Multiscale geological reservoir modelling in practice

Geological Society, London, Special Publications Multiscale geological reservoir modelling in practice Philip S. Ringrose, Allard W. Martinius and Jostein Alvestad Geological Society, London, Special Publications 2008; v. 309; p. 123-134 doi:10.1144/SP309.9

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Multiscale geological reservoir modelling in practice PHILIP S. RINGROSE, ALLARD W. MARTINIUS & JOSTEIN ALVESTAD Statoil Research Centre, N-7005 Trondheim, Norway (e-mail: [email protected]) Abstract: Geological systems exhibit variability and structure at a wide range of scales. Geological modelling of subsurface petroleum reservoirs has generally focused on the larger scales, driven by the types of measurement available and by computation limitations. Implementation of explicitly multiscale models of petroleum reservoirs is now realistically achievable and has proven value. This paper reviews the main approaches involved and discusses current limitations and challenges for routine implementation of multiscale modelling of petroleum-bearing rock systems. The main questions addressed are: (a) how many scales to model and upscale; (b) which scales to focus on; (c) how to best construct model grids; and (d) which heterogeneities matter most? The main future challenges identified are the need for improved handling of variance and more automated construction of geological and simulation grids.

This paper reviews implementation of multiscale geological modelling for oil and gas field reservoir studies. Multiscale reservoir modelling is defined here as any method which attempts to explicitly represent the rock properties at several scales within a petroleum reservoir. In geologically based multiscale modelling, the scales modelled are based on geological concepts and processes, and the models are designed for use in flow simulation, production forecasts and field development planning. The more general issue of scaling up flow properties is not considered in detail; that is, numerical or analytical methods for estimating effective or equivalent flow properties at a larger scale, given some set of finer-scale rock properties. Upscaling methods for single and multiphase flow are reviewed elsewhere (e.g. Renard & de Marsily 1997; Barker & Thibeau 1997; Ekran & Aaasen 2000; Pickup et al. 2005).

Multiscale geological modelling concepts The importance of multiple scales of heterogeneity for petroleum reservoir engineering has been recognized for some time. Haldorsen & Lake (1984) and Haldorsen (1986) proposed four conceptual scales associated with averaging properties in porous rock media: microscopic (pore-scale), macroscopic (representative elementary volume above the pore scale), megascopic (the scale of geological heterogeneity and or reservoir grid blocks) and gigascopic (the regional or total reservoir scale). Weber (1986) showed how common sedimentary structures including lamination, clay drapes and crossbedding affect reservoir flow properties, and Weber & van Geuns (1990) proposed a framework for constructing geologically based reservoir models for different depositional environments. Corbett et al. (1992) and Ringrose et al. (1993)

argued that multiscale modelling of water– oil flows in sandstones should be based on a hierarchy of sedimentary architectures, with smaller-scale heterogeneities being especially important for capillary-dominated flow processes (Huang et al. 1995). The hierarchy of sedimentary architectures may be difficult to infer. Campbell (1967) established a basic hierarchy of sedimentary features related to fairly universal processes of deposition, namely lamina, laminasets, beds and bedsets. Miall (1985, 1988) showed how the range of sedimentary bedforms can be defined by a series of bounding surfaces from a first order surface bounding the laminaset to fourth (and higher) order surfaces bounding, for example, composite point-bars in fluvial systems. Figure 1 illustrates the geological hierarchy for an example heterolithic sandstone reservoir. Lamina-scale, lithofacies-scale and sedimentary sequence-scale are the most important elements, although further scales and components can undoubtedly be argued. In addition to the importance of correctly describing the sedimentary length scales, structural (Fig. 1d) and diagenetic processes act to modify the primary depositional fabric. Numerical modelling at the pore-scale has been widely used to better understand permeability, relative permeability and capillary pressure behaviour for representative pore systems (e.g. Bryant & Blunt 1992; Bryant et al. 1993; McDougall & Sorbie 1995; Bakke & Øren 1997; Øren & Bakke 2003). Pore-scale modelling allows flow properties to be related to fundamental rock properties such as grain size, grain sorting and mineralogy. The application of pore-scale models routinely in larger-scale models requires a framework for assigning several pore-scale models within assumed lamina or lithofacies-scale models. Kløv et al. (2003) and

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 123– 134. DOI: 10.1144/SP309.9 0305-8719/08/$15.00 # The Geological Society of London 2008.

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Fig. 1. Field outcrop sketches illustrating multiscale reservoir architecture. (a) Sand and silt laminasets from a weakly bioturbated heterolithic sandstone. (b) Sandy and muddy bedsets in a tidal deltaic lithofacies. (c) Prograding sedimentary sequences from a channelized tidal delta. (d) Fault deformation fabric around a normal fault through an interbedded sand and silty clay sequence.

Theting et al. (2005) give recent examples where pore to field upscaling has been implemented. Statistical methods for representing the spatial architecture of geological systems generally fall into two classes. Sequential Gaussian or indicator simulation provides a robust framework for integrating sparse data from well or seismic observations and creating equiprobable maps of interwell architecture (e.g. Journel & Alabert 1990). Object modelling (e.g. Holden et al. 1998) involves the generation of discrete geological objects using a marked point process. Commonly, the two approaches are combined, with object-based models giving the geological framework and continuous Gaussian simulation providing a field of property variation within and between objects. Process-based approaches also employ conventional geostatistical methods but add further constraints to create more realistic models of 3D sedimentary architecture (e.g. Rubin 1987; Wen et al. 1998; Ringrose et al. 2003). Multipoint geostatistical and pattern recognition methods (Strebelle 2002;

Caers 2003) allow further potential for incorporating the detailed textures of 3D geological heterogeneities into reservoir simulation models. These developments have resulted in a wide range of methods available for geological reservoir modelling. Here, the implementation of multiscale modelling using these approaches is discussed. In particular, the following questions are considered: (1) How many scales to model and upscale? (2) Which scales to focus on? (3) How to best construct model grids? (4) Which heterogeneities matter most?

How many scales to model and upscale? Despite the inherent complexities of sedimentary systems, dominant scales and scale transitions can be identified (Fig. 2). These dominant scales are based both on the nature of rock heterogeneity and the principles of establishing macroscopic

MULTISCALE RESERVOIR MODELLING

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Fig. 2. Example of geologically based reservoir simulation models at four scales: (a) Model of pore space used as the basis for multiphase pore network models from Øren & Bakke 2003 (50 mm cube); (b) Model of laminasets within a tidal bedding facies from Nordahl et al. 2005 (dimensions 0.05 m 0.3 m 0.3 m); (c) Facies architecture model from a sector of the Heidrun Field showing patterns of tidal channel and bars (dimensions 80 m 1 km 3 km); (d) Reservoir simulation grid for part of the Heidrun Field illustrating grid cells displaced by faults in true structural position (dimensions 200 m 3 km 5 km).

flow properties. The four principal scales result in three scale transitions: (1) Pore to lithofacies. This is where a set of pore-scale models is applied to specific models of lithofacies architecture to infer representative or typical flow behaviour for that lithofacies. The lithofacies is a basic concept in the description of sedimentary rocks and presumes an entity that can be recognized routinely. The lamina is the smallest sedimentary unit at which fairly constant grain deposition processes can be associated with a macroscopic porous medium, and the lithofacies comprises some recognizable association of lamina and laminasets. In certain cases where variation between laminae is small, pore-scale models could be applied to the laminaset or bedset scales. (2) Lithofacies to geomodel. This is where a larger-scale geological model, comprising a sequence stratigraphic model and structural model, postulates the spatial arrangement of lithofacies or rock units. Here, the geomodel is taken to mean a geologically based model of the reservoir, typically resolved at the sequence or zone scale. Other terms used are shared earth model, geological architecture model or static rock model. Uncertainties are inherent in the geomodel; however, some degree of expectation of spatial trends is essential.

(3) Geomodel to reservoir flow simulator. This stage may often be mainly required due to computational limitations, but is nevertheless important to ensure good transformation of a geological model into three-dimensional grid optimized for flow simulation (e.g. within the constraints of finitedifference multiphase flow simulation). Features related to structural deformation (faults, fractures and folds) occur at a wide range of scales (Walsh et al. 1991; Yielding et al. 1992) and may not naturally fall into a stepwise upscaling scheme. Structural features are typically incorporated at the geomodel scale; however, effects of smaller-scale faults may also be incorporated as effective properties using upscaling approaches. Typically, structural features are included as a two-fold hierarchy: explicitly modelled faults and fractures (larger scale) and implicitly modelled faults and fractures (smaller scale). The incorporation of fault transmissibility into reservoir simulators is considered elsewhere (e.g. Manzocchi et al. 2002). Conductive fractures may also affect sandstone reservoirs, and are often the dominant factor in carbonate reservoirs. Approaches for multiscale modelling of fractured reservoirs have also been developed (e.g. Bourbiaux et al. 2002).

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Historical focus over the last few decades has been on including increasingly more detail into the geomodel, with only one upscaling step being explicitly performed. Full-field geomodels are typically in the size range of 1–10 million cells with horizontal cell sizes of 25–100 m and vertical cell sizes of order 0.5– 10 m. Multiscale modelling allows for better flow unit characterization and improved performance predictions (e.g. Pickup et al. 2000; Scheiling et al. 2002). There are also examples where million-cell models are applied at the sector or near-well model scale, reducing cell sizes to the dm-scale. Detailed modelling of the near-well region generally also requires methods to correctly model radial flow geometry (e.g. Durlofsky et al. 2000). Recent focus on explicit small-scale lithofacies modelling includes the use of million cell models with mm to cm size cells (e.g. Ringrose et al. 2005; Nordahl et al. 2005). Numerical pore-scale modelling employs 0.1–1 million network nodes (e.g. Øren & Bakke 2003). Model resolution is always limited by computational power, and although continued efficiencies and memory gains are expected in the future, the use of available numerical discretization at several scales within a hierarchy is clearly needed, instead of continually driving for higher resolution at one of the scales (typically the geomodel). Upscaling methods impose further limitations on the value and usability of models within a multiscale setting. In conventional upscaling from a geological model to a reservoir simulation grid, the various approaches used cover a range of degrees of simplification (we use a Cartesian coordinate convention with x and y as the horizontal axes and z as the vertical axis; Dx, Dy and Dz refer to grid cell dimensions): (1) Averaging of well data directly into the flow simulation grid. This approach essentially ignores upscaling and neglects all aspects of smaller-scale structure and flows. The approach is fast and simple and may be useful for quick assessment of expected reservoir flows and mass balance. It may also be adequate for very homogeneous and high permeability rock sequences. (2) Single-phase upscaling only in Dz. This commonly applied approach assumes a simulation grid designed with the same Dx and Dy as the geological grid. The approach is often used where complex structural architecture provides very tight constraints to design of the flow modelling grid. Upscaling essentially comprises use of averaging methods but ensures a degree of representation of thin layering or barriers. Also, where seismic data give a good basis for the geological model in the horizontal dimensions, vertical upscaling of fine-scale layering to the reservoir simulator scale is typically required.

(3) Single-phase upscaling in Dx Dy and Dz. With this approach, multiscale effective flow properties are explicitly estimated and the upscaling tools are widely available (diagonal tensor or full tensor pressure solution methods). Multiphase flow effects are however neglected. (4) Multiphase upscaling in Dx Dy and Dz. This approach represents an attempt to calculate effective multiphase flow properties in larger-scale models. The approach has been used rather too seldom due to demands of time and resources. However, the development of steady-state solutions to multiphase flow upscaling problems (Smith 1991; Ekrann & Aasen 2000; Pickup & Stephen 2000) has led to wider use in field studies (Pickup et al. 2000; Kløv et al. 2003). These four degrees of upscaling complexity help define the number and dimensions of models required. The number of scales modelled is typically related to the complexity and precision of the answer sought. Improved oil recovery (IOR) strategies and reservoir drainage optimization studies are usually the reason for starting a multiscale approach. A minimum requirement for any reservoir model is that the assumptions used for smaller-scale processes (pore-scale, lithofaciesscale) are explicitly stated. For example, a typical set of assumptions historically used might have been: ‘We assume that two special core analysis measurements represent all pore-scale physical flow processes and that all effects of geological architecture are adequately summarized by the arithmetic average of the well data.’ However, assumptions such as these were rarely stated, although implicitly assumed. More ideally, some explicit modelling at each scale should be performed using 3D multiphase upscaling methods.

Which scales to focus on? The Representative Elementary Volume (REV) concept (Bear 1972) provides the framework for understanding geological and measurement scales. This concept is widely referred to but infrequently implemented in a multiscale context. The original concept refers to the scale at which pore-scale fluctuations in flow properties approach a constant value both as a function of changing scale and position in the porous medium, such that a statistically valid macroscopic flow property can be defined. However, rock media present several such scales where smaller-scale variations approach a more constant value (Fig. 3). It is not generally clear how many such length scales exist in a particular rock medium, or indeed if an REV can be established at the scale necessary for reservoir flow simulation. However, a degree of representativity and


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Fig. 3. Sketch illustrating multiple scales of REV for permeability compared with a multiscale geological modelling framework and typical scales of measurement (adapted from Bear 1972; Nordahl 2004).

stability of estimated flow properties is required for flow modelling within a multiscale framework. Jackson et al. (2003) and Nordahl & Ringrose (2008) have shown that a lithofacies-scale REV can be achieved at the c. 0.3 m length scale for models of tidal heterolithic bedding. Whatever the true nature of rock variability, it is a common mistake to assume that the averaging inherent in any measurement method (e.g. electrical logs or seismic wave inversion) relates directly to the averaging scales in the rock medium. For example, core samples are often at an inappropriate scale for determining representativity (Corbett & Jensen 1992; Nordahl et al. 2005). Typical practice in petroleum reservoir studies is to assume that an average measured property for any rock unit is valid and that small-scale variability can be ignored. Valid statistical treatment of sample data is a large topic treated thoroughly elsewhere (e.g. Isaaks & Srivastava 1989; Jensen et al. 2000). An illustration of the challenge of correctly inferring permeability values from well data is illustrated here using an example well dataset (Fig. 4 and Table 1). This 30 m cored well interval comprises a tidal deltaic reservoir unit with heterolithic lithofacies and moderate to highly variable petrophysical properties. The permeability variations within this unit are large and determining an appropriate upscaled (or average) permeability is a challenge. The same well dataset is discussed in detail by Nordahl et al. (2005). Table 1 compares the permeability statistics for different types of data from this well: (a) high resolution probe permeameter data; (b) core plug data; (c) a continuous wireline

log based estimator of permeability for the whole interval; and (d) a blocked permeability log as might be typically used in reservoir modelling (blocking refers to averages of discrete intervals). Statistics for the natural log of permeability, ln(k), are shown (as the population distributions are approximately log normally distributed). It is well known that the sample variance should reduce as sample scale is increased. Therefore, the reduction in variance between datasets (c) and (d) is expected. It is, however, a common mistake in multiscale modelling for an inappropriate variance to be applied in a larger-scale model, e.g. if core plug variance were used to model the upscaled geomodel variance. Comparison of datasets (a) and (b) reveals another form of variance that is commonly ignored. The probe permeameter grid (2 mm spaced data over a 10 cm 10 cm core area) shows a variance, s2, of 0.38 [ln(k)]. The core plug dataset for the corresponding lithofacies interval (Estuarine bar), has s2 ln(k) ¼ 0.99, which represents variance at the lithofacies scale. However, blocking of the probe permeameter data at the core plug scale shows a variance reduction factor of 0.79 up to the core plug scale (column 2 in Table 1). Thus, in this dataset (where high resolution measurements are available), a significant degree of variance is missing from the datasets conventionally used in reservoir modelling. Improved treatment of variance in reservoir modelling is clearly needed and presents a challenge for future work. The statistical basis for treating population variance as a function of sample support volume is well established with

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Fig. 4. Example dataset from a tidal deltaic flow unit illustrating treatment of permeability data used in reservoir modelling.

the concept of Dispersion Variance (e.g. Isaacs & Srivastava 1989), where: s2 ða, cÞ ¼ s2 ða, bÞ þ s2 ðb, cÞ total variance variance variance within blocks between blocks where a, b and c represent different sample supports (for example, a ¼ point values, b ¼ block values and c ¼ total model domain). The variance adjustment factor, f, is defined as the ratio of block variance to point variance and can be used to

estimate the correct variance to be applied to a blocked dataset. With additive properties, such as porosity, treatment of variance in multiscale datasets is relatively straightforward, using the concept of Dispersion Variance. However, it is much more of a challenge with permeability data as flow boundary conditions are an essential aspect of estimating an upscaled permeability value. (The Dispersion Variance equation strictly applies only to additive, uncorrelated properties.) Multiscale geological modelling is an attempt to represent smaller-scale structure and variability as an upscaled block value. In this process, the principles of flow upscaling are


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Table 1. Variance analysis of example permeability dataset Estuarine bar lithofacies

Whole interval (flow unit)

(a) Probe k data

Probe data at plug scale

Core plug data

(b) Core plug data

(c) Wireline k-estimate

(d) Blocked well data

Scale of data

10 10 cm; 2 mm spaced data

c. 15–30 cm spaced core plugs

c. 15– 30 cm spaced plugs

15 cm digital log

2 m blocking

N ¼ Mean ln(k) s2 ln(k) Variance adjustment factor, f

2584 7.14 0.38 –

2 2 cm squares of 2 mm-spaced data 25 7.14 0.30 0.79

11 6.39 0.99 –

85 1.73 8.44 –

204 2.32 5.94 –

16 2.17 4.80 0.81

essential; however, improved treatment of variance is also critical. There is, for example, little point in rigorously upscaling a core plug sample dataset if it is known that the dataset is a poor representation of the true population variance. Within a multiscale geological framework, the recommended approach is to first identify the length scales where variance approaches a minimum, and then design the modelling and upscaling scheme to explicitly capture the effects of rock architecture at the scales where spatial variance cannot be ignored (Fig. 3).

How to construct geomodel and simulator grids? The construction of three-dimensional geological models from seismic and well data remains a relatively time-consuming task requiring considerable manual work both in construction of the structural framework and, not least, in construction of the grid for property modelling. Problems especially arise due to complex fault block geometries including reverse faults and Y-faults (i.e. Y-shaped intersecting faults in the vertical plane). Difficulties relate partly to the mapping of horizons into the fault planes for construction of consistent fault throws across faults. Problems also occur with lowangle stratigraphic intersections, where a decision has to be made to ignore cells thinner than a certain resolution. Currently, most commercial gridding software is not capable of automatically producing adequate 3D grids for realistic fault architectures, and significant manual work is necessary. Grid lines along fault surfaces are constructed and manual editing is mainly used to ensure that stratigraphic horizons correctly meet the fault planes. Upscaling procedures for regular Cartesian grids are well established, but the same

operation in realistically complex grids is much more challenging. The construction of 3D grids suitable for reservoir simulation is therefore also non-trivial and requires significant manual editing. The reasons for this are several: † The grid resolutions in the geological model and the simulation models are different, leading to missing cells or misfitting cells in the simulation model. The consequences are overestimation of pore volumes, possibly wrong communication across faults, and difficult numerical calculations due to a number small or ‘artificial’ grid cells. † The handling of Y-shaped faults using corner point grid geometries now widely used in black oil simulators is difficult. Similarly, the use of vertically staircased faults improves the grid quality and flexibility, but does not solve the whole problem. When using grids with staircased faults, special attention must be paid to estimation of fault seal and fault transmissibility. There is generally insufficient information in the grid itself for these calculations, and the calculation of fault transmissibility must be calculated based on information from the geological model. † The handling of dipping reverse faults using staircased geometry in a corner-point grid requires a higher total number of layers than for an unfaulted model. This is presently not available in simulation gridding software. † Regions with fault spacing smaller than the simulation grid spacing give problems for appropriate calculation of fault throw and zone to zone communication. Gridding implies that smaller-scale faults are merged and a cumulated fault throw is used in the simulation model. This is not possible with currently available gridding tools, and an effective fault transmissibility,

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including non-neighbour connections, must be calculated based on information from the geomodel, i.e. using the actual geometry containing all the merged faults. † Flow simulation accuracy depends on the grid quality, and the commonly used numerical discretization schemes in commercial simulators have acceptable accuracy only for ‘near’ orthogonal grids. Orthogonal grids do not comply easily with complex fault structures, and most often compromises must be made between honouring geology and keeping ‘near orthogonal’ grids. Figure 5 illustrates how some of these problems have been addressed in recent field studies. Solutions include: (a) detailed manual grid construction including staircase faults to handle Y-faults; (b) addition of smaller faults not explicitly modelled in the geomodel directly into the flow simulation grid; (c) decisions to ignore some faults when their effect on flow is expected to be minor. However, some gridding problems cannot be fully resolved using the constraints of corner point simulation grids, and optimal, consistent and

automated grid generation based on realistic geomodels is a challenge. The use of unstructured grids (e.g. triangular tessellation) reduces the gridding problems; however, robust, reliable and costefficient numerical flow solution methods for these unstructured grids are not widely available or efficient. Improved and consistent solutions for construction of structured grids and associated transmissibilities have been proposed (e.g. Manzocchi et al. 2002; Tchelepi et al. 2005); however, calculations for staircased faulted grids need improved formulation. Despite these challenges and the high degree of manual editing involved, the best approach for gridding geological and flow simulation models is to separate out structural features into their modelling categories: (a) Faults explicitly modelled in the structural framework of the geomodel. (b) Faults explicitly modelled in the flow grid – a subset of (a). (c) Small-scale faults represented in the flow grid as effective permeability factors. (d) Neglected faults (not included in (a) or (c)).

Fig. 5. Illustration of the transfer of a structural geological model to a reservoir simulation grid.


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Table 2. Summary of selected studies comparing multiscale factors on petroleum reservoir performance

Sequence model Sand fraction Sandbody geometry Vertical permeability Small-scale heterogeneity Fault pattern Fault seal

Shallow marine1

Faulted shallow marine2

V S

V S

S

S

n/a n/a

S S

Fluvial3

Tidal deltaic4

Fault modelling5

V S

S S V S n/a n/a

V n/a n/a n/a n/a S S

S n/a n/a

V ¼ Very significant factor; S ¼ Significant factor; n/a ¼ not assessed. 1 Kjønsvik et al. 1994 2 England & Townsend 1998 3 Jones et al. 1993 4 Brandsæter et al. 2001a, 2004 5 Lescoffit & Townsend 2005

Workflows will require some iteration and sensitivity analysis to confirm an appropriate choice of classes. Recent unpublished studies for large structurally complex petroleum reservoirs have c. 300 faults in class (a) and c. 100 faults in class (b). A similar scheme can be applied to fractures or stratigraphic barriers, where these are important.

Which heterogeneities matter? There are a number of published studies where the importance of different geological factors on reservoir performance have been assessed (e.g. the SAIGUP project, Manzocchi et al. 2008). Table 2 summarizes the findings of a selection of such studies in which a formalized experimental design with statistical analysis of significance has been employed. The table shows only the main factors identified in these studies (for full details, refer to sources). What is clear from this work is that several scales of heterogeneity are important for each reservoir type. While one can conclude that stratigraphic sequence position is the most important factor in a shallow marine depositional setting or that vertical permeability is the most important factors in a tidal deltaic setting, each case study shows that larger- and smaller-scale factors are always significant. This is a clear argument in favour of explicit multiscale reservoir modelling. Furthermore, in the studies where the effects of structural heterogeneity were assessed, both structural and sedimentary features were found to be significant. That is to say, structural features and uncertainties cannot be neglected and are fully coupled with stratigraphic factors.

Several projects have demonstrated the economic value of multiscale modelling in the context of oilfield developments. An ambitious study of the structurally complex Gullfaks Field (Jacobsen et al. 2000) demonstrated that 25 millioncell geological grid (incorporating structural and stratigraphic architecture) could be upscaled for flow simulation and resulted in a significantly improved history match. Both stratigraphic barriers and faults were key factors in achieving improved pressure matches to historic wells data. This model has further been used for assessment of IOR using CO2 flooding. Multiscale upscaling has also been used to assess complex reservoir displacement processes, including gas injection in thin-bedded reservoirs (Fig. 6) (Pickup et al. 2000; Brandsæter et al. 2001b, 2005), wateralternating-gas (WAG) injection on the Veslefrikk Field (Kløv et al. 2003), and depressurization on the Statfjord Field (Theting et al. 2005). These studies typically show of the order of 10–20% difference in oilfield recovery rates when advanced multiscale effects are compared with conventional single-scale reservoir simulation studies. The economic impact of multiscale modelling was estimated by Elfenbein et al. (2005) as giving at least 16 million barrels of additional oil for a typical large oilfield, and for marginal or challenging oilfields the value of detailed multiscaled modelling can represent the difference between success and failure.

Summary of potential and pitfalls Multiscale reservoir modelling has clearly moved from a conceptual phase, with method development on idealized problems, into a practical phase, with

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Fig. 6. Gas injection patterns in a thin-bedded tidal reservoir modelled using a multiscale method and incorporating the effects of faults in the reservoir simulation model (from a study by Brandsæter et al. 2001b). Reservoir cross-section is c. 25 m thick and c. 5 km long.

more routine implementation on real reservoir cases. The modelling methods have achieved sufficient speed and reliability for routine implementation (generally using steady-state methods on near-orthogonal corner-point grid systems). However, a number of challenges remain which require further developments of methods and modelling tools. In particular: † Multiscale modelling within a realistic structural geological grid is still a major challenge. † Correct handling of variance from multiplescale datasets is frequently neglected. † The tool-set for upscaling is still incomplete and far from integrated (e.g. multiphase flow, gridding and fault seal are generally treated in separate software packages and require much data conversion). We thank our colleagues for useful discussions and contributions to illustration and examples, especially Inge Brandsæter, Erlend Eldholm, Oddvar Lia, Andrew McCann, Tor Anders Knai, Kjetil Nordahl, Per Arne Slotte, Thomas Theting and Pa˚l Eric Øren. StatoilHydro ASA is thanked for permission to publish this material.

References B AKKE , S. & Ø REN , P.-E. 1997. 3-D pore-scale modelling of sandstones and flow simulations in pore networks. SPE Journal, 2, 136– 149. B ARKER , J. W. & T HIBEAU , S. 1997. A critical review of the use of pseudo relative permeabilities for upscaling. SPE Reservoir Engineering, 12, 138– 143. B EAR , J. 1972. Dynamics of Fluids in Porous Media. Elsevier, New York. B OURBIAUX , B., B ASQUET , R., C ACAS , M.-C., D ANIEL , J.-M. & S ARDA , S. 2002. An integrated workflow to account for multi-scale fractures in reservoir simulation models: implementation and benefits. SPE n8

78489 presented at Abu Dhabi International Petroleum Exhibition and Conference, 13–16 Oct. B RANDSÆTHER , I., W IST , H. T., N ÆSS , A. ET AL . 2001a. Ranking of stochastic realizations of complex tidal reservoirs using streamline simulation criteria. Petroleum Geoscience, 7, 53– 63. B RANDSÆTHER , I., R INGROSE , P. S., T OWNSEND , C. T. & O MDAL , S. 2001b. Integrated modelling of geological heterogeneity and fluid displacement: Smørbukk gas-condensate field, Offshore Mid-Norway. SPE n8 66391 presented at the SPE Reservoir Simulation Symposium, Houston, Texas, 11–14 Feb. B RANDSÆTHER , I., M C I LROY , D., L IA , O., R INGROSE , P. & N ÆSS , A. 2005. Reservoir simulation and modelling of the Lajas Formation outcrops (Argentina) to constrain tidal reservoirs of the Halten Terrace (Norway). Petroleum Geoscience, 11, 37–46. B RYANT , S. & B LUNT , M. J. 1992. Prediction of relative permeability in simple porous media. Physical Review A, 46, 2004– 2011. B RYANT , S., K ING , P. R. & M ELLOR , D. W. 1993. Network model evaluation of permeability and spatial correlation in a real random sphere packing. Transport in Porous Media, 11, 53–70. C AERS , J. 2003. History matching under training-imagebased geological model constraints. SPE Journal, 8, 218–226. C AMPBELL , C. V. 1967. Lamina, laminaset, bed, bedset. Sedimentology, 8, 7– 26. C ORBETT , P. W. M. & J ENSEN , J. L. 1992. Estimating the mean permeability: how many measurements do you need? First Break, 10, 89–94. C ORBETT , P. W. M., R INGROSE , P. S., J ENSEN , J. L. & S ORBIE , K. S. 1992. Laminated clastic reservoirs: the interplay of capillary pressure and sedimentary architecture. SPE n8 24699 presented at the 67th Annual Conference of the Society of Petroleum Engineers, Washington, 4 –7 Oct. D URLOFSKY , L. J., M ILLIKEN , W. J. & B ERNATH , A. 2000. Scaleup in the near-well region. SPE Journal, 5, 110–117. E KRAN , S. & A ASEN , J. O. 2000. Steady-state upscaling. Transport in Porous Media, 41, 245–262.

MULTISCALE RESERVOIR MODELLING E LFENBEIN , C., R INGROSE , P. S. & C HRISTIE , M. 2005. Small-scale reservoir modeling tool optimizes recovery offshore Norway. World Oil, Oct., 45–50. E NGLAND , W. A. & T OWNSEND , C. 1998. The Effects of Faulting on Production from a Shallow Marine Reservoir – A Study of the Relative Importance of Fault Parameters. SPE n8 49023 presented at the SPE Annual Conference, New Orleans, USA, 27– 30 Sept. H ALDORSEN , H. H. & L AKE , L. W. 1984. A new approach to shale management in field-scale models. Society of Petroleum Engineers Journal, August, 447–457. H ALDORSEN , H. H. 1986. Simulator parameter assignement and the problem of scale in reservoir engineering. In: L AKE , L. W. & C AROLL , H. B. (eds) Reservoir Characterization. Academic Press, Orlando, 293–340. H OLDEN , L., H AUGE , R., S KARE , Ø. & S KORSTAD , A. 1998. Modeling of fluvial reservoirs with object models. Mathematical Geology, 30, 473– 496. H UANG , Y., R INGROSE , P. S. & S ORBIE , K. S. 1995. Capillary trapping mechanisms in water-wet laminated rock. SPE Reservoir Engineering, November, 287–292. I SAAKS , E. H. & S RIVASTAVA , R. M. 1989. An Introduction to Applied Geostatistics. Oxford University Press, Oxford. J ACKSON , M. D., M UGGERIDGE , A. H., Y OSHIDA , S. & J OHNSON , H. D. 2003. Upscaling permeability measurements within complex heterolithic tidal sandstones. Mathematical Geology, 35, 499– 519. A LVESTAD , J., J ACOBSEN , T., A GUSTSSON , H., D IGRANES , P., K AAS , I. & O PDAL , S.-T. 2000. Modelling and identification of remaining reserves in the Gullfaks field. SPE n8 65412 presented at the SPE European Petroleum Conference, Paris, France, 24– 25 Oct. J ENSEN , J. L., L AKE , L. W., C ORBETT , P. W. M. & G OGGIN , D. J. 2000. Statistics for Petroleum Engineers and Geoscientists. 2nd Edn, Elsevier. J ONES , A., D OYLE , J., J ACOBSEN , T. & K JØNSVIK , D. 1993. Which sub-seismic heterogeneities influence waterflood performance? A case study of a low net-to-gross fluvial reservoir. In: D E H AAN , H. J. (ed.) New Developments in Improved Oil Recovery. Geological Society, London, Special Publication, 84, 5–18. J OURNEL , A. G. & A LABERT , F. G. 1990. New method for reservoir mapping. Journal of Petroleum Technology, February, 212–218. K JØNSVIK , D., D OYLE , J., J ACOBSEN , T. & J ONES , A. 1994. The effect of sedimentary heterogeneities on production from a shallow marine reservoir – what really matters? SPE n8 28445 presented at the European Petroleum Conference, London, 25–27 Oct. ˚ . ET AL . 2003. SPE K LØV , T., Ø REN , P.-E., S TENSEN , J. A n8 84549 presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA, 5–8 Oct. L ESCOFFIT , G. & T OWNSEND , C. 2005. Quantifying the impact of fault modelling parameters on production forecasting for clastic reservoirs. In: B OULT , P. & K ALDI , J. (eds) Evaluating Fault and Cap Rock Seals. AAPG Hedberg Series, no. 2, 137– 149.

133

M C D OUGALL , S. R. & S ORBIE , K. S. 1995. The impact of wettability on waterflooding: pore-scale simulation. SPE Reservoir Engineering, August, 208– 213. M ANZOCCHI , T., H EATH , A. E., W ALSH , J. J. & C HILDS , C. 2002. The representation of two-phase fault-rock properties in flow simulation models. Petroleum Geoscience, 8, 119– 132. M ANZOCCHI , T., C ARTER , J. N., S KORSTAD , A., F JELLVOLL , B., S TEPHEN , K. D. & H OWELL , J. A. ET AL . 2008. Sensitivity of the impact of geological uncertainty on production from faulted and unfaulted shallow-marine oil reservoirs: objectives and methods. Petroleum Geoscience, 14, 3 –15. M IALL , A. D. 1985. Architectural-element analysis: a new method of facies analysis applied to fluivial deposits. Earth Science Reviews, 22, 261–308. M IALL , A. D. 1988. Reservoir heterogeneities in fluvial sandstones: Lessons learned from outcrop studies. American Association of Petroleum Geologists’ Bulletin, 72, 882– 897. N ORDAHL , K. 2004. A petrophysical evaluation of tidal heterolithic deposits: application of a near wellbore model for reconciliation of scale dependent well data. Doctoral Thesis published by Norwegian University of Science and Technology, Trondheim. N ORDAHL , K., R INGROSE , P. S. & W EN , R. 2005. Petrophysical characterization of a heterolithic tidal reservoir interval using a process-based modelling tool. Petroleum Geoscience, 11, 17– 28. N ORDAHL , K. & R INGROSE , P. S. 2008. Identifying the representative elementary volume for permeability in heterolithic deposits using numerical rock models. Mathematical Geosciences, 40(7), 753– 771. Ø REN , P.-E. & B AKKE , S. 2003. Process-based reconstruction of sandstones and prediction of transport properties. Transport in Porous Media, 12, 1– 32. P ICKUP , G. E. & S TEPHEN , K. S. 2000. An assessment of steady-state scale-up for small-scale geological models. Petroleum Geoscience, 6, 203–210. P ICKUP , G. E., R INGROSE , P. S. & S HARIF , A. 2000. Steady-state upscaling: from lamina-scale to full-field model. SPE Journal, 5, 208–217. P ICKUP , G. E., S TEPHEN , K. D., Z HANG , M. J. & C LARK , J. D. 2005. Multi-stage upscaling: Selection of suitable methods. Transport in Porous Media, 58, 119– 216. R ENARD , Ph. & DE M ARSILY , G. 1997. Calculating equivalent permeability: a review. Advances in Water Resources, 20, 253– 278. R INGROSE , P. S., S ORBIE , K. S., C ORBETT , P. W. M. & J ENSEN , J. L. 1993. Immiscible flow behaviour in laminated and cross-bedded sandstones. Journal of Petroleum Science and Engineering, 9, 103–124. R INGROSE , P. S., S KJETNE , E. & E LFEINBEIN , C. 2003. Permeability Estimation Functions Based on Forward Modeling of Sedimentary Heterogeneity. SPE n8 84275 presented at the SPE Annual Conference, Denver, USA, 5–8 Oct. R INGROSE , P. S., N ORDAHL , K. & W EN , R. 2005. Vertical permeability estimation in heterolithic tidal deltaic sandstones. Petroleum Geoscience, 11, 29–36. R UBIN , D. M. 1987. Cross-bedding, bedforms and palaeocurrents. Concepts in Sedimentology and

134


Palaeontology, Volume 1. Society of Economic Palaeontologists and Mineralogists Special Publication. S CHEILING , M. H., T HOMPSON , R. D. & S IEFERT , D. 2002. Multiscale reservoir description models for performance prediction in the Kuparuk River Field, North Slope of Alaska. SPE n8 76753 presented at the SPE Western Regional/AAPG Pacific Section Joint Meeting, 20– 22 May, Anchorage, Alaska. S MITH , E. H. 1991. The influence of small-scale heterogeneity on average relative permeability. In: L AKE , L. W. ET AL . (eds) Reservoir Characterisation II. Academic Press. S TREBELLE , S. 2002. Conditional simulation of complex geological structures using multiple-point statistics. Mathematical Geology, 34, 1– 21. T CHELEPI , H. A., J ENNY , P., L EE , S. H. & W OLFSTEINER , C. 2007. Adaptive multiscale finite-volume framework for reservoir simulation. SPE Journal, June 2007, 188–195. T HETING , T. G., R USTAD , A. B., L ERDAHL , T. R. ET AL . 2005. Pore-to-field multi-phase upscaling for a depressurization process. Presented at the 13th European

Symposium on Improved Oil Recovery, Budapest, Hungary, 25– 27 April. W ALSH , J., W ATTERSON , J. & Y IELDING , G. 1991. The importance of small-scale faulting in regional extension. Nature, 351, 391–393. W EBER , K. J. 1986. How heterogeneity affects oil recovery. In: L AKE , L. W. & C ARROLL , H. B. (eds) Reservoir Characterisation. Academic Press, 487–544. W EBER , K. J. & VAN G EUNS , L. C. 1990. Framework for constructing clastic reservoir simulation models. Journal of Petroleum Technology, 42, 1248–1297. W EN , R.-J., M ARTINIUS , A. W., N ÆSS , A. & R INGROSE , P. S. 1998. Three-dimensional simulation of small-scale heterogeneity in tidal deposits – A process-based stochastic method. In: B UCCIANTI , A. ET AL . (eds) Proceedings of the 4th Annual Conference of the International Association for Mathematical Geology, Ischia, 129 –134. Y IELDING , G., W ALSH , J. & W ATTERSON , J. 1992. The prediction of small-scale faulting in reservoirs. First Break, 10, 449 –460.