Assessing fault reactivation tendency within and surrounding porous reservoirs during fluid production or injection

Assessing fault reactivation tendency within and surrounding porous reservoirs during fluid production or injection

ARTICLE IN PRESS International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1– 7 Contents lists available at ScienceDirect International Jo...

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ARTICLE IN PRESS International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1– 7

Contents lists available at ScienceDirect

International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms

Assessing fault reactivation tendency within and surrounding porous reservoirs during fluid production or injection Hamidreza Soltanzadeh, Christopher D. Hawkes  Department of Civil and Geological Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, SK, Canada S7N 5A9

a r t i c l e in fo

abstract

Article history: Received 21 August 2007 Received in revised form 5 March 2008 Accepted 7 March 2008 Available online 6 May 2008

This paper investigates fault reactivation tendency within and surrounding reservoirs during fluid injection or production. Induced stress analysis is performed using Eshelby’s theory of inclusions for a poroelastic material, and the concept of Coulomb failure stress change is implemented as a criterion for fault reactivation tendency. A methodology is developed to find the range of fault dip angles that tend towards reactivation in either thrust or a normal fault stress regimes. The results demonstrate that, during production from a reservoir in a normal fault stress regime, fault reactivation is likely to occur within the reservoir and adjacent to its flanks. For a thrust-fault stress regime, only faults located in rocks overlying and underlying the reservoir tend towards reactivation. The results for the analogous case of fluid injection are exactly the opposite. Sensitivity analyses show that the locations of the boundaries defining these regions of reactivation (or stabilization) tendency are not highly sensitive to the fault friction coefficient. The use of the proposed methodology is illustrated for a synthetic case study. & 2008 Elsevier Ltd. All rights reserved.

Keywords: Fault reactivation Induced seismicity Inclusions Poroelasticity Reservoir depletion Fluid injection Gas sequestration

1. Introduction During hydrocarbon production from a reservoir, fluid injection for enhanced oil recovery, waste disposal or greenhouse gas sequestration, stress changes induced within and surrounding the reservoir might lead to reactivation of existing geological discontinuities including faults, fractures and joints (collectively referred to as ‘‘faults’’ in this work). Various risks are related to the reactivation of these faults. After reactivation, these features are likely to serve as fluid leakage paths [1–3]. Furthermore, wellbores within or overlying the reservoir might be sheared and damaged [4,5], and the ground surface subsidence sometimes associated with fault reactivation (e.g., [6]) might damage surface structures. In extreme cases, earthquakes may be induced [7,8], with the potential for causing damage to operations equipment and civil structures. Various methods have been developed to assess fault reactivation tendency for existing faults induced by fluid production or injection within reservoirs. Streit and Hillis [9] used a Mohr–Coulomb failure criterion to predict the range of fault dip angles, which might be reactivated within the reservoir during oil production from the Ekofisk field, in the Norwegian sector of the North Sea. Their analysis assumed that no change in vertical stress occurred during production, but the minimum horizontal stress

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E-mail address: [email protected] (C.D. Hawkes). 1365-1609/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2008.03.008

decreased as the reservoir pressure was depleted. A constant ratio of pressure change to minimum horizontal stress change was used in their work, which was based on field measurements. Their approach was similar, in principle, to that presented by Hawkes et al. [10], who combined a uniaxial compression scenario with a Mohr–Coulomb failure criterion to predict the range of dip angles for faults within a reservoir that tend towards reactivation during injection or production. In the latter work, the proportionality between pore pressure change and horizontal stress change was based on poroelastic theory, for a reservoir of infinite lateral extent. Segall [11] examined the hypothesis that a major earthquake in Coalinga, California might have been triggered by production in an overlying oil field. He implemented a plane strain poroelastic model for stress and strain analysis based on the theory of strain nuclei. In addition, a one-dimensional solution for the diffusion equation was used to simulate fluid flow and pore pressure change within the reservoir. A Coulomb failure criterion was implemented to study the likelihood of fault reactivation. Although the model predictions compared favourably to the measured ground surface subsidence and pore pressure change in the reservoir, the model predictions of fault reactivation tendency did not show any correlation between the earthquake and fluid production. Using a similar concept, Segall et al. [12] implemented an axisymmetric, poroelastic model to simulate the productioninduced subsidence and seismicity occurring in the Lacq gas field, France. In their work, the linear correlation that was observed

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between gas production and the amount of maximum subsidence was considered as a supporting evidence for the poroelastic behaviour of the reservoir. Their comparison of the modelpredicted induced stresses with the distribution of seismic events showed reasonable agreement, based on the assumption of faults being optimally oriented for frictional sliding. Segall and Fitzgerald [13] implemented a simplified full-space solution for fluid production from a penny-shaped reservoir, in conjunction with a simplified implementation of the Coulomb failure stress change concept, to investigate the general patterns of fault reactivation within the reservoir and in the rock immediately adjacent to it. Their analyses showed that, during production, there is a tendency towards fault reactivation within the reservoir and adjacent to its lateral flanks in a normal fault stress regime. Similarly, they showed a tendency towards reactivation in overlying and underlying rocks in a thrust fault stress regime. Induced stress changes within a reservoir were studied by Rudnicki [14] for an ellipsoidal reservoir in a full space with elastic properties different from the surrounding rock. By applying a Coulomb failure criterion, it was shown that for a thrust fault stress regime, the induced stress changes always favour fault stabilization during production and de-stabilization during injection. For a normal fault stress regime, the effect of induced stress changes on fault stability was shown to depend on the fault surface frictional angle and the stress path. The latter parameter is a function of reservoir aspect ratio ( ¼ thickness/width), the ratio of shear moduli in the reservoir to the surrounding rock, and Poisson’s ratios of these two bodies. Soltanzadeh and Hawkes [15] used the theory of inclusions for a half-space to solve for induced stresses both within and outside of a reservoir under plane strain conditions, for reservoirs of rectangular and elliptical cross-section. Their work included both horizontal reservoirs, as well as reservoirs that dip within the cross-sectional plane. They integrated the induced stress analysis results with a Coulomb failure stress change (DCFS) methodology to provide a means of assessing the tendency of fault reactivation both within and outside of reservoirs as a consequence of fluid production or injection. This methodology was applied by Soltanzadeh and Hawkes [16] for fault reactivation assessment in the Lacq gas field, France, where predicted fault reactivation tendencies show a strong correlation with the recorded seismic event locations. In contrast to most previous work, the present paper addresses fault reactivation potential, not just within, but also surrounding the reservoir. This is done following the approach presented in Soltanzadeh and Hawkes [15]. What is unique about the work presented in this paper is the combined use of an induced stress change analysis, carried out with a semi-analytical, poroelastic model based on the theory of inclusions for plane strain conditions, with the DCFS concept for predicting patterns of fault reactivation tendency for normal and thrust fault stress regimes.

gaðijÞ ¼ Dsij =ðaDPÞ

The pore pressure change resulting from fluid production or injection in a reservoir will generate changes in effective stresses. The effective stress change Ds0 ij is related to the pore pressure change DP and the total stress change Dsij as follows: (1)

where a is Biot’s coefficient, dij is the Kronecker delta, and DP is considered positive for injection and negative for production. If a reservoir was a free body, effective stress changes would simply result in its contraction or expansion. However, due to the

(2)

Assuming that the normalized stress arching ratios for a given reservoir have been determined, the effective stress changes within the reservoir can be calculated as follows: Ds0ij ¼ ðdL dij  gaðijÞ ÞðaDPÞ

(3)

where dL is a location index which equals one within the reservoir and zero within the surrounding rock. The values of the normalized stress arching ratios are primarily dependent on the mechanical properties and geometry of the reservoir and its surrounding rock. For the special case of a homogeneous, linear elastic reservoir with the same elastic properties as the surrounding rock, the normalized stress arching ratios can be found using the theory of inclusions [18] as presented by Soltanzadeh and Hawkes [15] for infinitely long reservoirs (i.e., plane strain conditions). Example output for a plane strain stress analysis of a reservoir with rectangular cross-section, having a depth (to the reservoir top) of 3 km, a width of 6 km, and a thickness of 300 m is shown in Fig. 1a–c. These figures, respectively, show contour maps for horizontal, vertical, and shear normalized stress arching ratios. In these figures, regions with different stress change state (i.e., positive and negative values for arching ratios) are separated by a dashed contour. From Fig. 1a, during injection (i.e., DP40) horizontal compressive stresses are induced beyond the lateral flanks of the reservoir (i.e., where ga(H)40), while horizontal tensile stress changes are developed within the reservoir, and above and below it (i.e., where ga(H)o0). From Fig. 1b, during injection, vertical compressive stresses are induced above and below the reservoir (i.e., where ga(V)40), while vertical extensional stress changes will occur within the reservoir, and beyond its lateral flanks (i.e., where ga(V)o0). The results are exactly the opposite for the analogous case of production (i.e., DPo0). Fig. 1c shows that shear stresses are mostly concentrated at the flanks of the reservoir.

3. Coulomb failure stress change (DCFS) The DCFS method was previously developed to asses the likelihood of fault reactivation due to changes in effective stresses. In a production or injection scenario, wherein stress changes have been induced, the change in Coulomb failure stress can be evaluated as (e.g., [19]): DCFS ¼ Dt  ms Ds0n

2. Induced stress analysis using the theory of inclusions

Dsij ¼ Ds0ij þ aDPdij

fact that a reservoir is attached to its surrounding rock, the pore pressure change resulting from fluid production or injection will generate anisotropic changes in total stresses within and surrounding it. This phenomenon has been called arching (e.g., [17]). The ratios of the changes in total stress (Dsij) at any given point to the effective change in pore pressure (DP) within the reservoir have been referred to as the normalized stress arching ratios (ga(ij)) by Soltanzadeh and Hawkes [15]. i.e.,

(4)

Ds0n ,

respectively, are induced changes of shear and where Dt and effective normal stresses on the fault plane, and ms is the coefficient of friction. A positive DCFS value indicates a tendency towards fault reactivation. DCFS values as small as 0.1 MPa have been found to induce seismic activity in faulted settings where initial CFS values are close to zero (e.g., [12,19]). Based on the concept of Coulomb failure stress change, Soltanzadeh and Hawkes [15,16] defined the ‘‘fault reactivation factor’’ (l), which is a dimensionless parameter: l ¼ DCFS=ðaDPÞ

(5)

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þ dD gaðHVÞ ððsin2 y  cos2 yÞdF  2ms sin y cos yÞ

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Fig. 1. Contour maps for normalized stress arching ratios for a rectangular reservoir with depth of 3 km (from the surface to the reservoir top), thickness of 300 m and width of 6 km. (a) Normalized horizontal stress arching ratio (ga(H)); (b) normalized vertical stress arching ratio (ga(V)); and (c) normalized shear stress arching ratio (ga(HV)). All the values are normalized by (1–2n)/(1n), which is the maximum potential value for ga(H). This value is reached for reservoirs of finite finite thickness and infinite lateral extents [15].

Under plane strain conditions, for normal and thrust fault stress regimes this parameter can be written as [16] l ¼ ðdL  gaðHÞ Þ sin yðdF cos y þ ms sin yÞ  ðdL  gaðVÞ Þ cos yðdF sin y  ms cos yÞ

y (Depth)

-4

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(6)

where y is the fault dip angle, ga(H) is the normalized horizontal stress arching ratio, ga(V) is the normalized vertical stress arching ratio, ga(HV) is the normalized shear stress arching ratio, dF is the stress regime index, which equals to 1 for a normal fault stress regime and 1 for a thrust fault stress regime, and dD is the fault dip direction index, which equals to 1 for faults dipping towards to the bottom-left corner of the cross-sectional analysis plane and 1 for faults dipping towards to the bottom-right corner. Fault reactivation tendency for a reservoir during depletion or injection can be assessed by evaluating the fault reactivation factor (l) using Eq. (6). Fig. 2a and b shows the variation in l for the same reservoir analyzed in Fig. 1, for normal and thrust fault stress regimes, respectively. For the calculations shown in these figures, faults are dipping towards the bottom-left corner of the cross-sectional analysis plane (i.e., dD ¼ 1), and a friction coefficient (ms) of 0.6 has been assumed. In Fig. 2a, a normal fault stress regime was considered with faults dipping at 601 from horizontal. This figure shows that, during production, there is a tendency towards normal fault reactivation within the reservoir and in the rocks near the lateral flanks of the reservoir (i.e., the regions with lo0). Similarly, there

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Fig. 2. Variation in fault reactivation factor (l) for a rectangular reservoir with the same geometry as the reservoir analyzed in Fig. 1, and a Poisson’s ratio equal to 0.2, for (a) a fault dip angle of 601 in a normal fault stress regime; and (b) a fault dip angle of 301 in a thrust fault stress regime. For both figures, faults are dipping towards the bottom-left corner of the cross-section.

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is a tendency towards normal fault reactivation above and below the reservoir during injection (i.e., the regions with l40). In Fig. 2b, a thrust fault stress regime was considered, with faults dipping at 301. According to this figure, during production, there is a tendency towards thrust-fault reactivation in the rocks above and below the reservoir (i.e., the regions with lo0). Also this figure shows that there is no tendency towards fault reactivation with depletion anywhere within the reservoir. Similarly, there is a tendency towards thrust-fault reactivation everywhere within the reservoir and near its lateral flanks (i.e., the regions with l40) during injection.

0 1 2 y (Depth)

4

3 4 μs = 0.4

5

μs = 0.6

6 4. Effect of friction coefficient on potential regions for fault reactivation

8

The methodology presented above for identifying the regions tending towards fault reactivation for a prescribed dip angle may be extended to a more general methodology that accounts for all dip angles using the criterion l ¼ 0 (i.e., DCFS ¼ 0) to identify the boundary between regions of fault reactivation and stabilization. It is thus possible to predict the range of fault dip angles at any point in the cross-sectional plane of analysis that tend towards reactivation. Solving Eq. (6) for l ¼ 0 results in the following equation for critical fault dip angle (y): Mtan2 y þ N tan y þ Q ¼ 0

(7)

where: M ¼ ms Rs þ dD dF Rt N ¼ dF ðRs  1Þ  2ms dD Rt Q ¼ ms  dF dD Rt

(8)

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Fig. 3. Variation in the position of fault reactivation boundary line (l ¼ 0) for the rectangular reservoir analyzed in Fig. 1 for (a) faults dipping at 601 in a normal fault stress regime, and (b) faults dipping at 301 in a thrust stress regime. For both figures, faults are dipping towards to the bottom-left corner of the cross-section.

In this equation, Rs is the stress path ratio which has been defined previously [22,23] as the ratio of the horizontal effective stress change to the vertical effective stress change: Rs ¼

5. Identifying critical fault dip angles within and surrounding a reservoir

-6

0

y (Depth)

The precise value of a fault surface’s friction coefficient (ms) is one of the uncertainities in fault reactivation analysis. One useful application of the methodology described above is to study the sensitivity of the potential regions for fault reactivation to the value of ms. Byerlee [20] suggests that values of the friction coefficient vary between 0.65 and 0.8 for natural sliding surfaces in a broad range of rocks; however, there are known to be some faults with lower frictional strengths (e.g., [21]). For the sake of generality, a broad range of friction coefficients, between 0.4 and 0.8 (as used in [10]) is considered for the sensitivity analyses presented in this paper. Fig. 3a and b shows the positions of the boundary lines, which separate the likely regions for reactivation and stabilization (i.e., the l ¼ 0 contour lines) for ms values of 0.4, 0.6 and 0.8. Fig. 3a and b was generated for the same reservoir geometry, fault dip angles and dip directions, and material properties as Fig. 2a and b, respectively. The shaded areas in Fig. 3a and b denote the region within which this boundary position varies as the friction coefficient varies from 0.4 to 0.8. Compared to the dimensions of the reservoir and the cross-sectional plane of interest, the friction coefficient has a relatively modest effect on the boundaries of regions tending towards reactivation. Therefore, assuming an average ms value of 0.6 may be suitable for the purpose of identifying likely regions for fault reactivation with reasonable accuracy for most faults. It is important to note, however, that the friction coefficient is a very sensitive parameter when predicting the magnitude of pressure (hence stress) change required to reactivate a fault.

μs = 0.8

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Ds0H dL  gaðHÞ ¼ Ds0V dL  gaðVÞ

(9)

and Rt is the shear stress path ratio, which is defined here as the ratio of shear stress change to the vertical effective stress change: Rt ¼

gaðHVÞ DtHV ¼ Ds0V dL  gaðVÞ

(10)

The roots of Eq. (7) can be used to verify the sign of l (or DCFS) as shown by a flowchart given in Fig. 4. This flowchart provides the range of fault dip angles (i.e., yminoyoymax) where fault reactivation factor (l) is negative. l is positive for fault dip angles outside of this range. Therefore, any fault with a dip angle within this range has a tendency towards reactivation during production and towards stabilization during injection. In contrast, any fault with a dip angle outside of this range has a tendency towards stabilization during production and towards reactivation during injection. There is one special case (which is denoted by the bottom-right box in Fig. 4) for which the fault reactivation factor is negative over two ranges of dip angles. For this case, these two ranges are denoted yminymax and y0 miny0 max. The occurrence of

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Finding roots by solving the following equation: M tan2θ + N tanθ +Q=0 If there is no root, both roots are considered to be zero, if any root is less than zero it must be considered zero. As a result we have two roots: θ 1 and θ 2 where θ 1<θ 2. If M=0, there is just one root: θ 0

N (δ L − γ α (V )) ≥ 0

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θ max = 90 θ max ′ = θ1 Fig. 4. Procedure for the sign determination of the fault reactivation factor (l).

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6 this special case is rare for analyses of the type presented in this paper, in which induced stress changes have been predicted using the theory of inclusions. Figs. 5 and 6 demonstrate applications of this method for the rectangular reservoir analyzed in Figs. 1 and 2. These figures show the values of ymin and ymax as contour maps, respectively, for normal and thrust fault stress regimes. For both examples, faults are considered to be dipping towards to the bottom-left corner of the cross-section (i.e., dD ¼ 1). Due to the symmetrical nature of the problem, the results for the analogous case in which the faults dip towards to the bottom-right corner of the cross-section (i.e., dD ¼ 1) can be generated by mirroring the contours along the x ¼ 0 line. Figs. 5 and 6 can be used to identify the range of fault dip angles, which tend towards reactivation at any location throughout the cross-section. For instance, for a normal fault stress regime, at point A (Fig. 5a and b), ymin ¼ 01 and ymax ¼ 601. This means that faults passing through this point and having dip angles between 01 and 601 will tend towards reactivation during production, while faults with dip angles more than 601 tend towards stabilization. Similarly, at point B (Fig. 6a and b), ymin ¼ 01 and ymax ¼ 301. Therefore, in a thrust fault stress regime, faults with dip angles in the range of 0–301 tend towards reactivation during production, while faults with dip angles more than 301 tend towards stabilization. In both cases, the faults behave in the exact opposite sense during injection.

6. A synthetic case study To demonstrate the application of the methodology developed in this paper, a synthetic example in which fault locations and dips have been mapped out will be analyzed (Fig. 7a). The geometry and material properties of the reservoir are the same as those analyzed in Figs. 1 and 2, and a normal fault stress regime

0

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x Fig. 5. Contour maps for (a) ymin and (b) ymax for the rectangular reservoir analyzed in Figs. 1 and 2, in a normal fault stress regime for faults which are dipping towards to the bottom-left corner of the cross-section.

has been assumed. There are 14 faults with different dip angles and dip directions throughout the cross-section to be analyzed. Two different fault reactivation analyses were conducted: one for the faults dipping to the bottom-left corner of the cross-section (dD ¼ 1) and another for the faults dipping to the bottom-right corner of the cross-section (dD ¼ 1). The final results are shown in Fig. 7b, in which the faults that tend towards reactivation during production are identified using fat gray lines, and the faults that tend towards reactivation during injection are identified as thin black lines. As shown in Fig. 7b, there are 6 faults that tend towards reactivation during production, either fully or partly. These faults can be categorized into two main groups: Firstly, faults 1, 2, 9, 11 and a segment of fault 3, which are located near the lateral flanks of the reservoir; secondly, a segment of faults 7, which is located within the reservoir. The mechanisms of fault reactivation in these two groups are different. Faults in the first group tend towards reactivation due to the effective horizontal stress relaxation (tensile stress change) and vertical effective stress increase (compressive stress change). These stress changes apparently accentuate the existing normal fault stress regime (i.e., they increase the deviatoric stress), hence the tendency towards reactivation. Fault 7, on the other hand, tends towards reactivation because the increase in vertical effective stress is larger than the increase in the effective

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Fig. 6. Contour maps for (a) ymin and (b) ymax for the rectangular reservoir analyzed in Figs. 1 and 2, in a thrust fault stress regime, for faults which are dipping towards to the bottom-left corner of the cross-section.

horizontal stress. Even though both stress changes are compressive, the induced deviatoric stress is sufficient to force the stress state on the fault towards failure. However, depending on the amount of stress change within the reservoir, only a certain range of fault dip angles (i.e., moderate dip angles) tend towards reactivation. For example, because the dip angle of fault 6 is relatively steep, the component of induced shear stress resolved on its surface is small, hence it does not tend towards reactivation. According to Fig. 7b, the faults above and below the reservoir stabilize during production due to a stress state change that works to counter-act the deviatoric stress in the existing normal fault stress regime. As also shown in Fig. 7b, fault behaviour during injection is the exact opposite of the case discussed for production. 7. Summary and conclusion The fault reactivation tendency within and surrounding reservoirs during injection and production was studied for normal and thrust fault stress regimes. Stress analysis was conducted using a semi-analytical model based on the theory of inclusions for homogenous and isotropic material properties, under plane strain conditions. The DCFS concept was implemented to predict the fault reactivation tendency.

Fig. 7. (a) Geometry of the synthetic case study for fault reactivation tendency in a normal fault stress regime. Each fault is labelled with a reference number (i.e., 1 through 14), and a dip angle (which is circled) (b) Tendency towards reactivation during injection and production.

The general pattern of fault reactivation in a normal fault stress regime shows that, during production, the regions within and near the lateral flanks of the reservoir tend towards reactivation, while during injection, the underlying and overlying regions of the reservoir tend towards reactivation. For a thrust fault stress regime, the overlying and underlying rocks tend towards reactivation during production while, during injection, the reservoir and rocks near the lateral flanks of the reservoir tend towards reactivation. A sensitivity analysis has shown that the position of the boundary between regions tending towards reactivation and stabilization is relatively insensitive to the value of the friction coefficient. As such, the assumption of an average value of 0.6 for this parameter will likely give a reasonable estimate of this boundary’s position for most friction coefficients typically encountered. It should be noted, however, that a tendency towards reactivation will not necessarily result in a significant risk of fault reactivation in settings where the shear stresses on existing faults are relatively low. In such cases, it is more useful to use an induced stress change model of the type used in this work in conjunction with a methodology that assess the critical conditions required for fault reactivation in an absolute sense. In such analyses, the results are indeed very sensitive to the friction coefficient.

ARTICLE IN PRESS H. Soltanzadeh, C.D. Hawkes / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1–7

A new methodology was developed to find the ranges of fault dip angles that tend towards reactivation throughout the entire cross-sectional plane of analysis. The results have been presented using pairs of contour maps which, for any chosen point, allow the reader to determine the minimum and maximum fault dip angles that will tend towards reactivation. To demonstrate the application of the methodology, a synthetic case study including faults with various positions and orientations, was analyzed. Using the proposed approach, the likelihood for reactivation of all existing faults in the cross-sectional plane of analysis during injection and production was determined. The proposed methodology, while being relatively simple, is quite general and flexible in terms of its applicability. These attributes, coupled with the modest computational effort required to implement the methodology, make it ideally suited for parameter sensitivity analyses to: (i) identify key input parameters and understand their potential effects on reservoir performance; (ii) aid in the screening process during site selection for hydrocarbon production, waste disposal or geological sequestration; and (iii) account for parameter uncertainty in preliminary design analyses. In general, however, more detailed and sophisticated models may be required for the final performance prediction analyses for such projects.

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