当前位置:首页 >> 能源/化工 >>

Fluid Flow in a Fractured Reservoir Using a Geomechanically Constrained Fault-Zone-Damage Model


Fluid Flow in a Fractured Reservoir Using a Geomechanically Constrained Fault-Zone-Damage Model for Reservoir Simulation
Pijush Paul, SPE, and Mark Zoback, SPE, Stanford University, and

Peter Hennings, ConocoPhillips Summary Secondary fractures and faults associated with reservoir-scale faults affect both permeability and permeability anisotropy and hence play an important role in controlling the production behavior of a faulted reservoir. It is well known from geologic studies that there is a concentration of secondary fractures and faults in damage zones adjacent to large faults. Because there are usually inadequate data to fully incorporate damage-zone fractures and faults into reservoir-simulation models, this study uses the principles of dynamic rupture propagation from earthquake seismology to predict the nature of fractured/damage zones associated with reservoir-scale faults. We include geomechanical constraints in our reservoir model and propose a generalized workflow to incorporate damage zones into reservoir-simulation models more routinely. The model we propose calculates the extent of the damage zone along the fault plane by estimating the volume of rock brought to failure by the stress perturbation associated with dynamic-rupture propagation. We apply this method to a real reservoir using both field- and well-scale observations. At the rupture front, damage intensity gradually decreases as we move away from the rupture front or fault plane. In the studied reservoir, the secondary-failure planes in the damage zone are high-angle normal faults striking subparallel to the parent fault, which may affect the permeability of the reservoir in both horizontal and vertical directions. We calibrate our modeling with both outcrop and well observations from a number of studies. We show that dynamic-rupture propagation gives a reasonable first-order approximation of damage zones in terms of permeability and permeability anisotropy in order to be incorporated into reservoir simulators. Introduction Fractures and faults in reservoirs present both problems and opportunities for exploration and production. The heterogeneity and complexity of fluid-flow paths in fractured rocks make it difficult to predict how to produce a fractured reservoir optimally. It is usually not possible to fully define the geometry of the fractures and faults controlling flow, and it is difficult to integrate data from markedly different scales (i.e., seismic, well log, core) into reservoir-simulation models. A number of studies in hydrogeology and the petroleum industry have dealt with modeling fractured reservoirs (Martel and Peterson 1991; Lee et al. 2001; Long ¨ and Billaux 1987; Gringarten 1996; Matthai et al. 2007). Various methodologies, both deterministic and stochastic, have been developed to model the effects of reservoir heterogeneity on hydrocarbon flow and recovery. The work by Smart et al. (2001), Oda (1985, 1986), Maerten et al. (2002), Bourne and Willemse (2001), and Brown and Bruhn (1998) quantifies the stress sensitivity of fractured reservoirs. Several studies (Barton et al. 1995; Townend and Zoback 2000; Wiprut and Zoback 2000) that include fracture
Copyright ? 2009 Society of Petroleum Engineers This paper (SPE 110542) was accepted for presentation at the 2007 SPE Annual Technical Conference and Exhibition, Anaheim, California, USA, 11–14 November 2007, and revised for publication. Original manuscript received for review 2 August 2007. Revised manuscript received for review 31 July 2008. Paper peer approved 1 September 2008.

characterizations from wellbore images and fluid conductivity from the temperature and the production logs indicate fluid flow from critically stressed fractures. Additional studies emphasize the importance and challenges of coupling geomechanics in reservoir fluid flow (Chen and Teufel 2000; Couples et al. 2003; Bourne et al. 2000). These studies found that a variety of geomechanical factors may be very significant in some of the fractured reservoirs. Secondary fractures and faults associated with large-scale faults also appear to be quite important in controlling the permeability of some reservoirs. Densely concentrated secondary fractures and faults near large faults are often referred to as damage zones, which are created at various stages of fault evolution: before faulting (Aydin and Johnson 1978; Lyakhovsky et al. 1997; Nanjo et al. 2005), during fault growth (Chinnery 1966; Cowie and Scholz 1992; Anders and Wiltschko 1994; Vermily and Scholz 1998; Pollard and Segall 1987; Reches and Lockner 1994), and during the earthquake slip events (Freund 1974; Suppe 1984; Chester and Logan 1986) along the existing faults. Lockner et al. (1992) and Vermilye and Scholz (1998) show that the damage zones from the prefaulting stage are very narrow and can be ignored for reservoir-scale faults. The damage zone formed during fault growth can be modeled using dynamic rupture propagation along a fault plane (Madariaga 1976; Kostov 1964; Virieux and Madariaga 1982; Harris and Day 1997). Damage zones caused by slip on existing faults are important, especially when faults are active in present-day stress conditions because slip creates splay fractures at the tips of the fault and extends the damage zone created during the fault-growth stage (Collettini and Sibson 2001; Faulkner et al. 2006; Lockner and Byerlee 1993; Davatzes and Aydin 2003; Myers and Aydin 2004). In this paper, we first introduce a reservoir in which there appears to be significant permeability anisotropy associated with flow parallel to large reservoir-scale faults. Next, we build a geomechanical model of the field and then discuss the relationship between fluid flow and geomechanics at well-scale fracture and fault systems. To consider what happens in the reservoir at larger scale, we use dynamic rupture modeling to theoretically predict the size and extent of damage zones associated with the reservoirscale faults. Field-Scale Permeability Anisotropy and Project Motivation The chosen study area (CS field) is located in the Timor gap between Australia and Indonesia. Fig. 1 shows a structural map of the CS field, which has a number of large, reservoir-scale faults striking in the east-to-west direction. Some of these faults extend up to surface. Seismic data show dip-slip amounts as large as approximately 300 m on some of these faults. Seismic data also show several small-scale faults with a north-to-south orientation. These faults have smaller slip and do not appear to extend to depths shallower than the reservoir. The red-colored region in Fig. 1 indicates the main reservoir, which is a horst structure in between two half-grabens. This map also shows locations of the exploratory wells (CSB1, CSB2, CSB3, CSB4, CSB5, CSU1, CSU2, CSU3, CSU4, CSF1, CST1, and CSH1), production wells
August 2009 SPE Reservoir Evaluation & Engineering

562

Fig. 1—Structural map of the CS field showing exploratory-, production-, and injection-well locations along with field-scale faults. Red color indicates the highest points in the reservoir, and blue color indicates the deepest points.

(P1, P2, P3, P4, P5, P6, P7, and P8), and injection wells (I1, I2, I3, and I4) in the field. The exploration wells are all near vertical (the maximum deviation is approximately 5 ), while production and injection wells are deviated up to approximately 45 . Interference and tracer tests between injection and production wells show enhanced flow along the reservoir-scale faults.

The colored lines in Fig. 2 indicate established hydraulic connectivity between the wells. Fluid flow simulation of these tests show enhanced permeability in the zones associated with both the east-west and north-south trending faults. Larger east-west trending faults indicate a relatively high connectivity parallel to these faults in comparison to the north-south trending faults.

Fig. 2—Colored lines in the figures show established pressure contact between wells during interface and tracer tests. Flow along the faults show enhanced permeability with respect to the average matrix permeability of the reservoir. August 2009 SPE Reservoir Evaluation & Engineering 563

Fig. 3—Comparison of observed bottomhole pressure (BHP) (magenta) and simulated BHP from the base model (blue) and the damage-zone model (green) for two production wells (CSP3, CSP7) and one injection well (CSI3). The damage-zone model shows a significant improvement in the history matching in all the wells.

When we increase the permeability of blocks adjacent to the reservoir-scale faults in the base reservoir simulation model, an improvement in the production and injection history match results, suggesting a possibility of high-permeability zones associated with these damage zones. This study is based on the history matching of production data for % 2.5 years from the initial production. In Fig. 3, we see that the responses from the simulation model with damage zones match much better with the observed values than do the responses from the base model. We hypothesize that the enhanced flow parallel to the east-to-west-trending faults occurs because of damage zones associated with these faults. Below, we propose a new technique for predicting the extent of damage zones for the purpose of incorporating their effects into reservoir-simulation models.

Petrophysical and Geomechanical Model of the Study Area Logs from the exploration wells show that the reservoir section is separated into two parts (Formations 1 and 2) by an unconformity. Both of the formations are from a fluvial-deltaic-dominated depositional environment. They comprise alternating sandstone, siltstone, and mudstone layers. These formations show crossbedding, faulting, and occasional natural fractures. Borehole images show very low fracture density in the exploratory wells. The reservoirs mostly have matrix-dominated porosity and permeability. Average porosity is approximately 10 to 15%. Average reservoir permeability is ap564

proximately 100 to 200 md, but core and log measurements show permeability up to approximately 1,200 md in some locations, which correlates with production logs and well tests from those intervals. Dual-caliper measurements and core samples from Formations 1 and 2 suggest that while the sandstones are fairly strong, fractures in the core samples sometimes act as planes of weakness that decrease the strength. Triaxial and uniaxial compressive strength (UCS) measurements on core samples from Well CSU2 at Formation 1 (Castillo et al. 1999) are used to calibrate log-derived rock strengths. Average UCS value for sandstones is approximately 75 MPa, while for relatively shaly layers, it is approximately 65 MPa. We represent the continuous rock strength for the sandstone intervals using the empirical UCS model proposed by McNally (1987). For shaly intervals, we define the UCS by the power law using the dynamic Young’s modulus and compressive-wave (Pwave) slowness as proposed by Castillo et al. (1999) and Horsrud (2001), respectively. We analyzed wellbore resistivity images and dual-arm calipers to identify drilling-induced tensile fractures and breakouts within the reservoir section of the CS field. Analysis from all exploratory wells shows breakouts in approximately northwest-to-southeast orientation with approximately 30 to 70 of breakout widths and tensile fractures in the orthogonal (northeast-to-southwest) direction, thus giving the orientation of present-day maximum horizontal stress, SHmax (Fig. 4). This observation is consistent with the regional SHmax orientation found by Castillo et al. (1999). SHmax orientation is quite similar at all of the well locations around the
August 2009 SPE Reservoir Evaluation & Engineering

Fig. 4—Stress-induced wellbore breakouts and tensile wall fractures in the CS field consistently show a northeast-to-southwest direction of the maximum principal horizontal stress, SHmax. This direction is similar to the regional stress orientation, as shown in the world stress map.

field, but it varies with depth near some of the well-scale faults and bed boundaries. Following Zoback et al. (2003), we use a frictional faulting theory to constrain magnitudes of the horizontal principal stresses (SHmax and Shmin) and the vertical stress (Sv) is estimated by integrating bulk-density logs at well locations. We find that in the reservoir section, Sv is approximately 72.2 MPa at 3170 m of true vertical depth, and the overburden gradient is approximately 2.34 SG. Direct measurements of pore pressure in the reservoir section throughout the CS field indicate a hydrostatic pore pressure (Pp) gradient of %1.04 SG. Sonic-log and other measurements do not indicate any overpressure zones in the section above the reservoir, so we assume a hydrostatic pore pressure for the entire section. In-situ least principal stress (S3) is estimated using extended leakoff tests (XLOTs) of Well CSP2 at true vertical depths (TVDs) of 1926 and 2971 m. Analysis indicates fracture-closure pressures of approximately 785 and 2,018 psi at TVDs 1926 and 2018 m, respectively. These give an S3 gradient of approximately 1.62 SG. Pressure tests performed on other parts of the field show similar S3 gradients, as illustrated in Fig. 5. In the final step of the stress analysis, we estimate a magnitude of the maximum horizontal stress (SHmax) using the stress-polygon technique proposed by Zoback et al. (2003), in which each stress polygon indicates the range of permissible stress magnitudes on the basis of Coulomb frictional-faulting theory. This technique uses the estimated values of SV, UCS, Shmin, Pp, and wellbore failures as the guiding constraints. The presence of breakouts in the shaly zones of Formation 1 indicates that the maximum hoop stress around the borehole created by the principal horizontal stresses (SHmax and Shmin) is higher than the strength of a rock represented by UCS, approximately 72 MPa. Using the estimated Shmin value, we estimate a lower bound of SHmax gradient, which is approximately 2.52 SG. Formation 2 breakouts are similar in nature to Formation 1 breakouts, so we assume a similar stress gradient for both formations. Fig. 5 shows the principal-stress magnitudes estimated from different parts of the field. The stress state in some of the shaly sections at reservoir depths shows that SHmax may be equal to the overburden. Thus, we conclude a strike-slip/normal faulting environment (SHmax!Sv>Shmin) at reservoir depths, which is consistent with the tectonic setting of the study area (Harrowfield et al. 2003; Baillie et al. 1994).
August 2009 SPE Reservoir Evaluation & Engineering

Fracture Analysis at Well Scale In this section, we analyze the fractures from wellbore-image logs and correlate their flow properties using production and well-test data. Image logs show sets of bedding planes in the sandstone formations, laminations in the shaly layers, and fractures and

Fig. 5—Present-day stress profiles (Sv gradient %2.34 SG, SHmax gradient %2.52 SG, and Shmin %1.62 SG) and porepressure profile (Pp %1.04 SG) at reservoir depth of the CS field. Note that the data indicate a strike/slip faulting regime. 565

Fig. 6—The highest-density fracture zone in Well CSU2 shows that a small fault appears to separate high-angle fractures from lowangle fractures. A change in the observed SHmax orientation at the fault zone indicates that some of these fractures are active in the current stress field.

faults. Natural fractures are not prominent in any of the eight exploratory wells of the field. The possible reasons for low fracture density in the image logs are (1) actual fracture density is very low; (2) fractures have high dip angle, and probability of mapping a high-angle fracture using an image log of a vertical well is very low; (3) there are few wells in potential damage zones, and the image quality in some wells is poor. The fractures that we do observe in the wells are associated with well-scale faults and bed boundaries. Observed rotations of the principal-stress orientation associated with these fractured zones indicate shearing of some of these fractures (Zoback et al. 2003). Among all exploratory wells, Well CSU2 has a relatively large fractured/damage zone in the reservoir section. In Fig. 6, we show the fractures and faults from this well, which are characterized using the wellbore resistivity image (center column). The red curve is a possible well-scale fault, which separates high-angle fractures from low-angle fractures. The left column of Fig. 6 indicates a rotation in SHmax orientation just above the faulted zone. Modeling of the stress rotation confirms the stress model discussed above. Fluid Flow Through the Well-Scale Fractured Zone. We analyze production logs from the reservoir section of the wells to estimate the contribution of the fracture zone to the fluid production. Also, we correlate well-test analysis and core permeability
566

to quantify the effect of fracture porosity and permeability in the reservoir-flow model. Fig. 7 shows the petrophysical model (Column 1); the fractures (Column 2); the production logs, spinner and gradiometer (Column 3); the temperature logs (Column 4); and the core permeability (Column 5) from the same zone shown in Fig. 6. Both spinner and temperature logs indicate that most of the fluid enters into the well through the intervals with relatively clean sandstone but with generally low-to-negligible fracture density. Core measurements indicate a permeability on the order of approximately 800 to 1200 md for high producing intervals and approximately 200 md from the fractured interval. We believe that the explanation for the low fluid production from the fractured interval is the fact that the high matrix permeability in the adjacent zones masks the effect of fracture permeability within the entire test zone. Pressure-transient analysis of the well-test data supports this hypothesis, and the results are consistent with the production data. Effect of Stress on Fluid Flow. The laboratory experiments (Makurat et al. 1990; Olsson and Barton 2001) and field observations (Barton et al. 1995, 1998) indicate relatively high production from the fractures oriented in a shear-failure direction (critically stressed fractures). These results assume that the fractures are geometrically connected and are part of the same fracture network away from the borehole.
August 2009 SPE Reservoir Evaluation & Engineering

Fig. 7—In Well CSU2, petrophysical model (Column 1); fracture geometries as tadpoles (Column 2); production logs, spinner and gradiometer (Column 3); temperature logs (Column 4); and core permeability (Column 5) indicate that most of the fluid enters into the well through intervals 3103–3109 m and 3120–3124 m. Fractures are mainly concentrated at interval 3110–3114 m, but this interval does not show any significant contribution to fluid production. Rather, the intervals of significant flow concentrate with intervals of high intrinsic permeability (%1 darcy).

To evaluate the applicability of this concept, we analyze the fractures from Well CSU2. Fig. 8 illustrates the value of Coulomb failure function (CFF) on a stereonet (lower-hemisphere projection). Fracture and faults (shown as poles) in higher CFF range (red color area) or above frictional-failure line (in 3D Mohr diagram) are optimally oriented for shear failure in the given stress state. On the basis of this concept, they should add extra permeability to the reservoir matrix permeability. However, we see that

only a few fractures from Well CSU2 are critically stressed, which may be one explanation of why these fractures do not contribute significantly to fluid production. Note that this well is located far from potential damage zones. Fracture Density vs. the Distance From Reservoir-Scale Faults. In the preceding sections, we argued that the well-scale fractures/faults do not contribute significantly to fluid production

Fig. 8—In Well CSU2, the stereoplot showing CFF in a lower-hemisphere projection indicates optimally oriented zones (dark red color) (a) and a 3D Mohr diagram with frictional-coefficient line of 0.5 indicates that only a few fractures are in a frictional-failure state (b). August 2009 SPE Reservoir Evaluation & Engineering 567

Fig. 9—Observed data at well locations indicate that fracture density decreases as a function of log of distance from the reservoirscale faults.

in a reservoir with high matrix permeability. However, as illustrated in Fig. 2, interference tests performed between various production and injection wells in the field show preferential flow along the large reservoir-scale faults. In Fig. 9, we plot well-scale average fracture density at exploratory wells vs. fracture distance from the reservoir-scale faults. Well-scale average fractures are the fractures observed in wellbore images, which are related to reservoir-scale faults. In this classification, we removed all the fractures that are associated to any well-scale faults or bed boundaries. A logarithmic best-fit line gives the quantitative relationship (Eq. 1) between the background fracture density (fmd) and distance from the reservoir-scale fault (d in meters). fmd ? ?0:29 ln?d? ? 2:36: . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1) Eq. 1 gives a background fracture-density value of approximately 2 fractures/m at a distance approximately 50 m from the reservoir-scale faults, which is an order higher than its value away (>1000 m) from the faults. An exponentially increasing wellscale average fracture density toward the reservoir-scale fault indicates the presence of damage zones associated with the faults. However, most of the exploration wells in the study area are far from the reservoir-scale faults, so we propose to use geomechnically constrained models using dynamic-rupture-propagation techniques to define fault damage zones. Damage-Zone Modeling Using the DynamicRupture-Propagation Technique Field observations and laboratory data show that the displacement on a fault plane is maximum near the center, and it tapers off at the edges. When slip accumulates in the interior of the faults, stress concentrations at the fault tips also increase. Once a stress concentration exceeds the rock strength, the fault grows to reduce the stresses at the tip. So the faults may be considered as having originated at a point, but they grow with progressive slip. During this process, faults develop a highly fractured zone around the tip, which is called a process zone. These become the dominant part of the damage zone when the fault becomes mature with time. From field observations, shown in Fig. 10, we see that the width of the process zone increases with the fault length, suggesting a similar scaling law for the fault damage zones. However, this simple linear scaling relationship is only approximate (note that it is linear in log-log scale) and fails to include other dimensions of the fault and other factors. Hence, we use the propagation of a dynamic
568

rupture front along the fault plane to model the dimension of the damage zone. During an earthquake, the rupture starts on a small patch and propagates along the fault plane with time. Stress concentrations at the propagating tip of the rupture front give the dimension of the damage zone. Rupture events originating in different orientations and from different patches may explain the multiple fracture patterns associated with the damage zones. The fracture patterns and size of the damage zone control the large-scale permeability anisotropy in the reservoir. In this study, we combine the analytical solutions of the dynamic-rupture propagation by Freund (1979) and Madariaga (1976) to define the fault damage zones. The elastodynamic solution of dynamic-rupture propagation proposed by Freund (1979) assumes the earthquake source as a dynamically extending planar crack. The medium is considered to be an isotropic elastic material. The elastodynamic stress and deformation fields define the dynamic-stress intensity factor and the dynamic energy release for the crack propagation. Particle velocity near the crack tip defines the stress perturbations caused by a dynamic crack. The pre-existing fault provides a weak path for the growth of the crack. Because confining pressure reduces the effects of tensile stresses near the crack tip, the crack extends along the fault plane, which might otherwise lead to an oblique crack growth. The analytical solution proposed by Madariaga (1976) provides an on-plane solution of shear stress at the crack tip for a self-similar circular-shear crack. Assuming the dynamic crack as a self-similar circular-shear crack, we can combine the solutions proposed by Freund (1979) and Madariaga (1976) and estimate stress perturbation around the rupture front. By incorporating the in-situ stress and rock strength, we can estimate the extent and nature of the damage zone, which can be used in a reservoir-simulation model. In the next subsection, we discuss a method and the parameters required to estimate damagezone width using the dynamic-rupture-propagation technique. Method and Input Parameters. As discussed before, faults in the CS field show large throws, indicating several slip movements on these faults. In Fig. 8, we show the geometry of the features, which may slip in the present-day stress conditions indicated by the red zones. This suggests that the east-to-west-striking faults may not slip in the present-day stress condition because, even though they have favorable strike direction, their dip angle is too low (<60 ) at reservoir depth. Hence, slip movements at reservoir
August 2009 SPE Reservoir Evaluation & Engineering

Fig. 10—The width of the process zone scales linearly to the length of the fault [modified from Vermilye and Scholz (1998)].

depth on these faults must have occurred in a historical stress regime. However, some of the north-to-south-striking faults have both strike and dip optimally oriented for a shear failure in the present-day stress condition. Note that some of these faults seem to off set the east-to-west faults (Fig. 1), indicating a younger faulting event. Seismic data show a dominant dip-slip displacement on these faults, indicating a normal faulting regime (Sv>SHmax>Shmin) at the time of slip. This is consistent with the stratigraphic studies, which indicate that the reservoirs were at a shallow depth (approximately 2/3 of the current reservoir depth of approximately 3500 m) when most of the slip occurred in the east-to-weststriking faults. On the basis of this information, we estimate a historical lithostatic (Sv) gradient %1.56 SG, and corresponding horizontal stresses SHmax gradient %1.26 SG and Shmin gradient %1.05 SG, with SHmax oriented in the approximately east-to-west direction (perpendicular to the dip of the faults). These gradients are applied to pretend the historical stresses at the present-day reservoir depth. The other input parameters that are required to estimate damage-zone width in the dynamic-rupture-propagation technique are the velocity profiles (P-wave, S-wave, and rupture velocities), the rock strength, and the stress drop during rupture propagation. We define the P-wave velocity (Eq. 2) by calibrating a powerlaw model (Mavko et al. 1998) (determined in laboratory using multiple confining pressures) with observed log values at reservoir depth: a ? 55?Pconf ?1=4 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2) Here, a is the P-wave velocity in m/s, and Pconf is the confining pressure defined by the mean of principal stresses. S-wave velocity and rupture velocity are correlated to the P-wave velocity. The UCS is estimated from the P-wave slowness, Dt, as discussed in a previous section. Rock strength is related to the UCS, which is based on the triaxial measurements performed on the core samples at reservoir depths. Figs. 11a and 11b show the rupture-velocity and rock-strength profiles along a studied fault of the CS field. We assume that the stress drop of approximately 1 MPa is a typical value observed for earthquakes on faults of highly varied sizes (Scholz 1990). The rupture source/initiation point is the hypocenter of an earthquake. However, in absence of earthquake data in this study, we assume the source point at the bottom-center point of the fault (Fig. 12). This simulates a fault growing from bottom to top,
August 2009 SPE Reservoir Evaluation & Engineering

which is a reasonable assumption for normal faults. On the basis of the elastodynamic solutions used for the rupture propagation, a dynamic rupture starts from a source with a simple circular shape but gradually becomes elliptical with the long axis in the direction of in-plane shear. We use a global coordinate system at the source that is parallel to a local coordinate system at the rupture front (Fig. 13a). Figs. 13b, 13c, and 13d illustrate the components of the stress tensor at the rupture front in the directions 90, 45, and 0 from the fault plane, respectively. Stress values are calculated at the reservoir depth (approximately 3500 m) of the fault shown in Fig. 11. We see that the shear component, szy, is the largest component in all three cases, which creates high-angle features in the damage zone. These features are oriented subparallel to the strike of the parent fault in a normal faulting regime. Figs. 14a and 14b show schematics of the damage-zone dimension and the nature of failure planes in cross-sectional and map view, respectively. Stress intensity increases toward the rupture front, which results in a higher fracture intensity. A higher octahedral shear stress from rock strength defines the dimension of the damage zone around the rupture front (Fig. 13). In the damage zone of the studied fault, we simulated a normal faulting pattern for the secondary-failure features, which is consistent with the field observations. The orientation of these damage-zone faults/fractures (striking subparallel to the parent fault and dipping at an angle higher than that of the parent fault) makes them optimally oriented for shear failure in the present-day stress state, while the parent fault is not critically stressed. This gives a preferential flow parallel to the strike of the parent fault and in the vertical direction, consistent with the well interference and tracer tests observed in the CS field. Uncertainty Analysis. The input parameters and the stress values used to model the damage zone include great uncertainty. We used a Monte Carlo simulation of each parameter to consider these uncertainties. We used the best-possible value as the mean value and define a standard deviation around it to incorporate the range of uncertainty in the parameter. The analysis of 100 simulations indicates that stress drop is the most sensitive parameter in determining the width of the damage zone using the dynamicrupture technique. Figs. 15a and 15b show the mean and standard deviations of the damage-zone width, respectively, from all 100 simulations. At reservoir depths, the damage zone width is approximately 40 to 60 m at the center of the fault and approximately
569

Fig. 11—Rupture-velocity (m/s) (a) and rock-strength (Pa) (b) profiles along a reservoir-scale fault. These profiles are calculated using confining pressure at a depth %2/3 of the current depth to model the stress environment in which we postulate that fault slip occurred.

70 to 100 m at the edges of the fault, consistent with the field observation of the damage-zone width for the faults of this length (Fig. 10). The standard deviation or uncertainty range of the damage zone width is on the order of approximately 5 to 20 m at the reservoir depth but is higher in places where

the estimated damage-zone width is larger. Overall, the width of the damage zone decreases with depth because of increasing elastodynamic stress intensity factor from the rupture source (bottom-center point of the fault) and because of increasing rock strength with depth.

Fig. 12—Rupture is assumed to originate at the bottom center of the fault. The rupture zone initially has a circular pattern but gradually becomes elliptical. Color in the figure indicates dip on the fault plane. 570 August 2009 SPE Reservoir Evaluation & Engineering

Fig. 13—The coordinate system at the rupture front (a). In 90 (b), 45 (c), and 0 (d) direction, we see stress tensor, principal stresses, octahedral shear stress because of dynamic-rupture propagation, far-field octahedral shear stress, total octahedral shear stress, and rock strength at the rupture front. The damage zone is created when total octahedral shear stress is greater than rock strength.

Damage-Zone Modeling of the Nojima Fault. To calibrate the dynamic-rupture-propagation technique at well scale, we model the damage zones using the rupture propagated during the Kobe earthquake (1996) magnitude of 6.9 in the Richter scale

in the Nojima fault and compare them with core observations from scientific boreholes. The Nojima fault runs along the northwestern margin of Awaji Island, Japan. This fault is a right-lateral active fault with a minor reverse-slip component.

Fig. 14—Cross-sectional view of the damage zone along the strike (a) and map view of the damage zone (b). Away from the fault plane (90 ), failure planes are at higher angle than along the fault plane (0 ) and damage intensity increases as we get close to the fault. August 2009 SPE Reservoir Evaluation & Engineering 571

Fig. 15—The mean (a) and the standard deviation (b) of the damage-zone width (m) from 100 simulations. The average damagezone width at the reservoir depth varies from approximately 40 m at the center to approximately 80 m at edges. Standard deviation increases with the increase in the damage-zone width.

The dimensions and properties of the Nojima fault for this study are based on the study done by Wald (1996). Fig. 16 shows a schematic of the slip distribution found by Wald (1996) and the location of the rupture source. Figs. 17a and 17b illustrate the mean and standard deviation from 100 simulations of damage-zone width. At the intersection points of the Geological Survey of Japan (GSJ) borehole (% 625m) and National Institute of Earth Science and Disaster Management (NIED) borehole (% 1150, % 1320, % 1800 m) with the Nojima fault, the estimated damage-zone widths are approximately 44, 37, 33, and 23 m, respectively (Fig. 18), consistent with the damage-zone width observed in the core samples from the boreholes by Lockner et al. (1999). Lockner et al. (1999) observed a permeability 4 to 5 orders of magnitude higher in the damage zones relative to that of the intact rock. This is caused by the presence of shear planes in the damage zones. This again suggests that we may observe a field-scale permeability anisotropy associated with the damage zones of the faults. Damage-Zone Width for the Faults From the CS Field. In this section, we discuss the damage-zone-modeling results for all the faults of the CS field using the dynamic-rupturepropagation technique. For the east-to-west-trending faults, the average damage-zone width at the reservoir depth from all faults varies from approximately 60 m (center of the fault) to approximately 140 m (edges of the fault). However, most of the contributions in this average value come from the few large faults, and smaller faults have relatively narrow damage zones. Standard deviation for those 100 simulations varies from
572

approximately 15 to 40 m, with higher values corresponding to higher damage-zone widths. For north-to-south-striking faults, the average damage-zone width at reservoir depth is approximately 20 m at center and approximately 60 m at the edges, which is much smaller than that of the east-to-west-striking faults. This is because north-to-southstriking faults are much smaller in size in comparison to east-towest-trending faults. The standard deviation in this case varies from approximately 7 to 18 m. As discussed before, interference and tracer tests between production and injection wells show high permeability anisotropy along the east-to-west-trending faults, consistent with the modeling results because larger damage-zone widths along east-to-westtrending faults give prominent fluid-flow paths in comparison to the smaller north-to-south-trending faults. As shown in Fig. 3, incorporation of this permeability anisotropy into reservoir simulation matches the observed production history much better than a model with no damage zones. Conclusions In this paper, we present a workflow to estimate the damage zone associated with reservoir-scale faults using dynamic-rupture propagation. We discussed the workflow using a real field example using both field- and well-scale observations. At the reservoir depth of the studied field, we found a damage-zone width of approximately 50 to 140 m for the east-to-west-trending faults and approximately 20 to 60 m for the north-to-south-trending faults, which are reasonable values and are consistent with the field observations. The strikes of failure planes are subparallel to the parent fault, but dip angle is higher than that of the parent
August 2009 SPE Reservoir Evaluation & Engineering

fault. These damage-zone faults have an optimal orientation for shear failure in the present-day stress state. This may increase permeability along the strike of the parent fault and in the vertical direction, which is consistent with the preferential flow orientation indicated by the interference and tracer tests in the CS field. By implementing the effects of fractures associated with the reservoir-scale faults to a simulation model, we can quantify the permeability anisotropy in the reservoir because of damage zones and can improve production predictability. In this paper, we used analytical solutions to model damage zones, which give a reasonable first-order approximation and are easy to implement. However, numerical-modeling techniques using the same concepts will be needed for accurate results in a complex and dynamic environment. Nomenclature d = distance from the reservoir-scale fault fmd = background fracture density S3 = minimum principal stress Shmin = minimum horizontal stress SHmax = maximum horizontal stress Sv = vertical stress Szy = shear stress in z-y plane a = P-wave velocity Dt = P-wave slowness
Fig. 16—A cross-sectional view of the Nojima fault from the south. Gray dashed lines indicate slip on the fault because of the 1995 Kobe earthquake, estimated by combined source inversion technique (Wald 1996). Red dot is the hypocenter or rupture source point of the earthquake, which is located approximately 17 km beneath the surface at the north edge of the fault.

Acknowledgments We thank ConocoPhillips for providing the data for this investigation. We also want to thank the Stanford Rock Physics and Borehole Geophysics consortium for funding this project. We want to acknowledge Tapan Mukerji from the Department of Energy Resources Engineering at Stanford University for his useful advice during various parts of the project.

Fig. 17—Mean damage-zone width (a) and standard deviation (b) of the width in meters along the Nojima fault. Well intersection points are shown as 1,2,3, and 4. The damage-zone width decreases with increase in depth. August 2009 SPE Reservoir Evaluation & Engineering 573

Fig. 18—The damage-zone widths estimated using the rupture-propagation technique (shown in red lines) are consistent with the damage-zone width observed in GSJ and NIED boreholes. Matrix permeability measured at 50 MPa effective confining pressure indicate 4-to-5-order magnitude higher permeability in comparison to the intact-rock permeability (Lockner et al. 1999).

References
Anders, M.H. and Wiltschko, D.V. 1994. Microfracturing, paleostress and the growth of faults. J. of Structural Geology 16 (6): 795–815. DOI:10.1016/0191-8141(94)90146-5. Aydin, A. and Johnson, A.M. 1978. Development of faults as zones of deformation bands and as slip surfaces in sandstone. Pure and Applied Geophysics 116 (4–5): 931–942. DOI:10.1007/BF00876547. Baillie, P.W., Powell, C.McA., Li, Z.X., and Ryall, A.M. 1994. Tectonic framework of Western Australia’s Neoproterozoic to recent sedimentary basins. In The Sedimentary Basins of Western Australia, ed. P.G. and R.R. Purcell, 45–62. West Perth, Western Australia: Petroleum Exploration Society of Australia (PESA). Barton, C.A., Hickman, S.H., Morin, R., Zoback, M.D., and Benoit, D. 1998. Reservoir-Scale Fracture Permeability in the Dixie Valley, Nevada, Geothermal Field. Paper SPE 47371 presented at SPE/ISRM Rock Mechanics in Petroleum Engineering, Trondheim, Norway, 8–10 July. DOI: 10.2118/47371-MS. Barton, C.A., Zoback, M.D., and Moos, D. 1995. Fluid flow along potentially active faults in crystalline rock. Geology 23 (8): 683–686. DOI:10.1130/0091-7613(1995)023<0683:FFAPAF>2.3.CO;2. Bourne, S.J. and Willemse, E.J.M. 2001. Elastic stress control on the pattern of tensile fracturing around a small fault network at Nash Point, UK. J. of Structural Geology 23 (11): 1753–1770. DOI:10.1016/S0191-8141(01)00027-X. Bourne, S.J., Brauckmann, F., Rijkels, L., Stephenson, B.J., Weber, A., and Willemse, E.J.M. 2000. Predictive modelling of naturally fractured reservoirs using geomechanics and flow simulation. Paper ADIPEC 0911 presented at the Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, UAE, 15–18 October. Brown, S.R. and Bruhn, R.L. 1998. Fluid permeability of deformable fracture networks. J. of Geophysical Research 103 (B2): 2489–2500. DOI:10.1029/97JB03113. Castillo, D.A., Hillis, R.R., Asquith, K., and Fischer, M. 1998. State of stress in the Timor Sea area based on deep wellbore observations and frictional failure criteria: Application to fault-trap integrity. In The Sedimentary Basins of Western Australia II, ed. P.G. and R.R. Purcell, 325–341. West Perth, Western Australia: PESA. 574

Chen, H-Y. and Teufel, L.W. 2000. Coupling Fluid-Flow and Geomechanics in Dual-Porosity Modeling of Naturally Fractured Reservoirs— Model Description and Comparison. Paper SPE 59043 presented at the SPE International Petroleum Conference and Exhibition in Mexico, Villahermosa, Mexico, 1–3 February. DOI: 10.2118/59043-MS. Chester, F.M. and Logan, J.M. 1986. Implications from mechanical properties of brittle faults from observations of the Punchbowl fault zone, California. Pure and Applied Geophysics 124 (1–2): 79–106. DOI:10.1007/BF00875720. Chinnery, M.A. 1966. Secondary faulting; Part 1, Theoretical aspects; Part 2, Geological aspects. Canadian J. of Earth Sciences 3: 163–190. Collettini, C. and Sibson, R.H. 2001. Normal faults, normal friction? Geology 29 (10): 927–930. DOI:10.1130/0091-7613(2001)029<0927: NFNF>2.0.CO;2. Couples, G.D., Lewis, H., Reynolds, M.A., Pickup, G.E., and Ma, J. 2003. Upscaling Fluid-Flow and Geomechanical Properties in Coupled Matrix+Fractures+Fluids Systems. Paper SPE 79696 presented at the SPE Reservoir Simulation Symposium, Houston, 3–5 February. DOI: 10.2118/79696-MS. Cowie, P.A. and Scholz, C.H. 1992. Physical explanation for the displacement-length relationship of faults using a post-yield fracture mechanics model. J. of Structural Geology 14 (10): 1133–1148. DOI:10.1016/ 0191-8141(92)90065-5. Davatzes, N.C. and Aydin, A. 2003. The formation of conjugate normal fault systems in folded sandstone by sequential jointing and shearing, Waterpocket monocline, Utah. J. of Geophysical Research 108 (B10): 2478–2493. DOI:10.1029/2002JB002289. Faulkner, D.R., Mitchell, T.M., Healy, D., and Heap, M.J. 2006. Slip on “weak” faults by the rotation of regional stress in the fracture damage zone. Nature 44 (14 December 2006): 922–925. DOI:10.1038/ nature05353. Freund, L.B. 1979. The mechanics of dynamic shear crack propagation. J. of Geophysical Research 84 (B5): 2199–2209. DOI:10.1029/ JB084iB05p02199. Freund, R. 1974. Kinematics of transform and transcurrent faults. Tectonophysics 21 (1–2): 93–134. DOI:10.1016/0040-1951(74)90064-X. Gringarten, E. 1996. 3-D geometric description of fractured reservoirs. Mathematical Geology 28 (7): 881–893. DOI:10.1007/BF02066006. August 2009 SPE Reservoir Evaluation & Engineering

Harris, R.A. and Day, S.M. 1997. Effects of a low-velocity zone in a dynamic rupture. Bulletin of the Seismological Society of America 87 (5): 1267–1280. Harrowfield, M., Cunneen, J., Keep, M., and Crowe, W. 2003. Early-stage orogenesis in the Timor Sea region, NW Australia. J. of the Geological Society 160 (6): 991–1001. DOI:10.1144/0016-764903-020. Horsrud, P. 2001. Estimating Mechanical Properties of Shale From Empirical Correlations. SPE Drill & Comp 16 (2): 68–73. SPE-56017-PA. DOI: 10.2118/56017-PA. Kostov, B.V. 1964. Selfsimilar problems of propagation of shear cracks. J. Appl. Math. Mech. 28 (5): 1077–1087. DOI:10.1016/0021-8928(64) 90010-3. Lee, S.H., Lough, M.F., and Jensen, C.L. 2001. Hierarchical modeling of flow in naturally fractured formations with multiple length scales. Water Resources Research 37 (3): 443–455. Lockner, D., Naka, H., Tanaka, H., Ito, H., and Ikeda, R. 1999. Permeability and strength of core samples from the Nojima Fault of the 1995 Kobe earthquake. Proc., International Workshop on the Nojima Fault Core and Borehole analysis, Tsukuba, Japan, 22–23 November, Open File Report 00-129, 147–152. Lockner, D.A. and Byerlee, J.D. 1993. How geometrical constraints contribute to the weakness of mature faults. Nature 363 (20 May 1993): 250–252. DOI:10.1038/363250a0. Lockner, D.A., Byerlee, J.D., Kuksenko, V., Ponomarev, A., and Sidorin, A. 1992. Observations of quasi-static fault growth from acoustic emissions. In Fault Mechanics and Transport Properties of Rocks: A Festschrift in Honor of W.F. Brace, ed. B. Evans, T.-F. Wong, and W. Brace, 3–31. San Diego, California: International Geophysics Series, Academic Press. Long, J.C.S. and Billaux, D.M. 1987. From field data to fracture network modeling: An example incorporating spatial structure. Water Resources Research 23 (7): 1201–1216. DOI:10.1029/WR023i007p01201. Lyakhovsky, V., Ben-Zion, Y., and Agnon, A. 1997. Distributed damage, faulting and friction. J. of Geophysical Research 102 (B12): 27635– 27649. DOI:10.1029/97JB01896. Madariaga, R. 1976. Dynamics of an expanding circular fault. Bulletin of the Seismological Society of America 66 (3): 639–666. Maerten, L., Gillespie, P., and Pollard, D.D. 2002. Effects of local stress perturbation on secondary fault development. J. of Structural Geology 24 (1): 145–153. DOI:10.1016/S0191-8141(01)00054-2. Makurat, A., Barton, N., Rad, N.S., and Bandis. S. 1990. Joint conductivity variation due to normal and shear deformation. In Rock Joints, ed. N. Barton and O. Stephansson, 535–540. Rotterdam, The Netherlands: Balkema. Martel, S.J. and Peterson, J.E. Jr. 1991. Interdisciplinary characterization of fracture systems at the US/BK site, Grimesl Laboratory, Switzerland. International J. of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 28 (4): 259–323. DOI:10.1016/0148-9062(91) 90596-E. ¨ Matthai, S.K., Mezentsev, A., and Belayneh, M. 2007. Finite ElementNode-Centered Finite-Volume Two-Phase-Flow Experiments With Fractured Rock Represented by Unstructured Hybrid-Element Meshes. SPE Res Eval & Eng 10 (6): 740–756. SPE-93341-PA. DOI: 10.2118/ 93341-PA. Mavko, G., Mukerji, T., and Dvorkin, J. 1998. The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media, 289–301. Cambridge, UK: Cambridge University Press. McNally, G.H. 1987. Estimation of core measures rock strength using sonic and neutron logs. Geoexploration 24 (4–5): 381–395. DOI:10.1016/0016-7142(87)90008-1. Myers, R. and Aydin, A. 2004. The evolution of faults formed by shearing across joint zones in sandstone. J. of Structural Geology 26 (5): 947–966. DOI:10.1016/j.jsg.2003.07.008. Nanjo, K.Z., Turcotte, D.L., and Shcherbakov, R. 2005. A model of damage mechanics for the deformation of the continental crust. J. of Geophysical Research 110 (B07403). DOI: 10.1029/2004JB003438. Oda, M. 1985. Permeability tensor for discontinuous rock masses. Geotechnique 35: 483–495. Oda, M. 1986. An equivalent continuum model for coupled stress and fluid flow analysis in joined rock masses. Water Resources Research 22 (13): 1845–1856. DOI:10.1029/WR022i013p01845. Olsson, R. and Barton, N. 2001. An improved model for hydromechanical coupling during shearing of rock joints. Int. J. of Rock Mechanics and August 2009 SPE Reservoir Evaluation & Engineering

Mining Sciences 38 (3): 317–329. DOI:10.1016/S1365-1609(00) 00079-4. Pollard, D.D. and Segall, P. 1987. Theoretical displacements and stresses near fractures in rock; with applications to faults, joints, veins, dikes, and solution surfaces. In Fracture Mechanics of Rock, ed. B.K. Atkinson, 277–349. London: Academic Press. Reches, Z. and Lockner, D.A. 1994. Nucleation and growth of faults in brittle rocks. J. of Geophysical Research 99 (B9): 18159–18174. DOI:10.1029/94JB00115. Scholz, C.H. 1990. The Mechanics of Earthquakes and Faulting. Cambridge, UK: Cambridge University Press. Smart, B.G.D., Somerville, J.M., Edlman, K., and Jones, C. 2001. Stress sensitivity of fractured reservoirs. J. of Petroleum Science and Engineering 29 (1): 29–37. DOI:10.1016/S0920-4105(00)00088-7. Suppe, J. 1984. Principles of Structural Geology, 537. Upper Saddle River, New Jersey: Prentice-Hall. Townend, J. and Zoback, M.D. 2000. How faulting keeps the crust strong. Geology 28 (5): 399–402. DOI:10.1130/0091-7613(2000)28<399: HFKTCS>2.0.CO;2. Vermilye, J.M. and Scholz, C.H. 1998. The process zone: A microstructural view of fault growth. J. of Geophysical Research 103 (B6): 12223–12237. DOI:10.1029/98JB00957. Virieux, J. and Madariaga, R. 1982. Dynamic faulting studied by finite difference method. Bulletin of the Seismological Society of America 72 (2): 345–369. Wald, D.J. 1996. Slip history of the 1995 Kobe, Japan, earthquake determined from strong motion, teleseismic, and geodetic data. J. Physics Earth 44: 489–503. Wiprut, D. and Zoback, M.D. 2000. Fault reactivation and fluid flow along a previously dormant normal fault in the northern North Sea. Geology 28 (7): 595–598. DOI:10.1130/0091-7613(2000)28<595:FRAFFA>2.0. CO;2. Zoback, M.D., Barton, C.A., Brudy, M., Castillo, D.A., Finkbeiner, T., Grollimund, B.R., Moos, D.B., Peska, P., Ward, C.D., and Wiprut, D.J. 2003. Determination of stress orientation and magnitude in deep wells. Int. J. of Rock Mechanics and Mining Sciences 40 (7–8): 1049–1076. DOI:10.1016/j.ijrmms.2003.07.001.

SI Metric Conversion Factors ft* ? 3.048 E – 01 = m psi ? 6.894757 E + 03 = Pa
*Conversion factor is exact.

Pijush Paul works in the structure and geomechanics team of ConocoPhillips Subsurface Technology Group in Houston. Email:pijush.k.paul@conocophillips.com. He leads the team’s computational geomechanics program. Paul’s other projects focus on providing geomechanical models of reservoirs for completion and production optimization. He holds a PhD degree in geomechanics and MS degree in petroleum engineering from Stanford U., an MTech degree in applied geophysics from the Indian Institute of Technology, and a BS(Hons) degree in geology and physics from St. Xavier College, Mumbai, India. Mark Zoback has been a professor of geophysics at Stanford U. since 1984. His principal research interests are related to the forces that act within the Earth’s crust and their influence on processes related to plate tectonics, earthquakes, and oil and gas reservoirs. Zoback is the author of the technical reference book Reservoir Geomechanics, published in 2007 by Cambridge University Press. Peter Hennings is the manager of the structure and geomechanics group in ConocoPhillips Technology and is active in its global technical service, research, and knowledge sharing missions. He is an adjunct professor of geology at the U. of Wyoming and serves on the UW enhanced oil recovery advisory board. Hennings holds a PhD degree in structural geology from the U. of Texas (1991) and BS and MS degrees in geology from Texas A&M U. He is an honorary fellow of the Geological Society of America and is an American Association of Petroleum Geologists Distinguished Lecturer. Hennings’ geoscience specialties include seismic interpretation, fractured reservoir analysis, and geoscience instruction. 575


相关文章:
更多相关标签: