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Faults in nature commonly affect surrounding rock volumes and can as such be described as fault envelopes with a given internal geometry and architecture. Modeling techniques currently employed when modeling faults in petroleum reservoirs are mostly two-dimensional (2-D); hence, a need is present for more accurate and realistic description and quantification of deformational architectures and properties to accurately predict fluid flow in fault zones.
Fault facies (FF) modeling is a concept for three-dimensional (3-D) fault zone characterization, facies modeling of fault rocks and fluid flow simulation, which is presented here and demonstrated by the use of a synthetic fault model. FF modeling is performed by first generating a 3-D grid of the fault envelope, which includes the conventional fault plane. Second, a kinematic strain calculation is executed in the FF grid. The strain parameter is used to calculate a fault product distribution factor (FPDF), which describes the fault displacement in the fault envelope. This parameter together with strain distribution is subsequently used to condition the fault model for facies modeling. Finally, FF modeling is executed. To achieve adequate flexibility and realism, pixel-based modeling is combined with object-based modeling methods to populate the FF grid with facies.
This synthetic model shows that it is possible to honor structural outcrop observations in fault zones, and FF modeling is able to produce realistic looking fault zone deformation structures in 3-D. It is possible to implement faults with varying width and displacement, although the FF grid itself has a regular fixed width. This is highly advantageous as compared to controlling the fault geometry with the grid itself. We propose that FF modeling can improve fault zone characterization and also capture fluid flow uncertainty in fault zones in a more realistic way than is possible with 2-D methods.
Niclas Fredman received his M.Sc. degree in geology from the University of Gothenburg in 2003 and his Ph.D. in structural geology from the University of Bergen in 2007. As of 2007 he works for StatoilHydro in Stjørdal, Norway, as a structural geologist with early phase field development.
Jan Tveranger received his Ph.D. from the University of Bergen in 1995. He was working as a researcher at the Department of Earth Sciences at University of Bergen before being employed by Saga Petroleum and later at Norsk Hydro. As of 2003 he has held a position as a researcher and research program coordinator at CIPR.
Nestor Cardozo received his bachelor's degree in geology from the Universidad Nacional de Colombia in 1994 and his Ph.D. in geology from Cornell University in 2003. He is a researcher at the Centre for Integrated Petroleum Research in Bergen. His scientific interest covers faults, their related deformation, and their implementation in reservoir models.
Alvar Braathen holds a professor position at the University Centre in Svalbard, and an adjunct professor position at the University of Bergen. His main interest lies in structural geology, and especially the application of structural information to fluid flow descriptions and flow modeling. Current interests cover petroleum analog studies through extensional fault characterization by facies analysis, and fault impact on subsurface fluid flow in crystalline and metamorphic rocks.
Soleng has worked as a theoretical physicist at the University of Oslo (1987–1992), University of Pennsylvania (1992–1993), Nordic Institute for Theoretical Physics (1993–1994 and 1996–1997), and the European Organization for Nuclear Research (1994–1996). At the Norwegian Computing Center (1997–2007), he has implemented statistical geological modeling tools. He is currently working on joint seismic and electromagnetic inversion for Rock Solid Images.
Per Røe is a research scientist at Norwegian Computing Center in Oslo. He received his M.Sc. degree in industrial mathematics from the Norwegian University of Science and Technology in 2001. He joined the Norwegian Computing Center in 2002 and has been working with software development and research, currently with a focus on fault modeling.
Arne Skorstad is an assistant research director at the Norwegian Computing Center in Oslo. He holds an M.S. degree in industrial mathematics from the Norwegian University of Science and Technology. He joined the Norwegian Computing Center in 1992 and has been working with software developments and research on reservoir characterization, focusing on geostatistics.
Anne Randi Syversveen is a senior research scientist at the Norwegian Computing Center. She received her Ph.D. in statistics from the Norwegian University of Science and Technology in 1998. Since then she has worked at the Norwegian Computing Center. Her main research interest is stochastic facies models.
Faults may have a significant impact on fluid flow in hydrocarbon reservoirs, either as conduits or barriers (Caine et al., 1996; Fisher and Knipe, 1998; Fisher et al., 2001; Harris et al., 2003). The actual effect faults have on fluid flow is mostly determined by the 3-D architecture of the fault, and the spatial distribution and petrophysical properties of the fault elements inside the fault zone (Antonellini and Aydin, 1995; Knipe, 1997; Yielding et al., 1997; Flodin et al., 2001; Harris et al., 2003; Odling et al., 2004), the latter representing the volume of host rock affected by faulting. However, industrial reservoir modeling techniques include faults as 2-D planes regardless of fault zone architecture. Consequently, the impact of faults on fluid flow in reservoir models is commonly only included as a combination of grid offset and fault transmissibility multipliers across grid splits (Manzocchi et al., 1999). Fault transmissibility multipliers do not accommodate observed reservoir behavior, such as vertical- and along-strike fluid flow inside the fault zone, other than by ad hoc tuning of fault properties to production history, thereby limiting the use of these models for forecasting reservoir behavior. This is true especially for faults offsetting the entire reservoir interval. The limitations of present fault modeling methods promote the question addressed here; will faults represented as actual 3-D volumes in sandstone reservoir models improve our ability to forecast reservoir response? Considering the complexities involved in 3-D representation of deformed rock, let alone the daunting task of modeling and predicting their 3-D spatial distribution and petrophysical properties, a crucial question is whether it is technically feasible to do so.
The objective of this article is to present an approach for the 3-D volumetric representation of fault zones in siliciclastic rocks, herein referred to as fault envelopes. Concepts are highlighted by the use of a simplified synthetic reservoir model. The present study uses the fault facies (FF) method (Tveranger et al., 2005), which emphasizes subdivision of fault envelope architectures into volumetrically expressed building blocks with specific, empirically derived property attributes. FF grid cell distribution is conditioned to a calculated strain distribution in the fault envelope. This method uses 3-D object and pixel-based reservoir modeling tools to populate the fault envelope grid with FF. The present article expands on previous studies by Nøttveit (2005), Syversveen et al. (2006), and Fredman et al. (2007), who presented the first FF prototype workflow. Syversveen et al. (2006) includes a grid building algorithm that enables integration of fault envelope grids into conventional fault transmissibility multiplier reservoir models.
Within a fault envelope, deformation is highly heterogeneous and complex (Childs et al., 1997), and it is considered unfeasible to predict a single deterministic response from a faulting event in given sedimentary rocks, even if boundary conditions are fully known. Although comparable patterns can be identified when performing repeated analog experiments using identical boundary conditions, spatial arrangements will differ in detail (Davy et al., 1995). This heterogeneity favors the use of stochastic modeling techniques, which accommodate a wide range of possible outcomes treated as uncertainty in an overall general result.
Object- and pixel-based stochastic facies-modeling tools are here used to populate a synthetic fault envelope grid with FF, representing varying degrees of superimposed deformation of the host rock. Spatial distribution of fault modified rocks inside the fault envelope is controlled by a geometrical conditioning factor related to a displacement curve through the fault envelope. This is to establish the relative position inside the fault envelope of fault related rocks originating from specific beds. This displacement parameter is referred to as the fault product distribution factor (FPDF), which is calculated from a kinematic strain magnitude (or the relative variation of strain) in the fault envelope. The strain in the fault envelope is calculated based on the amount of displacement in the fault envelope grid (Cardozo et al., 2008). FF types are subsequently derived by combining the results of the spatial rock distribution with a strain inside the fault envelope.
FAULT FACIES MODELING TECHNIQUE
Introduction to Volumetric Fault Modeling
A reliable reservoir model must incorporate both depositional and structural heterogeneities. Stochastic object- and pixel-based modeling are well established methods and extensively used for producing 3-D digital models of sedimentary architectures and properties in petroleum reservoirs (Haldorsen et al., 1987; Haldorsen and Damsleth, 1990; Petit et al., 1994; Deutsch and Wang, 1996; Holden et al., 1998; Strebelle, 2002; Vargas-Gusmán and Al-Quassab, 2006). Structural heterogeneities, however, are at present mainly implemented as deterministic 2-D surfaces in reservoir models. Two-dimensional surfaces are an oversimplified way of representing the complex architectures that many faults exhibit. The impact of faults in reservoir models is therefore limited to the effects caused by the offsetting of the grid (juxtaposition) and modified flow properties expressed as fault transmissibility multipliers (Manzocchi et al., 1999). This approach is to a large extent dictated by software constraints and grid building conventions in existing standard reservoir modeling and simulation software.
Seismic scale faults as observed in outcrop exhibit a wide range of fault-architectural elements that together define a volumetrically expressed fault envelope, which is generated during the deformation of the host rock. Fault envelopes can be subdivided into a fault core and a surrounding damage zone (Wallace and Morris, 1986; McGrath and Davison, 1995; Caine et al., 1996). A fault envelope has three main characteristics. (1) It accommodates the total displacement of the fault, which is expressed as a displacement curve or function at right angles to fault strike, rather than along a single fault plane. (2) The fault envelope contains rocks (elements) originating from the undeformed host rock but with altered petrophysical properties that correspond to the degree of deformation it has been subjected to. The main elements are (a) fault rocks (breccia, gouge), including shale gouge smear in membranes and pockets; (b) slip surfaces and other fractures; (c) lenses of more or less preserved host rock, as well as fault rock; and (d) discrete, tabular zones, such as deformation bands (Braathen et al., 2007). (3) A fault envelope generally exhibits significant petrophysical anisotropy, with fault envelope elements arranged with their longest axes parallel to fault strike and dip. These three factors together ultimately influence fluid flow inside the fault envelope and may even provide communication across faults in situations where the fault offsets the entire reservoir section. Observations of structural heterogeneities of extensional faults in sandstone-shale sequences advocate modeling of seismic scale faults as volumetric entities to capture complex architectures. Present techniques do not account for 3-D fault zone architecture inside the fault envelope other than by adding deterministic links between nonjuxtaposed cell interfaces during simulation history matching.
The FF modeling method (Tveranger et al., 2005; Braathen et al., 2007) is a concept aimed at 3-D fault envelope description and stochastic fault modeling. In the same way that sedimentary facies are used to describe depositional environments using “structural building blocks” of different scales (Reading, 1986), FF are used to describe tectonically deformed rock volumes, which will benefit the analysis of fault envelope elements and architectures. A complete FF modeling workflow consists of four modeling steps: (1) FF grid construction, (2) facies modeling, (3) petrophysical modeling, and (4) fluid flow simulation. In this study, we are only dealing with the first two steps, grid construction and facies modeling. Previous studies of facies modeling of fault rocks along similar lines have been attempted by Nøttveit (2005), Syversveen et al. (2006), Berg and Øian (2007), Fredman (2007), and Fredman et al. (2007).
An FF modeling workflow starts with the construction of an FF grid (Figure 1), which envelopes the fault that should be modeled. The commercial fault modeling system Havana (Hollund et al., 2002) is used for converting a conventional reservoir model with faults expressed as displacements across grid splits into an FF reservoir model with 3-D volumetrically gridded faults. In Havana, it is possible to define the width of the FF grid, as well as the desired xyz-grid resolution (Syversveen et al., 2006). Havana needs two input parameters to implement an FF grid in a standard corner point grid (Ding and Lemonnier, 1995): (1) a conventional grid file using the eclipse format (GRDECL) (2) and a description of the fault pillars, e.g., the RPF format (reservoir modeling software [RMS] pillar fault format) (see Roxar, 2006, for details on file format).
Once the FF grid is generated, the next step is to populate the grid with relevant FF. The standard method for modeling sedimentary facies is the classical two-stage approach (Haldorsen and Damsleth, 1990; Damsleth et al., 1992), where the first stage is discrete facies modeling, and the second stage is petrophysical modeling. With minor adaptations, this approach is also suitable for FF modeling. In this study, only facies modeling has been addressed using facies-modeling tools that were originally developed for sedimentary facies modeling. To facilitate flexible and realistic FF modeling, a combination of object modeling (Haldorsen and Damsleth, 1990; Wietzerbin and Mallet, 1993) and sequential indicator simulation (SIS) (Seifert and Jensen, 1997) was used. Object-based modeling approaches are commonly useful if shapes and sizes of the modeled objects in the reservoir are known. Object modeling can thus be an appropriate method for modeling sand or mud lens objects. If limited knowledge is available about reservoir geometries, variogram-based pixel modeling methods are more useful, where it is possible to acknowledge trends, reservoir direction continuities, and facies fractions. Thus, a combined use of object- and pixel-based tools is an efficient way to facilitate FF modeling.
Reservoir trends and facies fractions can commonly be observed from well logs or, in a larger scale, from seismic data. However, it is not a common practice to core faults during drilling, which means that detailed fault data are lacking from most reservoirs. This is however not a problem because the FF modeling method uses the surrounding host rock lithology and regional and local deformation style to stochastically predict fault architecture and petrophysical properties in the fault envelope. An FF database including information on predeformation lithology and postdeformation facies volume fraction, fault architecture and continuity, and petrophysical properties of the generated fault rocks is currently being compiled (Braathen et al., 2007; Rotevatn et al., 2007; Schueller and Braathen, 2007). The FF database is based on outcrop and subsurface data, as well as literature studies (Torabi and Skar, 2004) and experimental data (Torabi et al., 2007). Especially, field analogs with relevant lithologies and deformation histories to the Norwegian Continental Shelf reservoirs have been investigated.
FF describes fault deformation in terms of structural building blocks, which is based on three main structural elements. Extensional faults in siliciclastic rocks can be described by isolated structural elements or element combinations of (1) fractures, slip surfaces, and deformation bands; (2) fault rock membranes; and (3)lenses.
This approach is similar to the classical sedimentary facies and facies associations (Reading, 1986), which describe depositional environments. In this study, we use these three structural elements to demonstrate how a simple synthetic fault envelope can be described and modeled stochastically using the FF approach.
Discrete structures can be subdivided into shear and tension fractures, and mm-wide tabular shear zones. In sandstone, such zones occur as deformation bands. The latter commonly reveal shear and may host fault rocks with low permeability (e.g., Aydin, 1978; Antonellini and Aydin, 1994). Fault rocks (Sibson, 1977; Braathen et al., 2004) appear in intensely sheared and relatively thin zones, here referred to as fault rock membranes, which commonly define the fault core. In an FF modeling context, fault rock membranes can be gouge formed from cataclasis of sandstone or shale gouge smear. For more details on lenses and fault rock membranes, see, e.g., Gibbs (1984), Gabrielsen and Clausen (2001), Clausen et al. (2003), and Berg (2004), Kristensen et al. (2005). Lenses are here defined as ellipsoid bodies of host rock (sometimes bound by slip surfaces) that have been incorporated into the fault envelope at the time of deformation. In outcrop analogs, lenses in faults may exhibit well-preserved host rock or display varying degrees of deformation. An FF model includes lenses and fault rock membranes as explicit features, whereas damage zone fractures and deformation bands are typically included implicitly as upscaled features. We are not dealing with upscaling of fault architecture in this article, but the interested reader can find related information in Wen and Gomez-Hernandez (1996), Odling et al. (2004), and Nøttveit (2005), and a general review of upscaling of geological models is compiled by Durlofsky (2005).
Fault Facies Grid Conditioning
The FF gridding of the fault envelope results in a larger volume than what was originally included in the grid (Figure 2). Therefore, it is necessary to compensate for this extra volume. This is done either by filling up the extra volume with facies that originate from above and below the modeled interval or by making the extra volume undefined. For a regular fault, the extra volume is calculated (Figure 2) according to equation 1, but the increase is ultimately controlled by the FPDF function. In equation 1, V is the extra volume, W is the FF grid width (m), l is the fault length (m) in strike direction, and d is fault displacement (m). The spatial distribution of the modeled facies inside the fault envelope is controlled in two different ways. The pixel-based modeling is conditioned to an FPDF function, whereas the object-based modeling (lenses) is conditioned to a manually defined lithology-dependent 3-D grid parameter. An FPDF function is a mathematical way to characterize fault displacement statistically across the FF grid, and it also serves as a conditioning factor for the facies modeling. Generally, a fault envelope in sandstone is highly heterogeneous and consists of a discrete number of slip planes (e.g., Aydin and Johnson, 1978; Shipton et al., 2002; Shipton and Cowie, 2003), but it is considered unfeasible to actually predict fault deformation response deterministically. Thus, a slip-surface frequency function (Figure 3) describes fault displacement in the FF grid, where the bulk displacement occurs in the central part of the fault envelope, defined as the fault core. The FPDF can be calculated in two different ways: (1) via a volume-based strain algorithm (Cardozo et al., 2008) or (2) through a user-defined FPDF function. The volume-based strain algorithm is based on a simple fault displacement model (displacement decreases with the square of the distance from the fault). Displacement is assigned to the nodes of the regular grid based on the displacement model of the entire grid (the summation of the displacement models of all faults in the grid). Finite strain is then computed via maximum principal stretch in the regular grid using a finite difference scheme and subsequently is interpolated into the FF grid (Figure 4).
Once the strain has been calculated, it is imported into the reservoir modeling software as a continuous 3-D grid parameter, from which the FPDF function subsequently is calculated via a series of transformation functions (Figure 5). To avoid FF displacement inconsistencies, the strain grid parameter is first averaged in the z-direction. Thus, occasional strain extreme values are eliminated, which facilitates a more robust and smooth displacement pattern inside the fault envelope.
The user can also define the FPDF manually, either by defining a cumulative distribution function or a piecewise linear function mathematically (Figure 3). The use of a mathematical function provides flexibility to define arbitrary deformation styles and displacement patterns across the fault, and it is also possible to modify a previously Havana calculated strain. The FPDF function operates on the grid cells in the fault envelope, i.e., displacement is implemented (Figure 6) regardless of lithology, which means that it is a strict geometrical operation. Note, however, that the grid itself is not being physically displaced, but displacement is implemented by changing grid cell values. Figure 7 shows four examples of FPDF functions and the implications of using different displacement patterns through the FPDF functions. Berg and Skar (2005) argue that the damage zone in the hanging wall commonly is wider and more intensely deformed than the footwall, in which case the FPDF can shift the deformation toward the hanging wall (Figure 7b), or a specific width of the fault core can be explicitly defined. A simpler staircase geometry of the fault envelope is acquired with the piecewise linear function, whereas the cumulative distribution function generates a more complex, smooth geometry.
The volume fraction of each FF that should be present in the fault envelope grid is extracted from the prefaulted grid, based on the host rock lithology on each side of the fault.
Explicit Modeling of Lens Objects
To model lens objects in fault envelopes, lens size, shape, volume fraction, and lens-lens interaction must be defined (see Fredman et al., 2007, for more details on lens modeling). A theoretical maximum lens object height (Figure 8) can be extracted from the host rock layer thickness from where the lens originates. The theoretical maximum height of a single lens (originating from a single lithological layer) is calculated by equation 2: where aH and aF are the faulted layer's thickness in meters (nearest grid block, hanging wall and footwall side of the fault, respectively), h is the maximum height, and α is the angle at which the lens is cut by the fault. L is a lithology and deformation-style-dependent parameter, which describes the ability of a particular lithology to form lenses when exposed to faulting. For example, a competent lithology generally forms larger lenses than a less competent lithology. This is based on the more competent lithology's mechanical properties, which favor a more brittle deformation style (Lindanger et al., 2007). The angle α at which a lens object is detached from the host rock is likely to approximate with a local fault dip, which may facilitate a greater lens height than the host rock layer thickness (Figure 8). However, one has to keep in mind that multilayer lenses are also observed in outcrop. Lenses formed during more ductile conditions may also exhibit vertical lengths (lens height) exceeding the thickness of the host rock from which they originated because of local stretching. If stretching is suspected, the L parameter can be used to adjust the length of the vertical axes to the expected value.
From the outcrop data, it has been observed that sand lenses can be bound by slip surfaces and/or shear zones (Clausen et al., 2003). Lenses are thus commonly enveloped by low-permeability fault rock membranes, which is why we have included a modeling option to implement such membranes around each lens object. This is done by a search algorithm that scans through all grid cells in the FF grid and converts all grid cells in each lens object that are in physical contact with another lens object, or in physical contact to a nonlens facies, to lens-membrane facies.
Fault Facies Properties
The link between host rock and post faulting FF is one of the most important issues in FF modeling, because the petrophysical properties of fault rocks and fault architecture strongly influence fluid flow inside fault envelopes. As mentioned previously, FF modeling links host rock lithology and deformation style by using a database, which is derived from outcrop, subsurface, and experimental data. It is not the scope of this article to address the implementation of this database and its properties (e.g., permeability, porosity, and architecture), but instead, we include an example of an FF workflow to demonstrate the potential of the method.
RESULTS OF SYNTHETIC FACIES MODELING
Pixel-Based Facies Modeling
A synthetic model (Figure 9) with a single normal fault was constructed to illustrate the different steps in an FF modeling workflow (model details in Table 1). FF structural building blocks numbers 1 and 2 have been modeled using SIS, where the simulation was conditioned using precalculated FPDF functions. The model has five sandstone units of different thicknesses, and they are interbedded with six mudstones of equal thicknesses. Nine facies were included in the model: two host rock facies, six FF, and one undefined facies. A brief description of the included facies and their potential properties is presented in Table 2. The previously described modeling workflow (Figure 5) was applied to the FF grid to displace it and subsequently distribute these FF in the fault envelope grid. Facies F11, F12, F21, and F22 were modeled with SIS, whereas the lens/lens-membrane facies (F4, F44) (structural building block number 3) were modeled with object modeling, which is described in the next section.
Strain distribution inside the fault envelope was calculated using Havana and imported into the reservoir modeling software RMS (Roxar, 2006) as a continuous 3D grid parameter, where it subsequently was converted to a cumulative displacement parameter (Figure 10). Four FF probability functions, one for each FF, were then calculated (Figure 11a–d). Two indicator (SIS) realizations were executed using these four probability functions as conditioning factors for each of the four facies F11, F12, F21, and F22), where the outcomes are shown in Figure 11e–f. Also, a piecewise linear FPDF function was manually defined as a continuous 3D grid parameter and subsequently used as a conditioning factor for a third indicator simulation (Figure 11g–h). The piecewise linear function (Figure 11g) shows an example of a narrower fault envelope and, consequently, a different spatial distribution of the FF appears, where the damage zone is less intensely deformed than in the previous two examples. It is also clearly visible that facies F21 is discontinuous in Figure 11h, which is a direct consequence of the discontinuous conditioning factor it used for the facies modeling (Figure 11g). In this case, the mudstones are considered too thin to form a continuous smear along the entire fault displacement (Shale Gouge Ratio (SGR) ranges between 0.095–0.195). This example illustrates a way to include the Shale Gouge Ratio (Yielding et al., 1997) algorithm into the FF modeling workflow.
The width and architecture of the fault are completely controlled by the FPDF function, although the fault envelope grid has a predefined width. Fault envelope architecture and width may thus vary both along strike and dip, which illustrates the flexibility of the method. It does not matter that the FF grid itself is completely regular in xyz, the fault envelope width and architecture are even so controlled by the FPDF function.
Object-Based Modeling of Lenses
Although facies F11 may be considered to be sand lenses, it may be desirable to explicitly model lens facies objects separately from the other facies and subsequently merge them with the previously executed indicator realization. Sand layer 2 (80-m [262.5 ft]-thick sandstone) was subjected to lens object modeling using a Gaussian object size of 10 × 100 × 80 m (32.8 × 328 × 262.5 ft) (xyz). Because of a high strain in the center of the fault envelope (fault core), less probability of encountering intact lens-shaped bodies there is observed. For spatial conditioning, we manually defined a linear discontinuous probability function, from hanging wall to footwall. To reflect the low sand lens probability, this probability function has a local minimum value in the center of the fault envelope (Figure 12a). An object-based modeling job was executed, and the output is seen in Figure 12b. Lens-membrane (F44) implementation was also executed (Figure 12c) by converting enveloping lens facies (F4) to lens-membrane facies (F44). In Figure 13, the lens object-based modeling outcome is seen in 3-D view, where the lens objects have been merged with the indicator simulation in Figure 11e. A complete workflow for the facies modeling is shown in Figure 14.
We present a new fault modeling method that transforms a faulted, conventional reservoir model to a volumetric grid (FF grid). The transformation (grid construction) is conducted, as described by Syversveen et al. (2006), and subsequently populated with four FF, which represent varying degrees of deformation. The emphasis herein is on representing and modeling structural features in a volumetric representation of a fault, highlighting the actual modeling technique. Much of the data input to FF modeling remains to be established, for instance, detailed data about lens sizes and shapes, spatial distribution, and petrophysical properties of fault rocks. Despite this, it is important to establish a complete technical framework, which allows these features to be included in reservoir models. This article shows the feasibility of 3-D fault envelope modeling and hopefully stimulates further research into fault rock properties and fault architectures with the main objective of fault representation in reservoir models.
FF modeling aims at reproducing complex fault architecture by the use of stochastic methods. An important validation is therefore to compare FF modeling results both with faults in outcrop, and with modeling results from other modeling tools using dynamic deformational algorithms based on, for example, material properties. Realism of the presented fault models is illustrated in Figure 15, where two outcrop examples and two discrete element models (DEM) exhibit similarities with the FF models. The DEM models (Figures 15c, f) have been modeled as assemblages of rigid particles, where at particle contacts the mechanical behavior is represented by springs in compression and shear. A slip model allows for particle slip whenever the ratio between shear and normal contact forces is greater than the particle friction. The radius of the particles has been varied randomly between 35 and 70 mm (1.4 and 2.8 in.), and the model has 30,000 particles. The blue layers have higher friction than the yellow layers and additionally have bonding (cement with a shear and tensile strength) between the particles. Therefore, the blue layers are more competent and brittle than the yellow layers.
Fault Geometry and Spatial Distribution of Facies
Pixel-based modeling was also tested on faults with more complex geometries, such as varying fault displacement (Figure 16). This shows that FF modeling is not limited to simple, regular faults but can be applied on more advanced geometries as well. Pixel-based FF modeling should work regardless of fault geometry and fault throw variations because it accepts any 3-D grid parameter as a conditioning factor. This means that the strain calculation and the gridding algorithm are actually the limiting factors for FF modeling, not the facies modeling. The similarity of the strain field of the FF modeling with the strain field of a 3-D trishear simulation (Figure 16d) further supports the validity of the FPDF method. Trishear is a kinematic model for fault propagation folding in which the decrease in displacement along the fault is accommodated by heterogeneous shear in a triangular zone radiating from the tip line.
We believe that pixel-based FF modeling is capable of handling even more complex situations, such as varying fault dip and throw, intersecting faults, and listric and curved faults, provided that a 3-D strain parameter is available. At present, however, it is not possible to calculate strain for faults that change dip perpendicular to strike (e.g., listric faults), caused by current software limitations in Havana.
For object-based modeling, the situation is slightly more complex, because at present there are no means of linking object size to geometrical position in the grid, i.e., present software does not allow object-based modeling with object size as a function of fault throw. Hence, more work is required to execute object-based modeling in more complex FF grids, with large variations in fault throw as the main complicating factor.
Several factors control fault envelope width such as lithology, fault displacement, fault type, deformation style, and deformation history. Preferably, all these factors should be used as guidance when implementing the FF grid and FPDF function. For example, a shale-rich sequence that is faulted in an unconsolidated state will promote a thinner fault envelope than a faulted well-consolidated sandstone will (e.g., Sperrevik et al., 2002). For technical reasons, it is at present not feasible to implement the FF grid to follow a varying fault envelope width. Instead, the FPDF function controls the fault envelope width via the calculated strain function. In this way, it is possible to implement faults with varying fault width along strike and dip, although the fault envelope grid itself possesses a regular geometry. Faults in nature commonly show large variance in width in all directions along the fault (Shipton et al., 2002; Walsh et al., 2002). In FF modeling, width variance is so far limited to variations that are controlled by geometrical constraints; e.g., a dying out fault will get a more narrow strain distribution toward the fault tip because the displacement decreases, which promotes a narrower fault envelope (Figure 16b, c). Additional variance can be statistically defined by facies-modeling variograms. However, lithology- and deformation-style-dependent fault envelope variation has not been addressed here, because the Havana strain calculation is so far only based on fault displacement. To be able to implement lithology and deformation style dependent fault envelope width variation, the most obvious way forward is to include an option for deformation style and lithology-based parameters in the strain calculation. This opens up for more realistic fault geometries, and fault intersections and overlapping fault envelopes would especially benefit from such considerations (Rotevatn et al., 2007).
Grid Resolution and Modeling
For standard modeling of sedimentary structures, a grid resolution that is less than half of the smallest object size that is to be modeled is generally recommended. In our case, the modeled lens object size is 10 × 100 × 80 m (32.8 × 328 × 262.5 ft) (xyz), which indicates a theoretical coarsest possible grid resolution in the FF grid of 5 × 50 × 40 m (16 × 164 × 131 ft) (xyz) to maintain reasonable reservoir description of the fault envelope. However, for object modeling in fault envelopes, the spatial vertical distribution is important, which further increases the need for a high grid resolution. Although connectivity and volume fraction will be reasonably honored with such a grid resolution (5 × 50 × 40 meters, [16 × 164 × 131 ft]), the vertical accuracy will be lost. More likely, the thinnest host rock layer that will be incorporated as an FF will determine the coarsest possible vertical grid resolution instead of object sizes from discrete layers. With the present gridding algorithms, it is not possible to implement coarser fault envelope grid sizes than the surrounding host rock grid resolution.
A flow calculator (e.g., Eclipse) favors an orthogonal grid when it solves the flow equations, preferably with the longest axis (commonly, x and y axes) parallel with the major flow direction in the grid. A grid cell's relative axis lengths are referred to as grid cell aspect ratio. A typical geocellular model might have a grid resolution of approximately 50 × 50 × 1 m (164 × 164 × 3.3 ft) (xyz), which means that the horizontal (x and y axes) grid resolution is 50 times less than the vertical grid resolution (z direction). The major flow direction is commonly in the x-y direction, which means that the grid cell aspect ratio in this case is favorable. In 3-D fault envelopes, however, the fluid flow direction is commonly perpendicular to the reservoir scale fluid flow direction, which means that the grid cell aspect ratio in this case is not favorable. To minimize the grid cell aspect ratio problem, we propose that if the horizontal grid resolution in the geocellular model is small (1–2 m [3.3–6.6 ft] or less), FF modeling may better be executed directly in the simulation grid, where the vertical grid resolution is lower. Generally, we conclude that a vertical grid resolution that corresponds to 1/50 of the horizontal grid resolution is more than enough for FF modeling.
Another issue with FF grid resolution is when modeling includes small objects, for example, lenses (F4) with enveloping lens membranes (F44), which requires an even higher grid resolution. The FF modeling in this article was executed with a grid resolution in the fault envelope of 3.33 × 10 × 3.33 m (10.9 × 32.8 × 10.9 ft) (xyz), which yields adequate resolution for the modeled lens size of 10 × 80 × 100 m (32.8 × 262.5 × 328 ft) (xyz). To accurately model the impact of enveloping lens membranes, however, a higher grid resolution is required, which is easily seen in Figure 17. In Figure 17, the previously presented fault model (Figure 17a–c) is compared to a corresponding model (Figure 17d–f) with a higher grid resolution. Notice that both models have the same resolution in z direction. It was previously proposed that the z direction resolution is generally not a problem for FF modeling, which is also seen in Figure 17. The x direction grid resolution, however, is drastically affecting the number of grid cells ascribed lens-membrane facies. The lens-membrane facies/lens facies ratio is 0.77 for the coarser model, whereas it is only 0.49 for the high-resolution model.
Because the contrast in fluid flow properties between lenses (defined as more or less deformed host rock) and enveloping fault rock membranes is large, up to several orders of magnitude (Antonellini and Aydin, 1994), the lens membranes in Figure 17c will significantly reduce the bulk effective permeability and thus reduce fluid flow across the fault. For this purpose, it is proposed that for further development of FF object modeling, upscaling techniques that specifically can handle highly contrasting lens permeabilities should be developed. A simple approach is to apply the harmonic average across the fault envelope, which in fact will not generate very different results between Figure 17c and f. However, outcrop observations indicate that lenses are sometimes enveloped by discontinuous fault rock membranes. In this case, the harmonic average might underestimate the bulk permeability across the fault. We suggest that outcrop studies and small-scale fluid flow simulation studies be undertaken to properly evaluate lens impact on fluid flow. Similar approaches to the ones by Odling et al. (2004) and Nøttveit (2005) might be appropriate.
Grid cells in the outer damage zone can possibly be upscaled to near or equal to host rock grid resolution. However, the interface between the fault envelope and the unfaulted host rock should preferably be smooth to facilitate subsequent discretization of the fluid flow equations. Possibly, a stepwise increase in grid resolution is necessary to facilitate adequate accuracy of fluid flow computation across the fault.
Fault Facies in Carbonates
So far, FF modeling has mainly been focusing on siliciclastic reservoirs, but roughly 50% of the world's petroleum reservoirs are found in carbonates. Depositional mechanisms differ considerably for carbonates as compared to siliciclastic rocks. Fault deformation, however, shows in many cases similarities between carbonates and siliciclastic rocks, with many common elements such as lenses, breccias, slip surfaces, cataclasis, and deformation band development (e.g., Nøttveit, 2005; Bonson et al., 2007) . Once the FF modeling workflow has been established (FF gridding, facies modeling, petrophysical modeling, and fluid flow simulation), the modeling technique can be applied to any database, carbonates or siliciclastic rocks. In addition, many carbonates are heavily fractured, which means that fault parallel fluid flow in fault envelopes is an important component, which could be addressed with facies modeling.
The main objective of this article is to demonstrate the feasibility of a new concept for 3-D volumetric FF modeling of fault envelopes. The focus has been on the technical issues concerning FF modeling and especially how to produce realistic fault envelope architectures, which is a starting point for further refinement and improvement of the FF method. The following conclusions may be drawn from this article:
By honoring structural outcrop observations, FF modeling is able to produce realistic looking fault envelope deformation structures in 3-D, as well as producing similar geometries as are produced by mechanical DEM modeling and kinematic fault modeling. This shows that it is technically feasible to represent and stochastically model faults as volumetric entities. FF modeling is also proposed to have the potential of capturing fluid flow uncertainty in fault envelopes in a more realistic way than what is done with current methods.
The FPDF concept makes it possible to implement faults with varying width and displacement, although the grid itself has a regular fixed width. To be able to realistically model faults as volumetric entities, this is an absolute prerequisite. Also, it is highly advantageous to control the fault geometry with an FPDF function, instead of the grid itself.
A typical North Sea geocellular model grid resolution is 50 × 50 × 1 m (164 × 164 × 3.3 ft), which may pose a problem to grid aspect ratio in FF modeling. The major heterogeneity direction in a dip-slip fault is perpendicular to the fault, whereas the grid resolution might be up to 50 times higher in the z direction (vertical). This anisotropy can lead to nonfavorable grid aspect ratios. To improve the grid cell aspect ratio in the fault envelope grid, it may be beneficial to execute the FF modeling directly in the upscaled simulation grid, which commonly has a lower vertical grid resolution than the geological grid.
Lens-membrane modeling requires high grid resolution, especially in the grid direction normal to the modeled fault. At this time, it is not believed that explicit detailed lens modeling is feasible for a full-scale reservoir model. However, if upscaling techniques can be employed in such a way that permeability contrasts between lenses and lens membranes can be preserved, it will be possible to capture lens impact on fluid flow in larger models (more grid cells) as well.
The authors would like to thank the Norwegian Research Council for financial support through the Petromaks program, and Statoil and ConocoPhillips are thanked for sponsoring the Fault Facies project. Jim Granath and one anonymous reviewer are thanked for the help on improving the quality of this manuscript.
- Manuscript receivedJune 30, 2007.
- Revised manuscript receivedNovember 7, 2007.
- Revised manuscript receivedMay 5, 2008.
- Final acceptanceJune 9, 2008.