Integrating rock physics modeling, prestack inversion and Bayesian classification Brian Russell
Introduction Today, most geoscientists have an array of tools available to perform seismic reservoir characterization. However, the complexity of these tools increases year by year, and can be overwhelming at times. In this talk, I will discuss several analysis and visualization tools that improve the user-friendliness of the reservoir characterization process. These tools will include both statistical methods and deterministic methods, and will combine both well log measurements and pre-stack inversion. I will illustrate the various methods with an example from an oil sand play in the North Sea. 2
North Sea Example Our example includes a 3D inverted pre-stack seismic dataset and three wells over a field from the North Sea. This was an oil-sand play and the location of the field is confidential. This study indicates that by-passed oil had been missed between the wells C and D. We will display our results over both the full survey and the extracted line shown on the right. 3
Well B MD (m) Tops P-imp (m/s*g/cc) 2000 12000 Vp/Vs 1.5 3.5 Phie 0 0.3 Facies TVD (m) The well logs from well B, showing P-impedance, Vp/Vs ratio, porosity and facies. 1850 1850 The facies will be discussed in more detail later, but note that the green facies represents the oil sands. 2050 2050 4
Well log crossplot A cross-plot of V P /V S ratio versus P-impedance (ρv P ) for wells A D, with porosity as the colour attribute. 4.5 Porosity 0.3 We can analyze this crossplot either statistically or deterministically. We will start with statistical clustering and then use a deterministic approach to explain the clusters. 5 Vp/Vs Ratio 1.5 2000 P-impedance 12000 (m/s*g/cc) 0.0
Automatic clustering Five clusters have been identified using Mahalanobis K-means clustering. 4.5 Porosity 0.3 The key question is how to interpret these five clusters. We will next discuss a rock physics template method which allows us to perform such an interpretation. Vp/Vs Ratio 1.5 2000 P-impedance (m/s*g/cc) 12000 0.0 6
The rock physics template (RPT) Ødegaard and Avseth (2003) developed a rock physics template in which the fluid and mineralogy of a reservoir could be displayed on a cross-plot of V P /V S ratio vs acoustic impedance. The elastic constants are computed as a function of porosity, pressure and saturation using Hertz-Mindlin theory, the lower Hashin-Shtrikman bound and Gassmann fluid substitution. Notice the pressure, clay content, porosity, cement and fluid trends. from Ødegaard and Avseth (2003)
Interpreting the clusters The clusters from the previous plot can be interpreted as shown using the Ødegaard and Avseth RPT template. This is one use of the rock physics template. A second use, shown next, is to draw a set if curves on the cross-plot as a function of saturation and porosity, or any other two parameters. Vp/Vs Ratio 4.5 1.5 2000 Gas Sand Shale Wet Sands P-impedance (m/s*g/cc) Cemented Sands 12000 Porosity 0.3 0.0 8
A porosity versus saturation template The rock physics template for the soft sand model is shown here, as a function of water saturation and porosity. 4.5 Porosity 0.3 Note that the template fits the gas sand well for low S W and high porosity. Vp/Vs Ratio Later, we will colour-code this RPT and display the results on the seismic. 1.5 35% 100% S W 0% Porosity 5% 0.0 9 2000 P-impedance 12000 (m/s*g/cc)
Creating V P /V S and P-impedance volumes Using a technique called simultaneous pre-stack inversion, we can transform the seismic angle gathers into estimates of P-impedance, S- impedance and, if the angle range is great enough, density. The ratio of P-impedance to S-impedance will then give us the V P /V S ratio over the whole seismic volume. By cross-plotting V P /V S ratio versus P-impedance using the seismicderived values, we can therefore do the same type of rock physics analysis over the whole seismic dataset as we did at the well. This is illustrated next for the North Sea example. 10
North Sea Example 10 o Angle Stack 1800 Well C Well D Well B Time (ms) 2100 11 A display of the 10 o angle stack from the extracted line through the wells.
North Sea Example 20 o Angle Stack 1800 Well C Well D Well B Time (ms) 2100 12 A display of the 20 o angle stack from the extracted line through the wells.
North Sea Example 30 o Angle Stack 1800 Well C Well D Well B Time (ms) 2100 13 A display of the 30 o angle stack from the extracted line through the wells.
North Sea Example Full Stack 1800 Well C Well D Well B Time (ms) 2100 14 A display of the full stack from the extracted line through the wells.
North Sea Example Pre-stack inversion Well C Well D Well B 1800 Time (ms) 2100 15 The inverted P-impedance (Ip) from the extracted line through the wells.
North Sea Example Pre-stack inversion Well C Well D Well B 1800 Time (ms) 2100 16 The inverted Vp/Vs ratio from the extracted line through the wells.
North Sea Example Pre-stack inversion Well C Well D 1800 Zone 2 Time (ms) Zone 1 Zone 3 1900 17 A blow-up of the Vp/Vs data, with 3 picked zones. Zone_1 (red) is low Vp/Vs, low Ip, Zone_2 (blue) is high Vp/Vs, low Ip, and Zone_3 (yellow) is medium Vp/Vs, high Ip.
The picked zones Here is a Vp/Vs vs P- impedance plot of the three picked zones. Note that these three zones appear to correlate with hydrocarbon sands (red), shales (blue) and cemented sands (yellow). 2.5 Vp/Vs Ratio 18 1.7 1600 P-impedance 6200 (m/s*g/cc)
Superimposing a rock physics template This figure shows the superposition of a rock physics template of S W vs Porosity on the seismic cross-plot, optimized by adjusting V shale and pressure. Note that the red points from the oil sand show higher porosity and lower water saturation, as expected. 19 Porosity S W
Colouring the rock physics template We can now fill in a colour template for the RPT. Note that each colour fills in a grid cell delineated by porosity and water saturation increments. In this case, we have used a rainbow type colour scheme. 20
Superimposing the colours Here is the application of the new colour palette on the RPT with opacity turned on so we can still see the points. Although the oil sand shows up as the orange colour, the rainbow colours makes this display too busy to easily interpret. Porosity S W 21
Re-colouring the rock physics template Thus, we set the colours to white and then slowly fill them in with red, blue and yellow to match the zones as shown on the left. 22 Porosity S W
Seismic volume coloured by the PEM Well C Well D Well B 1800 Time (ms) 2000 Here is the final colour scheme superimposed on the seismic section, clearly showing the oil sands. 23
Bayesian Classification Now that we have identified the clusters associated with oil sands, shales and cemented sands on the crossplot, we can assign a Bayesian probability classification scheme to the three clusters. For K clusters, the k th cluster, or class, can be defined by the Gaussian pdf f(x c k ). Note that x can be a single variable, in which case the pdf is a Gaussian curve, or a two-dimensional vector, in which case the pdf is an ellipse. We then compute the separation between the i th and j th clusters using a Bayesian decision boundary. 24
North Sea Example Cross plot from extracted zones A re-display of the cross-plot of the P- impedance and Vp/Vs ratio data extracted from the three zones. Note that the histograms of the two variables are now shown. 25
North Sea Example Bivariate Gaussian pdfs Bivariate Gaussian pdf functions fitted to the three extracted zones shown in the previous plot. 26
North Sea Example Application to seismic data Well C Well D Well B 1800 Time (ms) 2100 27 Projection of the Gaussian pdfs back on the seismic data.
North Sea Example User picked zones Bivariate Gaussian pdf functions fitted to the three extracted zones shown in the previous plot. 28
North Sea Example Application to seismic data Well C Well D Well B 1800 Time (ms) 2000 29 Projection of the zones back on the seismic data.
An alternate approach Note that the previous display shows interesting anomalies that could be related to hydrocarbon pay. However, note that we did not use the wells directly in this analysis, only indirectly in the building of the model for the inversion. We will now take a different approach to what we have been doing so far and actually use the well logs as part of the calibration. This will involve the use of the RockSI and LithoSI programs. 30
North Sea Example Cross plot showing facies 3.0 Facies Coal Shale Sand Oil Calcite Facies Coal Shale Sand Oil Calcite Vp/Vs 31 1.6 Ip (m/s*g/cc) 3000 12000 A cross-plot of measured Vp/Vs ratio vs P-impedance showing facies in colour. 3000 12000 Same cross-plot but using predicted values from rock physics templates.
3.5 North Sea Example Monte Carlo simulation Facies Coal Shale Sand Oil Calcite Vp/Vs 32 1.5 3000 Ip (m/s*g/cc) Same cross-plot but using Monte Carlo simulated values from rock physics templates. 12000 3000 Ip (m/s*g/cc) 12000 Non-parametric pdf fit to the simulated facies in LithoSI.
North Sea Example Most likely facies Calcite Oil Sand Water Sand Shale Coal 33 Most likely facies prediction from LithoSI.
North Sea Example Oil probability on section Oil sand probability from LithoSI. Note that there is a large area of by-passed production between wells C and D. 34
North Sea Example Comparison with Bayesian fit Well C Well D Well B 1800 Time (ms) 2100 35 Note that the Bayesian fits gives a similar answer, but much less detailed.
North Sea Example Oil probability on time slice 36 This time slice of oil sand probability at 1860 ms also shows a large area of by-passed production between wells C and D.
Conclusion In this talk, I have discussed several analysis and visualization tools that improve the user-friendliness of the reservoir characterization process. These tools will included both statistical methods, such as clustering and Bayesian analysis, and deterministic methods such as rock physics modeling. The methods combine both well log measurements and pre-stack inversion. I illustrated the various methods with an example from an oil sand play in the North Sea. For Hampson-Russell users, note that the analysis involved new tools found in the Geoview program as well as both the RockSI and LithoSI programs. 37