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1 Subsurface Consultancy Services Porosity from Reservoir Modeling Perspective Arnout Everts with contributions by Peter Friedinger and Laurent Alessio FESM June 2011 LEAP Energy Main Office: G-Tower, level 14 Kuala Lumpur, Malaysia Tel: Web: info@leap-energy.com

2 Objective of this paper Discuss some of the key issues in dealing with porosity data in a 3D reservoir modeling environment Upscaling of well based Porosity evaluations Porosity mapping the inter-well domain constrained with other data (e.g., seismic) Create awareness of common issues and propose potential solutions and workarounds

3 Agenda Upscaling of Porosity data How to avoid Double-dipping Mapping the Inter-well Domain Principles of Geo-statistical Gridding Data Representativeness Defining Spatial Trends Use of depth trends consistency issues in context of porosity cut-offs Use of seismic derived trends what does the seismic see Quantifying Uncertainty Summary and Conclusions

4 Porosity Upscaling

5 Porosity upscaling principles From log scale to 3D model scale GR sand flag POR sand flag Net-to-Gross POR Typically ½ ft scale Typically m - scale Successful upscaling: Minimizes Net pore Volume differences Upscaled Porosity values are representative enough e.g., to use as input into saturation-height For a volumetrically correct solution, upscaling should weigh Porosity values with Net Rock Volume

6 Alternative Porosity upscaling approaches Reservoir modeling tools offer a range of alternative approaches The Net Reservoir Porosity approach is least prone to problems Using input Porosity curves that are 0-ed in the non-net intervals can give seriously flawed results A Input Curves Reservoir flag Upscaled Curves Lith Reservoir flag flag PHI Most Of Continuous N2G PHI no bias PHI Net Res Simple N2G Shale=0 Sand=1 PHI Bias to sand /shale Lith flag Most of PHI Bias to lith flag B Zone B net-weighed avg PHI:

7 Mapping Porosity Principles of Geostatistical Gridding Data Representativeness well sampled Porosity versus population (=field) Mean Depth and Spatial Trends

8 Geo-statistical gridding - kriging and related algorithms Kriging solution Distribution model Assumed population Mean, StDev Stochastic simulation conditioned to the kriged solution Back transformation Spatial de-trending (depth and/or lateral trends) Normalization (normal score and/or other transforms) Kriging engine Variogram model (controls data weighing)

9 Example of biased sampling Well 1 Net Pay/ Net Pore Volume / HCPV Well 2 Exploration high-grades prospects and drilling occurs on high amplitude Predictive model Seismic attribute Amplitude / Seismic attribute sampled at wells (RED) are typically not representative Net sand, Net Pore Volume or HCPV/km2 Distribution Well (2) Well (1) Net sand, Net Pore Volume or HCPV/km2 Distribution Well (2) Well (1) As a result, wells (RED) are biased and a correction should be made before volume calcs But often, this happens!

10 Biased and spatially clustered Sampling Clustered sampling with a sampling bias occurs when wells are clustered on/near presumed reservoir sweet spots Very common in the energy industry because of a desire to drill good reservoir combined with drilling access limitations How can we obtain the real distribution? Hi-porosity samples are clustered PHIT Distribution PHIT distribution biased towards high end

11 Sample De-clustering Cell size 2 x 2 PHIT Distribution

12 Sample De-clustering Cell size 5 x 5 PHIT Distribution

13 Sample De-clustering Cell size 10 x 10 PHIT Distribution

14 Sample De-clustering Cell size 20 x 20 PHIT Distribution

15 Sample De-clustering Cell size 26 x 26 PHIT Distribution

16 Distribution models: de-clustered versus original original distribution declustered distribution

17 Statigraphic zone / facies bias Porosity sampling per stratigraphic zone is even more limited How do we know the data is representative? Depth-normalized porosity all zones Porosity histogram Zone A Zone B Regional Por-Z model Zone C

18 Porosity mapping Depth trends

19 Porosity Depth trends - a lead into the issue Some common knowledge: 1. Porosity generally declines with depth because of compaction 2. In formation evaluation of wells, the concept of a porosity floor is often used to discriminate flowable reservoir from tight rock On a well-by well basis, this is all fine HOWEVER Wells intersecting the same reservoirs at different depth but using the same porosity floor to flag reservoir, can create a very messy situation for the geologist trying to map or model Net Reservoir and Porosity across the field

20 Porosity Impact of Porosity cut-off on Por-depth and N2G trends Use of Porosity cut-off may cause underestimation of porosity decline with depth Well logs PHIT w/o cutoff, colored by reservoir flag Red = Zone avg with Por cut-off Blue = Zone avg without Por cutoff Use of porosity cut-off may introduce a trend of decreasing net-to-gross towards downflank N2G: 0.83 PHI: N2G: 0.82 PHI: N2G: 0.31 PHI: Well A TVDss Well A shifted 500 ft downdip N2G: 0.60 PHI: N2G: 0.65 PHI: N2G: 0.23 PHI: 0.132

21 PHIT Modeling with Depth Trend NTG/VCL PHIT PHIT_cutoff

22 PHIT_cutoff Modeling with Depth Trend NTG/VCL PHIT PHIT_cutoff

23 Statistics of Porosity Modelling Modeling of Porosity will be too optimistic at depth when using porosity cut-off PHIT_cutoff PHIT low tail is squeezed into cut-off value

24 Porosity mapping seismic-based areal trends

25 Seismic-based porosity trends a lead into the issues Impedance = * V Interplay of lithology, porosity and fluid fill Forward model of generating seismic Inverse wavelet Seismic Inversion

26 Typical3D modeling workflow Porosity Depth convert seismic (inversion) Volumes Sample into 3D grid Seismic attribute vs porosity Cross plotting QC position relative to model depth horizons / surfaces Multiple realizations using different statistical techniques (e.g., co-kriging, trend kriging) and / or different attributes (e.g., P- Impedance, S-Impedance) QI attribute

27 Some of the key choices Which seismic attribute to use to constrain porosity, e.g., Absolute versus relative impedance P- or S-Impedance How to access reliability of the seismic porosity prediction? What correlation coefficient to use in the co-kriging? Which seismic attribute to use as secondary variable? Correlation coefficient =?

28 Porosity Porosity Porosity versus impedance Porosity usually declines with depth because of compaction For the same reason, Acoustic Impedance increases with depth In some instances, a significant part of the correlation between AI and porosity is contributed by these depth trends Well logs, net reservoir only Points colored by depth S-Impedance Seismic AI sampled into 3D grid Points colored by depth S-Impedance (seismic volume)

29 Where does the AI-depth trend come from? The low-frequency trend of increasing AI with depth actually comes from the well logs, not from the seismic! Therefore, a critical check on reliability of inversion-based porosity mapping should consider correlating relative AI with de-trended ( relative ) porosity Relative Acoustic Impedance ( bandpass-filtered ) + low frequency AI trend model (from well-log data) = Absolute Acoustic Impedance

30 Correlation between P-Impedance and Porosity before and after removal of depth trend R^2 around 0.5 Depth trend in Porosity X-plot of RT P-Impedance and Phi (includes the depth trend, relatively stronger negative correlation) Typically, the correlation between bandpass filtered AI and de-trended porosity is poorer than that of absolute AI versus porosity X-plot Bandpass filtered P-Impedance and normalized porosity (depth trend removed) R^2 around 0.3

31 HCPV HCPV (ft) Net pay Gaszone Net-Sand Thickness (ft) PHIT net Porosity Seismic constraining in clastic reservoirs The seismic responds to changes in impedance that reflect the interplay of mineralogy, porosity and fluid fill effects Should we use the seismic to constrain the Net, the Porosity or both? And how to correct for fluid fill? y = x R² = y = 0.023x R² = Amplitude vs HCPV How much of this is contributed 25 by the Net, how much is Porosity? Normalized Amplitude Seismic Amplitude (A over B, smoothed) 0 Normalized Amplitude Seismic Amplitude (A over B, smoothed) Top reservoir structure map with amplitude backdrop y = x R² = Normalized Amplitude Seismic Amplitude (A over B, smoothed)

32 Consistency checking of seismically constrained models N2G Net-to-Gross HCPV (ft) HCPV Example: stacked reservoirs situation Q-factor attribute Two independent workflows: 1): Q-factor => NTG 2) Q-factor => HCPV Final step (3) involves comparison/ consistency cross check between the two methods y = x R² = y= x y = x R² = Steep trend Attribute Q-Factor Attribute y= x Q-Factor gentle trend Crosscorrelation with Net-to-Gross Crosscorrelation with HCPV Seismically conditioned HCPV Seismically conditioned Net-Sand distribution + Porosity (P-impedance constrained) + Sw (via saturation-height function) HCPV Consistency check

33 Porosity Uncertainty - Quantifying the impact

34 Porosity Uncertainty holistic view Petrophysical Evaluation Uncertainty + Population Mean Uncertainty (= sampling bias) Localised errors (individual zones/ wells) Systematic errors (affecting all wells) Use Z-test principle to simulate sampling bias Quantify, use as variogram nugget sill nugget Quantify, simulate as a stochastically sampled bulkshift range + Distribution Uncertainty Local distribution pattern Field-wide trends Random seed in stochastic simulation Consider alternative trend models

35 Summary and Conclusions As usual, discipline integration is the key to successful porosity modeling: Geologist understanding what are the various porosity evaluations done by the petrophysicist; Petrophysicist understanding how the geologist is going to use his evaluations in the modeling / mapping; Geologist and Petrophysicist communicating with the Geophysicist / QI specialist to understand what he / she believes are the strengths and limitations of various attribute maps and volumes; Geologist understanding how the Reservoir Engineer is going to use his / her reservoir model (including porosity property).

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