qualitative (and not quantitative) measure of event measurement confidence and so by no means reflect error in time (see Zimmer et al. [22] for description of uncertainty characterization). In other words, they attempt to present additional information about microseismic event quality to help further scrutinize the  plot. Three microseismic trigger (or forward front)  curves are shown for apparent diffusivities of 1.25 m^{2}/s, 0.60 m^{2}/s, and 0.40 m^{2}/s using (1). These curves represent subjective endmember  curves for the forward front microseismicity. Also shown is an  curve for the back front for an apparent diffusivity of 0.10 m^{2}/s using (4).
(a)
(b)
4.1.2. Supercritical CO_{2} Injection
Figure 1(b) displays a map view of the recorded microseismicity during the supercritical CO_{2} fracture treatment. The microseismicity follows a more diffuse trend compared with the watergel treatment with an absolute correlation coefficient of 0.65. The length and width of the microseismic cloud are approximately 120 m and 50 m. In Figure 4, the microseismic events are plotted in  space. Three forward front  curves are shown for apparent diffusivities of 1.20 m^{2}/s, 0.80 m^{2}/s, and 0.30 m^{2}/s and a back front  curve for an apparent diffusivity of 0.90 m^{2}/s.
4.2. SeepageForce Triggering
Figures 5 and 6 show the same observed  data with the predicted seismicitytriggering and seismicitysuppression fronts based on seepageforce modelling. In these figures, we assume and . For the water treatment (Figure 5), we use an average differential injection pressure of 14 MPa to define MPa and MPa. The best fitting seismicitytriggering and seismicitysuppression fronts were obtained using the following values: perforation interval of 20 m, MPa, m^{2}/h and m^{2}/h. For the supercritical CO_{2} treatment (Figure 6), we use an average differential injection pressure of 15 MPa to define MPa and MPa. The best fitting seismicitytriggering and seismicitysuppression fronts were obtained using the following values: perforation interval of 20 m, MPa, m^{2}/h, and m^{2}/h.
4.3. Permeability Estimates
4.3.1. PorePressure Triggering
The average reservoir porosity is assumed to be 10% (an upper end for tight sand reservoirs). The reservoir fluid viscosity and compressibility are estimated to be Pa·s and , respectively, based on typical values for oil given by Dake [23]. For the watergel treatment, the average injection rate is 0.09 m^{3}/s, the pressure difference 15 MPa, and fracture height 70 m. For the supercritical CO_{2} treatment, the average injection rate is 0.08 m^{3}/s, the pressure difference 15 MPa, and fracture height 100 m. We assume a fracture width of 0.01 m for both fracture stimulations. Table 1 compiles the results for the estimated fluidloss coefficient (3), fracture halflength (2), and reservoir permeability (5).

4.3.2. SeepageForce Triggering
Assuming that the pore volume compressibility is negligible with respect to the reservoir fluid compressibility (i.e., ), the permeability estimates based on (10) are summarized in Table 2. The assumption of negligible pore volume compressibility suggests that our estimates of formation permeability are conservative (i.e., an underestimate).

Estimates of apparent permeability from both approaches are within the same order of magnitude between 10 mD and 100 mD. Note that we use the term “apparent” permeability for two reasons. First, the permeability estimates are typically higher than the true formation permeability through enhancement via hydraulic stimulation. Second, the apparent permeability is indirectly calculated from microseismic data and depends on assumed values of Biot’s constant, Poisson’s ratio, and the internal angle of friction.
For the watergel fluid injection, the formation permeability estimates based on porepressure triggering range between 34 mD and 106 mD, whereas those based on seepageforce triggering range between 67 mD and 94 mD. For seepageforce triggering, there are two estimates for formation permeability. This is because two values of diffusivity were needed to fit the microseismic data: for the diffusivity during hydraulic stimulation and for the diffusivity due to negative porepressure perturbation in fractured rock. Thus, the estimate of mD during hydraulic stimulation is more representative of formation permeability during fluid injection, whereas the estimate of mD is more representative of the formation after fracture damage. For the supercritical CO_{2} fluid injection, the formation permeability estimates based on porepressure triggering are lower and range between 14 mD and 58 mD, whereas those based on seepageforce triggering range between 53 mD and 92 mD. Permeability estimates based on seepageforce triggering are more consistent between the watergel and supercritical CO_{2} injection. The permeability estimates for the fractured formation are nearly equal as would be expected for similar geological formations. As per the conclusions of Verdon et al. [20], we see little evidence for a different seismic response when CO_{2} rather than water is the injected fluid.
Besides examining event locations and magnitudes, Verdon et al. [20] used shearwave splitting to image the induced fracture networks. Although not robustly constrained, inversions based on the SWS measurements appeared to show that the fracture network created during water injection was slightly more intense. This may account for what differences are there in formation permeability between supercritical CO_{2} and watergel injection, as estimated by the porepressure method. However, the permeability estimates for the fractured formation (i.e., based on diffusivity estimate ) would suggest that both fluids generate similar fracture density. One possible explanation for the difference might be in terms of the size of fractures generated. The watergel treatment may generate large fractures that are effectively constant in dimension (e.g., displaying a Gaussian distribution), whereas the supercritical CO_{2} treatment may generate fewer large fractures yet many smaller fractures (i.e., skewed distribution). Based on the geometry of the microseismic monitoring array, the detectability limitations would be biased towards larger fractures. This would certainly explain the lower number of events recorded from the supercritical CO_{2} injection yet similar fractured formation permeability.
5. Discussion and Conclusions
We examined two approaches of estimating formation permeability using microseismic data: the porepressure triggering and the seepageforce triggering mechanisms. Based on microseismic data from a hydraulic fracture experiment injecting water and supercritical CO_{2} during different stages, we compared permeability estimates between the two approaches. The two hydraulic stimulation treatments were performed separately on two formation intervals having similar geological, geomechanical, and in situ stress conditions and only differed in terms of the injection fluid used. Both approaches (porepressure triggering and the seepageforce triggering) provided estimates of permeability within the same order of magnitude. However, the seepageforce mechanism (i.e., effective stress perturbation) provided more consistent estimates of permeability between the two different injection fluids.
Urbancic et al. [24] monitored significant microseismicity during a field test injecting 10,000 tons CO_{2} over a period of one month. They observed that microseismicity can be used to identify the position of the CO_{2} plume, and, although microseismicity was significant, there was no evidence of reduced cap rock integrity. Verdon et al. [25] demonstrated the added benefit of microseismic monitoring for the geological storage of CO_{2} during injection, where, for example, it was shown that microseismic activity is a natural consequence of fluid production and injection and does not necessarily imply leakage from the storage formation. Our results show that permeability estimates based on the seepageforce triggering mechanism technique using microseismic monitoring have strong potential to constrain formation permeability limitations for largescale CO_{2} injection.
Acknowledgments
The authors would like to thank Pinnacle Technologies Ltd. for making the microseismic data available and Alexander Rozhko for providing the Matlab scripts to compute the seepageforce curves. This research was partially funded by the BUMPS consortium, UK Energy Research Center (UKERC), and Research Councils UK (RCUK). J. P. Verdon is a Natural Environment Research Council (NERC) EarlyCareer Research Fellow (Grant no. NE/I021497/1).
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Copyright
Copyright © 2013 D. A. Angus and J. P. Verdon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.