Field development of fluvio-marine reservoirs is challenging because the sand distribution in these systems is complex and difficult to predict. The rivers interacting with the marine systems create diverse depositional settings, from river channels and tidal flats to deltas and floodplains. Within these settings, many sedimentary structures are formed, and within these structures, the size, shape and sorting of the grains – all with influence on permeability – are highly variable. The uncertainty in understanding how reservoir properties vary in these complex architectures creates the need to utilize more advanced quantitative interpretation techniques and integrate them with petrophysical and sedimentological data to reveal the reservoir structure.

In this paper, we present a novel interdisciplinary method to identify high-permeability layers and show that permeability can be inferred from the distribution of reservoir fluids above the free water level (FWL) and their effects on the elastic rock properties. Using the rock physics model from a previous study on the Hugin reservoir in the North Sea Volve oilfield, we show that anomalously high-permeability layers exhibit significant shifts of the bulk volume of water (BVW) log from the field-predicted values and that these zones can be correlated to fluid-induced changes in Vp/Vs.

Permeability measurements were only used to confirm the findings. They validated the method’s ability to accurately identify very thin, highly permeable layers at the wells, even within sands with similar porosities and clay content. We show the importance of establishing the link between contrasts in log and field-predicted BVW and elastic properties in order to characterize facies within a seismic volume. Using the corresponding seismic attributes, we characterized the permeability facies within the seismic volume and successfully identified the highly permeable Middle Hugin layer.

Method and application

The Hugin Formation is a shallow marine sandstone with fluvio-deltaic influences and very heterogeneous permeability. Core samples with similar porosities, situated within a one-meter distance, showed permeability shifts of more than two orders of magnitude (Statoil, 1993). Because permeability is related to how easily fluids can flow through the rock pore system (Figure 1), understanding this significant variability is essential for identifying the flow barriers and guiding the location of the wells. However, permeability cannot be measured directly by geophysical methods, so it poses a significant challenge for characterization.

Figure 1. A rock is permeable if the pores are connected, allowing fluid flow. Pore interconnectivity depends on the shape and size of the pores. A rock such as cemented sand or shale may be porous but not very permeable.

We propose an interdisciplinary approach to infer the reservoir permeability from the structure of its pore space. The pore structure can be understood by examining how the fluids are distributed within the reservoir and how they affect the rock’s elastic properties. This approach involves:

▪ connecting mineralogy, diagenesis, and fluids to the elastic rock properties
▪ modelling the bulk volume of water above the free water level to understand the distribution of fluids at the field scale, and
▪ using rock physics crossplots to observe how this distribution affects the elastic rock properties at wells.

BVW is calculated for each well using resistivity and porosity electrical logs, as well as data from core analysis. Field-wide crossplots of BVW versus the height above the FWL usually show a simple relationship that is independent of permeability. However, beds with extremely high permeability exhibit an unusually low BVW, which helps identify these beds. This identification is done by comparing the field-derived BVW function with the BVW logs from individual wells.

We also used corresponding seismic inversion attributes with crossplots to map the highly permeable facies throughout the field. Figure 2 shows how we applied this methodology to investigate these geological changes.

Figure 2. Proposed workflow for identifying and mapping high-permeability facies.

1. Rock-physics modelling of the Hugin sandstone reservoir

Through rock physics models, various geological reservoir properties, such as porosity, mineralogy, and saturation, can be connected to seismic properties, such as P- and S-impedances or density. When constrained by local known or assumed geological factors, the rock physics models can help us avoid interpretation ambiguities that sometimes occur between sand and shale, porosity and saturation, or lithology and fluids (Avseth, 2010).

A rock physics model was calibrated to the Hugin reservoir using the constant-cement sand model (Dvorkin and Nur, 1996) and used to estimate the bulk and shear moduli of the porous dry frame. The properties of pore fluids were calculated based on their composition and in-situ temperature and pressure (Batzle and Wang, 1992). Lastly, fluid substitution (Gassmann, 1951) was used to account for pore fluid effects and predict the effective properties of the oil-saturated sand. A quartz cement fraction of 2% was found from fitting lines of constant cement on crossplots of Vp versus porosity and Vs versus porosity (Figure 3, left).

Figure 3. Cement calibration on Vp versus porosity crossplot (left). Crossplots to classify different reservoir facies, showing the rock physics template and well data, from Talinga and Reine, 2019 (right).

This model was used to create rock-physics templates covering various scenarios of clay volume and porosity to anticipate the expected changes that can occur away from the wells. Figure 3 ( right), shows the model plotted as density versus MuRho, properties that we can then use to interpret high, medium and low porosity sandstones. More details on rock physics and the main lithology classification were previously discussed by Talinga and Reine (2021).

A continuous permeability log was calculated from multivariable regression analysis between porosity (ɸ) and shale volume (VSH) logs against overburden-corrected core permeability (kcore) published in the Statoil technical report (2018) (Figure 4):

This relationship was also applied to the porosity and shale values of the rock-physics model, allowing for the new quantity to be plotted on the templates. The separation of low and high permeabilities is best observed on rock physics templates of porosity, clay volume and permeability displayed on Vp/Vs and density crossplots (Figure 5).

Figure 4. The correlation between the core measured permeability and the values from regression (Statoil, 2018) (left) is very good for permeabilities higher than 0.5 mD. An example of a calculated permeability log is shown (right).

Figure 5. Crossplot templates showing variations in porosity, clay volume and permeability, expressed in density and VpVs ratio. Green lines indicate constant permeability calculated from the relationship between core permeability and log porosity and shale volume.

While the rock physics templates demonstrate that high permeabilities are typically associated with high porosities and small clay volumes, it is important to note that the well data may contain variations in porosity and facies, leading to a similar but not identical trend. The introduction of permeability in the rock physics templates is a useful tool, but its reliability diminishes in the presence of rapid changes between sand and shale. In these cases, obtaining a good correlation between core and log permeability may be challenging due to potential poor correlations with porosity and shale fractions.

2. Modelling the bulk volume of water above the free water level

The key factor in understanding permeability is the structure of the pore space. In a reservoir, the porous space is divided between oil, which occupies the large pores, and capillary-bound water, or the bulk volume of water, usually contained in the small pores (Figure 6, left).

BVW quantifies the pore geometry, which is determined by the size and shape of the grains and how they are arranged. Therefore, it is connected to both permeability and porosity. If the pore geometry (porosity and permeability) is highly different between zones, we will see a deviation between the calculated BVW log and the fitted trend above the free water level (BVW-height function, or fractal function (Cuddy, 1993)).

Figure 6. The bulk volume of water. This is a generalized representation, as the oil is forced into increasingly smaller pores further they are from the free water level (left). The deviation between the calculated BVW log and the field-predicted BVW suggests changes in the porosity-permeability relationship (right).

The BVW-height function predicts the volume of water as a function of height above the free water level. The function shows how the formation porosity is divided between hydrocarbon and water and is calculated from the height above the FWL, H, and two constants, a and b (Cuddy, 2017):

BVW = a H b

Using the BVW trend obtained by plotting the BVW against the true vertical depth, the FWL was identified at 3200 m for one of the wells. Next, the parameters of the fractal function were calculated by linear regression on logarithmic scales plot of BVW against height above FWL:

BVW = 0.153 H -0.369

Only the best data was used, free of boundary effects, such as the middle of massive clean layers (Figure 7).

Figure 7. Modelling of the BVW trend above the free water level. Highlighted zones are intervals used to model the BVW function. As BVW decreases with height above the FWL, the large pores near the FWL will contain mainly water, and the small pores far above the FWL will contain mostly oil. As the resistivity log is adversely affected by nearby conductive shales, the BVW permeability prediction works best in thick beds. Permeability identification in thin beds could be improved with resistivity log modelling.

Figure 8. Petrophysical logs showing zones subdivided based on the shift between the BVW log and the best-fit BVW-height function in a well with a free water level at 3200 m (left). Comparison of log and field-derived BVW (right).

When comparing the log with the field-derived BVW, we can see that the field function overpredicts BVW in some of the beds, which indicates that these beds have a different porosity-permeability relationship compared to the other facies. As a consequence, the log-derived BVW is shifted in these intervals. The highly permeable beds stand out as having a much lower BVW than what the field-derived BVW function predicts, as seen in the example in Figure 8. This observation has been successfully used to predict highly permeable beds in the Buzzard field in the Central North Sea (unpublished).

3. Investigating the link between BVW, permeability and elastic rock properties

In this section, we will discuss how the elastic rock properties relate to the permeability through the bulk volume of water.

Figure 9 illustrates that, when combined with rock physics, the core-to-log high permeabilities are matched to the same degree by overestimations of the predicted BVW values. Here, the rock physics model is seen in the P-wave velocity versus density domain, as the well does not have a shear sonic log to calculate the VpVs ratio. The comparison implies that the BVW function, with its ability to capture the high permeability beds, could be a versatile solution, particularly when core heterogeneity is strong.

Figure 9. P-wave velocity log data versus density and superimposed rock physics model. On the left, data points are coloured by permeability, and on the right, by the highlighted high-permeability beds seen in Figure 8. The match is very good, suggesting that BVW could be used as an indicator in the absence of permeability data.

Consider a scenario where we have no prior knowledge of permeability, only the observed shifts in BVW. By defining a polygon on the density-Vp crossplot to encompass these clusters of points, we notice the accuracy with which the high-permeability layers are captured, even the thinnest ones. Occasionally, errors in the calculated BVW log may cause the function to miss these layers, but the elastic properties effectively identify them (Figure 10).

Figure 10. Defining a polygon around BVW shifts on density and Vp crossplot effectively predicts high permeability intervals.

Now, we use the polygon relating the BVW shifts to the elastic properties defined from one well to project it to the other wells, and we observe that they are also predicted remarkably well and at a high resolution. Not only that the BVW shifts and elastic properties capture the massive layers, but also thinner intervals that are 0.2 m or less. We can also observe that sands with lower permeability, possibly due to changes in cementation, are classified correctly (Figure 11).

Figure 11. Prediction of the high-permeability layers (green) using well data points from the well in Figure 10.

4. Rock physics modelling of saturation effects on elastic properties

Next, we investigated the saturation effects on the rock’s elastic properties and the separation of the net reservoir from the non-net reservoir by modelling a fully water-saturated and a fully oil-saturated state. This will permit us to observe if fluid ambiguity exists.

The density-Vp crossplot reveals that oil and water saturations overlap, which implies a low sensitivity of density and Vp with fluid saturation changes. It also implies that points with low and high bulk water volumes cannot be differentiated on these crossplots, which can result in a classification ambiguity of the high permeability layers (Figure 12, left).

However, the density versus Vp/Vs shows a separation between oil- and water-saturated points, as the increase in Sw and BVW will shift the high-porosities toward higher Vp/Vs. Therefore, the Vp/Vs can effectively reduce fluid and porosity ambiguity and prevent us from misinterpreting the seismic response as a reduction in porosity instead of a change in fluid from hydrocarbon to water. (Figure 12, right).

Figure 12. Rock physics modelling of fluid saturation effects on density and Vp (left), and on density and Vp/Vs (right), with points coloured by permeability. Note on the first crossplot how the 0.25 porosity of wet sands mimics the 0.2 porosity of oil sands, but are separated on the second crossplot by their differing Vp/Vs. Unlike the density and Vp, which are not affected by changes in fluid filling the pores, the VpVs ratio of the rock is lowered by the increase in oil saturation. The shift between the high porosities on oil- and water-saturated templates indicates that high permeabilities, generally characterized by high porosities and low BVW, correlate with high porosities of low BVW and low Sw.

With this insight, we revisited one of the dipoles. We used the BVW anomalies once again to highlight the intervals and delineate an area around them, and we found that the highly permeable beds were accurately captured (Figure 13).

Figure 13. Highly permeable intervals are accurately predicted from BVW and Density and Vp/Vs crossplots.

5. Permeability facies classification using inversion attributes

The application within the 3D survey was realized by crossplotting the seismic attributes obtained by simultaneous inversion to separate the main lithologies based on their differences in elastic properties, such as the Cretaceous limestones and marls, the Jurassic porous reservoir sandstone, and the silty claystone caprock, as seen in Figure 14. A more detailed discussion can be found in Talinga and Reine, 2021.

The reservoir sandstones were further classified into high-permeability and low, medium, and high-porosity sands using the rock-physics templates obtained for the constant-cement model. The interpretation of permeability classes was guided by the rock physics saturation templates and the identified shifts between the log and field-derived BVW.

A cross-section and a horizon slice through the reservoir show an excellent correlation between the high permeability facies and the permeability logs, which enabled imaging of the highly permeable Middle Hugin unit on the eastern flank of the structure (Figure 15). Localized regions of increased permeability in the east and southeast of the study area suggest lateral changes in the depositional environment. Looking at the map view, we can also see the permeability sweet spots, which are important if they are undrilled and stratigraphically trapped.

Figure 14. Crossplots to classify different lithologies on elastic properties crossplots. The top and center crossplots are shown with unclassified (left) and classified seismic points (right). The points are coloured by their crossplot density and class, respectively. The bottom figure shows the separation of high-permeability on density versus Vp/Vs crossplot.

Figure 15. Classified seismic data is shown on vertical cross-section (red line) and horizon slice 30 ms above the reservoir base, showing the high porosity sands subdivided based on permeability. The permeability log is inserted in black to the right of the well trajectory.


A novel method has been proposed and applied for detecting high-permeability layers by combining seismic, well, and core data through rock physics, petrophysical evaluation, and seismic inversion.

The reservoir sandstone was modelled as a cemented sand, with changes in mineralogy and porosity calculated based on known conditions and a constant cement fraction calibrated to the reservoir. Rock physics modelling of saturations showed that the VpVs ratio is sensitive to fluid changes, but the fluid has no significant effect on density and Vp. Core permeability expressed as a function of log porosity and shale volume allowed the creation of permeability logs and substitution of permeability in the model to analyze whether permeability trends can be used. However, the most accurate classification of the high-permeability layers was realized based on the shifts of the BVW log from the field-predicted values and the associated elastic properties, so permeability was only used to validate the results.

This case example demonstrates that the pore geometry changes are evident through the BVW deviations. Therefore, the advantage of combining advanced quantitative interpretation techniques with BVW modelling is that the BVW can assist in differentiating anomalous permeabilities in the 3D volume even when permeability measurements are unavailable.


We gratefully acknowledge Equinor, ExxonMobil, Bayerngas, and the Norwegian Petroleum Directorate for the Volve field dataset. Thanks also to Laurie Weston and Carl Reine at Sound QI for providing the software and Alex Turta for motivating me to explore this topic (Draga). We thank the CSEG RECORDER journal for inviting us to write this article.


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Cuddy, S. (1993). The Fractal function – a simple, convincing model for calculating water saturations in Southern North Sea gas fields: Transactions of the 34th Annual Logging Symposium of the SPWLA, Calgary, Canada.

Cuddy, S. (2017). Using fractals to determine a reservoir’s hydrocarbon distribution, SPWLA 58th Annual Logging Symposium.

Dvorkin, J., & Nur, A. (1996). Elasticity of high-porosity sandstones: Theory for two North Sea data sets. Geophysics, 61, 1363-1370

Gassmann, F. (1951). Elastic waves through a packing of spheres: Geophysics, 16, 673-685.

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Talinga, D., and Reine, C. (2021). Integrating pore pressure and lithology prediction from well and seismic data to characterize abnormal pressures in the compartmentalized Volve oil field, Central North Sea: CSEG Recorder, 46, no. 02.

About the Authors

Draga Talinga is a Geophysicist with 20 years of experience in resource evaluation, including reservoir characterization and monitoring, anisotropy and natural fractures, and pore pressure and stress, in various basins worldwide. Draga obtained her BSc and MSc from the University of Bucharest, followed by a PhD from the University of Calgary and a Postdoctoral Fellowship from Simon Fraser University, all in geophysics. She recently joined Cenovus Energy as a Senior Geophysicist responsible for asset development and optimization. Draga is very passionate about integrating interdisciplinary data with quantitative interpretation techniques to extract meaningful geological information about the subsurface.


Steve Cuddy is a retired Petrophysicist, having worked with Schlumberger, BP, and Baker Hughes. He holds a PhD in petrophysics at Aberdeen University. He also has a BSc in physics and a BSc in astrophysics and philosophy. He is the inventor of the Fractal FOIL Function that describes the distribution of fluids in the reservoir model. He writes AI software and has 50 years industry experience in petrophysics. In recognition of outstanding service to the SPWLA, he was awarded the Distinguished Service Award in 2018.