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Second EAGE Workshop on Rock Physics Rock Physics: Integration & Beyond12-14 January 2014

Muscat, Oman

Introduction

Carbonates are known for their highly varying and complex rock frames and pore structures that spanseveral size orders in scale. This makes the modelling of physical properties of carbonateschallenging. It is well known that the relation between permeability and porosity can be complex, butstudies like e.g. Baechle et al. (2008), Weger et al. (2009) and Xu & Payne (2009) have pointed outthat by including velocity in the permeability porosity relationship, a larger part of the permeabilityobservations can be explained. Velocity is related to permeability mainly through porosity and poreshape. Generally high porosity entails lower velocities and high permeability. The carbonate porestructure can influence these relations. Isolated rounded pores can for example result in high velocitiesand low permeabilities in high porous carbonates. The effect of fractures can be opposite low

porosity fractured carbonates can have high permeability and low velocity.

This study is based on the database with carbonate core measurements published by Weger et al.(2009), which is used as a training dataset. We have used a modified version of the rock physicsmodel for carbonates of Sun (2000, 2004), to estimate permeability solely as a function of P-wavevelocity and porosity. The results were tested against an independent database with 101 carbonate

core measurements from seven different locations (the blind test data set). The test results are promising, indicating that over 72 % of the permeabilities can be predicted within one order ofmagnitude. An analysis of the prediction errors indicated the validity areas of the model. Thismethodology elucidates the intricate link between carbonate rock frame stiffness and pore structureflow properties. It offers the potential to improve permeability predictions from wireline sonic data.

Method

Sun (2000, 2004) presented a rock physics model that accounted for various pore types in carbonatesthrough a parameter called frame flexibility factor ( ):

dry (1)

The is the frame flexibility factor for shear modulus ( ), and is porosity. We can derive theeffective dry shear modulus from Vs and density of the rock: Vs 2. This can be used withEquation 1 to estimate the frame flexibility factor for shear stresses. A similar relation can be used for

bulk modulus. In theory the frame flexibility is an important parameter in addition to porosity, whenestimating permeability. In this work we have modified the expression in Equation 1 to include P-wave velocities (Vp) in brine saturated rocks instead of elastic moduli:

Vp Vp

(2)

This is done since Vp is a more common and less uncertain property compared to elastic moduli. We

also use the brine saturated samples directly, without the need for fluid substitution. The frameflexibility factor for P-wave velocities can now be directly expressed by Vp and porosity:

)1(log)(log

10

10

VpVp (3)

Permeability (K) can now be predicted by using the frame flexibility factor for Vp together with porosity. A multivariate regression was performed to find four coefficients (a,b,c and d) to in thefollowing crossproduct:

d cba VpVp )(log)(log)(log 101010 (4)

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that minimized the error between predicted and measured permeabilities. We now have an empiricalmodel for predicting permeability directly from P-wave velocities and porosity.

Figure 1 Predicted versus measured helium core plug permeabilities on the Weger et al. (2009)training data set. The white stippled line in the middle is where predictions coincide withmeasurements (perfect fit), while the two other stippled lines are for deviations of one order ofmagnitude. The indicates how much of the data that are predicted with less than one order ofmagnitude error. Thin sections of the cores marked with green dots are displayed in the upper part of

Figure 3.

Results

Calibration of the model to the training data shows a clear link between permeability, velocity and porosity. Figure 1 shows predicted versus measured results of the calibrated data. The correlation between predicted and measured data was high and more than 78 % of the data was predicted with anerror less than one order of magnitude.

The established relationship between permeability, Vp and porosity can be expressed as a rock physics template, like shown in Figure 2. This template can be practical for visualization purposes,and data can be plotted directly upon it to get a visual impression of the permeability. The velocity-

porosity values shown are calculated by Hashin-Shtrikman bounds, and added 200 m/s, to include a broad range of Vp combinations.

An implication of the model that can be seen in the template, is that permeability for a given porosityvalue increases when Vp increases. This was confirmed from the training data (cf. Weger et al. 2009).The reason for this is that cores with high amounts of micro pores lead to low velocities. Micro poresalso have a demolishing effect on permeability, hence the concurrent increase of velocity and

permeability as concentration of micro pores decrease.

Figure 3 shows thin sections of six samples from the training data. The upper three thin sections areexamples on where permeability predictions are good, even if permeability varies with more than 4orders of magnitude. All the samples are from grainstones with interpaticle porosity. The low

permeability in the sample to the left is caused by high amounts of micro porosity. The two othersamples have low amounts of micro porosity. The three thin sections below show rocks withapproximately the same porosity. Sample 1 (left) is a grainstone with moldic pores and intermediateamounts of micro pores, which together leads to low permeability despite relatively high porosity.Sample 2 is a recrystallized dolomite with vuggy pores, and sample three is a framestone with vuggy

pores. Sample 2 and 3 have low amounts of micro pores. The model predicted too high permeabilityfor sample 1, while sample 2 was well predicted. The extremely high permeability caused by thevuggy framestone in sample 3, was not possible to reproduce with the model.

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The model performance was further tested against the test data set, with 101 carbonate core plugs withmeasured helium plug permeability equal or higher than 0.1 mD. Permeabilities lower than 0.1 mDand higher than 4000 mD are set to be the model limits. As before permeability is modelled from P-wave velocity and porosity. The results can be seen in Figure 4. The correlation coefficient is 0.48.This is partly due to the high scatter at the lower limit of the model, 0.1 mD. More than 72 % of thedata are predicted within one order of magnitude deviation, which is encouraging. When analysing thedata in Figure 4, we find that the model digressed with reproducing low porosity high permeabilitydata, where permeability predictions were too low, see Figure 5. Also predicting high porosity low

permeability data was challenging, since permeability predictions were too high. By analysing thereported pore types in each core, it became clear that the permeability prediction errors were related tospecific pore types; predictions of permeability in high porosity samples with oomoldic porosity arealmost exclusively too high, and predictions in low porosity samples with intercrystaline/inter particle

pores are generally too low. This is consistent with observations from the calibration dataset.

Figure 2 Rock physics template of Vp, porosity and permeability. The white stippled lines are iso- permeability lines according to the model.

Figure 3 The upper three thin sections show examples where permeability predictions are good overa range of more than 4 orders of magnitude. Permeability increases from left to right. The lower thin

sections show examples with approximately constant porosity, where the model 1) overpredicts permeability 2) predicts permeability and 3) underpredicts permeability.

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Figure 4 Predicted versus measured permeability on the test data set. White stippled lines are asdefined in Figure 1.

Figure 5 Identification of permeability prediction on the test data set that was more than one order of

magnitude (OM) too low (magenta) and more than one order of magnitude too high (red). Green dotswere predicted with less than one order of magnitude deviation.

Conclusions

Permeability has been predicted from velocity and porosity by using an empirical approach. Themodel is calibrated to a database, with more than 78 % of the predicted permeabilities deviating lessthan one order of magnitude. A template for visual permeability analysis is constructed. Whenevaluating the model for a test dataset of 101 core measurements, the model managed to reproducemore than 72 % of the permeabilities within one order of magnitude. Analysis of pore types in thedifferent samples (Figure 3 and Figure 5) shows that there is a clear correlation between data with toohigh predictions and pore types: Permeability in moldic and oomoldic pores are predicted to be higher

than measured, since they result in low permeability even at very high porosities. Close integrationwith geological information can improve the predictability of the model. By excluding the fewmeasurements on oomoldic pores from Figure 4, there is hardly any data that are predicted with toohigh permeability, and more than 78 % of the data are predicted within one order of magnitude.Various pore types contribute in the carbonate cores with too low predicted permeability. Thecommon feature of these pores is that they manage to maintain a network, and maintain flow

properties even for low porosities. The velocity - permeability model is fast and simple, and a naturalnext step will be to test it on well logs where also core measurements are available. Ultimately, the

presented model can potentially be used to identify flow units in a reservoir from seismic data.

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Acknowledgements

We would like to thank our colleagues Aart Jan Van Wijngarden and Giulio Cassini for discussionsand constructive contributions to this work, and Statoil for permission to publish this study. Further,we thank the Comparative Sedimentology Laboratory at the University of Miami for data andcooperation.

References

Baechle, G.T., Colpaert, A., Eberli, G.P. and Weger, R. [2008] Effects of microporosity on sonicvelocity in carbonate rocks. The Leading Edge , 27 (8), 1012-1018. doi:10.1190/1.2967554

Sun, Y.F. [2000] Core-log-seismic integration in hemipelagic marine sediments on the eastern flankof the Juan de Fuca Ridge. In: Fisher, A., Davis, E.E. and Escutia, C. (Eds.) Proc. ODP, Sci. Results,168: College Station, TX (Ocean Drilling Program), 21-35.

Sun, Y.F. [2004] Seismic signatures of rock pore structure. Applied Geophysics , 1(1), 42-49.

Weger, R.J., Eberli, G.T., Baechle, G.P., Massaferro, J.-L. and Sun, Y.F. [2009] Quantification of pore structure and its effect on sonic velocity and permeability in carbonates. AAPG Bulletin , 93 ,1297-1317. doi:10 .1306/05270909001

Xu, S. and Payne, M.A. [2009] Modelling elastic properties in carbonate rocks. The Leading Edge ,28 , 66-74.

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