Shale samples .1 Sample #8 .1 Sample #8

4.2 Shale samples 4.2.1 Sample #8

Sample #8 is a shale-oil sample, the location of depth is 8212.17ft, the effective porosity is 6.63%, gas filled porosity is 6.34%, and the mobile oil saturation is 1.27%. In general, the main IP response recorded of shale rocks will be caused by the membrane polarization, which see the IP effect at a higher frequency (500 to 1000 Hz). About 6.64% of disseminated pyrite is found in this sample by QEMSCAN measurement, it is in sufficient concentrations to produce its own electrode IP peak at lower frequency, and the IP response was observed between 0.01 and 1Hz. But it does not record the membrane polarization at high frequency response. Figure 4.7 shows the observed data along with the predicted data using the two-phases ellipsoidal GEMTIP model.

Figure 4.7. Inversion result of sample #8 using the two-phases ellipsoidal GEMTIP model.

Figure 4.8 is a misfit functional of sample #8 plotted with relaxation parameter and time constant. Figure 4.9 shows the inversion result using the three-phases model, but only shows the imaginary part of the data fitting. The final misfit is 5% and 3.2%, respectively. Table 4.3 shows the inversion parameters result. The recovered volume fraction value for the two-phases and three-phases model is close to each other, which is a very reasonable value compared with QEMSCAN pyrite volume fraction (6.64%) and gas filled porosity (6.34%). While the three-phases inversion result exactly separates these two effects, one represents electrode polarization cause by disseminated pyrite, and another phase (4%) represents membrane polarization caused by hydrocarbon.

Figure 4.8. The misfit functional of sample #8, plotted with relaxation parameter (C) and time constant (τ).

Figure 4.9. Inversion result of sample #8 using the three-phases ellipsoidal GEMTIP model.

Table 4.3 Inversion parameters for sample #8 using the ellipsoidal GEMTIP model Parameter Units Initial value Two-phases Three-phases

39 - 30

% 10 10 6.35

- 0.1 0.45 0.27

seconds 0.1 1.19 2.15

% - - 4

- - - 0.59

seconds - - 0.46

4.2.2 Sample #33

Sample #33 is a shale-gas sample, the location of depth is 6197.4 ft, the effective porosity is 12.23%, gas filled porosity is 7.98%, the mobile oil saturation is 17.03% and 1.41% of disseminated pyrite was found in this sample by QEMSCAN measurement. The total clay is 0.6%. In this sample, the IP response was observed to be less than 0.01 Hz.

However, it does not record the membrane polarization. Figure 4.10 shows the observed data along with the predicted data using the two-phases randomly oriented ellipsoids GEMTIP model.

Figure 4.10. Inversion result of sample #33 using the two-phases ellipsoidal GEMTIP model.

Figure 4.11 is a misfit functional of sample #8 plotted with shaded isolines signifying the direction of decreasing misfit. Figure 4.12 shows the inversion result using the three-phases model, but only shows the imaginary part data fitting. Both models predicted data fit the observed data very well. The final misfit is 5% and 3.5%, respectively. Table 4.4 shows the inversion parameters result. The recovered volume fraction value is reasonable in comparison with the known value. The three-phases inversion result separate the pyrite (2.41%) and hydrocarbon (8.11%) very well. The recovered pyrite is a little higher than the real value (1.41%), which is why sample #33 has a calcite matrix, it easily reacts with the solution, and surrounding the pyrite, then increases the pyrite volume fraction.

Figure 4.11. The misfit functional of sample #33, plotted with relaxation parameter (C) and time constant (τ).

Figure 4.12. Inversion result of sample #33 using the three-phases ellipsoidal GEMTIP model.

Table 4.4 Inversion parameters for sample #33 using the ellipsoidal GEMTIP model Parameter Units Initial value Two-phases Three-phases

36 - 46

% 10 13 2.41

- 0.1 0.35 0.28

seconds 0.1 2.93 8.59

% - - 8.11

- - - 0.43

seconds - - 3.69

4.2.3 Sample #45

Sample #45 is a laminated shale gas sample, the location of depth is 13843.51 ft, the effective porosity is 2.39%, gas filled porosity is 1.19%, the mobile oil saturation is 33.52%, and 3.53% of disseminated pyrite was found in this sample by the QEMSCAN measurement. In this sample, we can clearly see two IP peaks: one is attributed to its large amount of pyrite grains (electrode polarization), and the IP response was observed at 0.1 Hz, another one is attributed to the hydrocarbon bearing shale (membrane polarization), the IP response was observed at 100 Hz. Figure 4.13 shows the observed data along with the predicted data using the two-phases randomly oriented ellipsoidal GEMTIP model.

Figure 4.13. Inversion result of sample #45 using the two-phases ellipsoidal GEMTIP model.

Figure 4.14 is a misfit functional of sample #8 plotted with shaded isolines signifying the direction of decreasing misfit. The model steps are plotted using red solid dots. The final model is shown as a solid triangle. Figure 4.15 shows the inversion result using the three-phases model, but only shows the imaginary part data fitting. The predicted data fit the observed data well. Table 4.5 shows the inversion parameters result.

The final misfit is 7% and 6.26%, respectively. Both models recovered volume fraction is close to the real value: 3.53% pyrite and 1.19% gas filled porosity. The three-phases inversion result separates the pyrite and hydrocarbon very well.

Figure 4.14. The misfit functional of sample #45, plotted with relaxation parameter (C) and time constant (τ).

Figure 4.15. Inversion result of sample #45 using the three-phases ellipsoidal GEMTIP model.

Table 4.5 Inversion parameters for sample #45 using the ellipsoidal GEMTIP model Parameter Units Initial value Two-phases Three-phases

78 - 89

% 10 6.6 4.41

- 0.1 0.42 0.35

seconds 0.1 1.55 2.15

% - - 1

- - - 0.77

seconds - - 1.29

4.3 Discussion

In summary, two igneous rock samples and three shale samples were analyzed using the ellipsoidal GEMTIP model. All tested samples showed IP peaks at relatively low frequencies. Modeling these IP phenomena with two-phases and three-phases ellipsoidal GEMTIP model proved to be very effective, and reasonable inversion results were recovered, especially the volume fraction parameter, which is very close to X-ray microtomography results or QEMSCAN measurement results, however, the three-phases ellipsoidal GEMTIP model can display more.

For two mineral rock samples, the three-phases inversion result of sample K01 not only recovered the real volume fraction value, but also separated the different size minerals. The three-phases inversion result of sample #13 separated the pyrite from chalcocite. For three-shale samples, the three-phases inversion result separated electrode polarization caused by disseminated pyrite and membrane polarization, which was caused by hydrocarbon contained in the shale samples. This study shows that the GEMTIP model can be used in the hydrocarbon bearing shale rocks.

It was also noted by Pelton (1978) that as one decreases the grain size, the time constant also decreases. The inversion result of this study supports this observation. Table 4.6 shows the parameters value of the shale sample. Figure 4.16 shows the plot of relationship time constant and grain size of shale samples. It is found that the time constant increases as the grain size increases.

Table 4.6 GEMTIP parameters value of shale samples

Sample Pyrite grain size ( m) Time constant (s)

#8 10.21 1.19

#45 12.39 1.55

#33 13.56 2.93

Figure 4.16. Relationship between GEMTIP model parameters of shale samples: time constant vs. grain size.

CONCLUSIONS

A thorough study of complex resistivity of rocks using GEMTIP analysis shows that the exact cause of the IP effect is quite complicated, however, being able to model it can be very useful in improving mineral discrimination techniques. This research focused on the randomly oriented ellipsoidal GEMTIP model. Forward modeling has been done to see how varying individual parameters of the model can affect complex resistivity data. Seeing how the parameters influence the data is very useful for understanding the complex nature of these models.

Two mineral rock and three shale samples containing disseminated sulfides were examined by the ellipsoidal GEMTIP model. Complex resistivity data was obtained by TechnoImaging. Three shale samples and sample #13 were analyzed by QEMSCAN at the University of Utah, Department of Geology and Geophysics. QEMSCAN was used to obtain quantitative values for parameters such as volume fraction, grain type and grain size. All of these measurements combined to form a detailed quantitative analysis of the samples that were then be used for inversion.

The regularized conjugated gradient method was used in a two-phases GEMTIP model inversion, and the extensive search method was used in a three-phases GEMTIP model inversion, reasonable inversion results were recovered. The geologic information from QEMSCAN provides a good comparison with recovered parameters (volume

fraction). By comparing the two-phases with the three-phases inversion results, the mineral rock samples study shows that the three-phases GEMTIP model can separate the different mineral sizes and different mineral types from the same sample; the shale samples show the three-phases GEMTIP model can separate the membrane polarization, caused by the internal structure of the shale samples, from electrode polarization caused by disseminated pyrite. This study shows that the GEMTIP model can be used in hydrocarbon bearing shale rocks. The inversion recovered parameters time constant shows that as the grain size increases the time constant also increases.

In the future, it would be useful to continue collecting complex resistivity data sets for shale samples in order to further analyze the relationship between GEMTIP model parameters and actual rock characteristics. For example, relationships between grain size and volume fraction, relationships between grain size and relaxation parameters are very important factors in identifying minerals for geophysicist. Lots of sample studies can find a direct correlation between GEMTIP model parameters and mineral type. The application of GEMTIP model will be a good tool for mineral exploration.

APPENDIX A

INVERSION RESULT

The following tables contain two-phases and three-phases GEMTIP model parameters value and inversion results of all samples used in the project. is matrix resistivity, is the grain size of type mineral, is ellipticity of the type mineral,

Table A.2 Three-phases inversion result

Parameter Units K01 #13 #8 #33 #45

80 188 30 46 89

mm 1 0.05 0.01 0.013 0.01

- 10 10 10 10 2.3

% 3.59 1.2 6.35 2.4 4.4

- 0.59 0.59 0.28 0.28 0.77

s 0.022 0.16 2.15 3.69 2.15

⁄ 0.5 0.013 0.00012 0.0002 0.0002

mm 2 0.1 0.001 0.001 0.001

- 10 10 10 3.9 1

% 5.99 5 4 8.1 1

- 0.22 0.22 0.59 0.43 0.35

s 0.001 0.001 0.46 8.5 1.29

⁄ 0.5 0.013 0.00012 0.0002 0.0002