Probabilistic Fisher discriminant analysis based on Gaussian mixture model for estimating shale oil sweet spots

doi:10.1007/s11707-021-0926-5

Front. Earth Sci.

2022, Vol. 16

Issue (3) : 557-567 https://doi.org/10.1007/s11707-021-0926-5

RESEARCH ARTICLE

Probabilistic Fisher discriminant analysis based on Gaussian mixture model for estimating shale oil sweet spots

Kun LUO, Zhaoyun ZONG(

)

School of Geosciences, China University of Petroleum, Qingdao 266555, China

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Abstract

The delineation of shale oil sweet spots is a crucial step in the exploration of shale oil reservoirs. A single attribute such as total organic carbon (TOC) is conventionally used to evaluate the sweet spots of shale oil. This study proposes a probabilistic Fisher discriminant approach for estimating shale oil sweet spots, in which the probabilistic method and Gaussian mixture model are incorporated. Statistical features of shale oil facies are obtained based on the well log interpretation of the samples. Several key parameters of shale oil are projected to data sets with low dimensions in each shale oil facies. Furthermore, the posterior distribution of different shale oil facies is built based on the classification of each shale oil facies. Various key physical parameters of shale oil facies are inversed by the Bayesian method, and important elastic properties are extracted from the elastic impedance inversion (EVA-DSVD method). The method proposed in this paper has been successfully used to delineate the sweet spots of shale oil reservoirs with multiple attributes from the real pre-stack seismic data sets and is validated by the well log data.

Keywords probabilistic Fisher discriminant analysis sweet spots shale-oil facies Bayesian inversion

Corresponding Author(s): Zhaoyun ZONG

Online First Date: 30 November 2021 Issue Date: 29 December 2022

Cite this article:

Kun LUO,Zhaoyun ZONG. Probabilistic Fisher discriminant analysis based on Gaussian mixture model for estimating shale oil sweet spots[J]. Front. Earth Sci., 2022, 16(3): 557-567.

URL:

https://academic.hep.com.cn/fesci/EN/10.1007/s11707-021-0926-5
https://academic.hep.com.cn/fesci/EN/Y2022/V16/I3/557

Algorithm 1 PFDA algorithm for estimating shale oil sweet spots.
Input: Data matrix $x j (k)$ of each class $G j$
1: Calculate the within scatter matrix $S w$ in (3) and the between scatter matrix $S b$ in Eq. (4).
2: Calculate the discriminative projection matrix $W$ by maximizing the function given in Eq. (2).
3: Obtain the samples $y j (k)$ after projection of the raw data set by calculating the function given in Eq. (8).
4: Calculate the means vectors and covariance matrix, $μ j d$ , $Σ j d$ , $Σ n$ , $μ n$ .
5: Estimate the shale oil sweet spots by the discriminant probability function given in Eqs. (11) and (12).
End

Fig.1 The workflows of the probabilistic Fisher discriminant approach for estimating shale oil sweet spots.

Fig.2 From left to right: (a) P-wave velocity, (b) S-wave velocity, (c) density, (d) Young’s modulus, (e) Poisson’s ratio, (f) porosity, (g) pyrolysis S1, (h) clay, (i) total organic carbon, and (j) lithofacies distribution.

Fig.3 The classification of shale oil facies and the statistical characteristics of key evaluation parameters of shale oil; the three types are (

G 1

) organic-rich mudstones with high maturity, (

G 2

) organic-lean intervals of sand, and (

G 3

) organic-rich mudstones with low maturity.

Fig.4 Cross plot of key parameters of shale oil facies: (a) Young’s modulus and clay content, (b) total organic carbon (TOC) and clay content, (c) Poisson’s ratio and clay content, (d) S1 and clay content, (e) Porosity and clay content, (f) Poisson’s ratio and clay content, (g) Young’s modulus and S1, (h) Porosity and S1, (i) Poisson’s ratio and Young’s modulus, (j) Poisson’s ratio and porosity, (k) Porosity and TOC, (l) Young’s modulus and TOC, (m) Poisson’s ratio and TOC, (n) Porosity and Young’s modulus. The yellow circles, black circles and dark blue circles represent the facies of

G 1

G 2

, and

G 3

, respectively.

Fig.5 The mean and standard deviation of new two-dimensional data sets of each type and the cross plot of shale oil facies after Fisher dimension reduction. The coordinate “dimension 1” and “dimension 2” are obtained by the dimension reduction of model parameters.

Fig.6 The inversion results of six key shale oil parameters, (a) clay content, (b) total organic carbon, (c) Young’s modulus, (d) pyrolysis S1, (e) Poisson’s ratio, and (f) porosity.

Fig.7 The comparison of the delineation of shale oil sweet spots from (a) single TOC attribute and (b) the delineation obtained by FPDA method from multiple attributes.

1	D AbuZeina, F S Al-Anzi (2018). Employing fisher discriminant analysis for Arabic text classification. Comput Electr Eng, 66: 474–486 https://doi.org/10.1016/j.compeleceng.2017.11.002
2	Y S Bao, L Y Zhang, J G Zhang, J Y Li, Z Li (2016). Factors influencing mobility of Paleogene shale oil in Dongying Sag, Bohai Bay Basin. Oil & Gas Geo, 37(3): 408–414
3	S Chen, W Z Zhao, Q C Zeng, Q Yang, P He, S H Gai, Y Deng (2018). Quantitative prediction of total organic carbon content in shale-gas reservoirs using seismic data: a case study from the Lower Silurian Longmaxi Formation in the Chang Ning gas field of the Sichuan Basin, China. Interpretation (Tulsa), 6(4): SN153–SN168 https://doi.org/10.1190/INT-2018-0038.1
4	J Q Chen, X Q Pang, X L Wang, Y X Wang (2020). A new method for assessing tight oil, with application to the Lucaogou Formation in the Jimusaer depression, Junggar Basin, China. AAPG Bull, 104(6): 1199–1229 https://doi.org/10.1306/12191917401
5	P Connolly (1999). Elastic impedance. Leading Edge (Tulsa Okla), 18(4): 438–452 https://doi.org/10.1190/1.1438307
6	J Espitalie, J L Laporte, M Madec, F Marquis, P Leplat, J Paulet, A Boutefeu (1977a). Rapid method for source rock characterization and for determination of their petroleum potential and degree of evolution. Oil & Gas Sci Techn Revue, 32(1): 23–42
7	R A Fisher (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7: 179–188
8	D H Foley, J W Sammon (1975). An optimal set of discriminant vectors. IEEE Trans Comput, C-24(3): 281–289 https://doi.org/10.1109/T-C.1975.224208
9	K E Gorynski, M Tobey, D Enriquez, T Smagala, J Dreger, R Newhart (2019). Quantification and characterization of hydrocarbon-filled porosity in oil-rich shales using integrated thermal extraction, pyrolysis, and solvent extraction. AAPG Bull, 103(3): 723–744 https://doi.org/10.1306/08161817214
10	D Grana, E Della Rossa (2010). Probabilistic petrophysical-properties estimation integrating statistical rock physics with seismic inversion. Geophys, 75(3): O21–O37 https://doi.org/10.1190/1.3386676
11	D Grana, T Fjeldstad, H Omre (2017). Bayesian Gaussian mixture linear inversion for geophysical inverse problems. Math Geosci, 49(4): 493–515 https://doi.org/10.1007/s11004-016-9671-9
12	R Y Guo, Y Q Bai, C N Li, Y H Shao, Y F Ye, C Z Jiang (2021). Reverse nearest neighbors Bhattacharyya bound linear discriminant analysis for multimodal classification. Eng Appl Artif Intell, 97: 104033 https://doi.org/10.1016/j.engappai.2020.104033
13	R Hu, L Vernik, L Nayvelt, A Dicman (2015). Seismic inversion for organic richness and fracture gradient in unconventional reservoirs: Eagle Ford Shale, Texas. Leading Edge (Tulsa Okla), 34(1): 80–84 https://doi.org/110.1190/tle34010080.1
14	R Z Huang (1984). A model for predicting formation fracture pressure. J China U Petrol (Nat Sci), 8: 335–347
15	C R Jiang, L H Chen (2020). Filtering-based approaches for functional data classification. Wiley Interdiscip Rev Comput Stat, 12(4): 1–15 https://doi.org/10.1002/wics.1490
16	D M Jarvie (2012). Shale resource systems for oil and gas: part 2—shale-oil resource systems. AAPG Mem, 97: 89–119 https://doi.org/10.1306/13321446M973489
17	K Luo, Z Y Zong (2020). Pyrolysis S1 discrimination of shale gas with Pre-stack seismic inversion. In: Annual Meeting of Chinese geoscience union 2020, Beijing
18	K Li, X Y Yin, Z Y Zong (2020). Facies-constrained pre-stack seismic probabilistic inversion driven by rock physics. Scientia Sinica Terrae, 50(6): 832–850
19	K Luo, Z Y Zong (2019). Sweet spots discrimination of shale gas with Pre-stack seismic inversion. In: Annual Meeting of Chinese Geoscience Union 2019, Beijing, 53: 29–31
20	L Ma, Z L Lin, H F Hu, D Zhou (2020). Seismic prediction method of fracture pressure in a shale formation. In: SEG International Exposition and 90th Annual Meeting, 1068–1072 https://doi.org/10.1190/segam2020-3428109.1
21	S Ouadfeul, L Aliouane (2016). Total organic carbon estimation in shale-gas reservoirs using seismic genetic inversion with an example from the Barnett Shale. Leading Edge (Tulsa Okla), 35(9): 790–794 https://doi.org/10.1190/tle35090790.1
22	O Ogiesoba, U Hammes (2014). Seismic-attribute identification of brittle and TOC-rich zones within the Eagle Ford Shale, Dimmit County, South Texas. J Pet Explor Prod Technol, 4(2): 133–151 https://doi.org/10.1007/s13202-014-0106-1
23	M Raji, D R Gröcke, C Greenwell, C Cornford (2015). Pyrolysis, porosity and productivity in unconventional mudstone reservoirs: free and adsorbed oil. In: Unconventional Resources Technology Conference, 11: 270–279 https://doi.org/10.15530/urtec-2015-2172996
24	R Rickman, M J Mullen, J E Petre, W V Grieser, D Kundert (2008). A practical use of shale petrophysics for stimulation design optimization: all shale plays are not clones of the Barnett Shale. In: SPE Technical Conference and Exhibition https://doi.org/10.2118/115258-MS
25	C R Rao (1948). The utilization of multiple measurements in problems of biological classification. J R Stat Soc B, 10(2): 159–193 https://doi.org/10.1111/j.2517-6161.1948.tb00008.x
26	A Sena, G Castillo, K Chesser, S Voisey, J Estrada, J Carcuz, E Carmona, P Hodgkins (2011). Seismic reservoir characterization in resource shale plays: “sweet spot” discrimination and optimization of horizontal well placement. In: 81st Annual International Meeting, SEG, Expanded Abstracts, 1744–1748.
27	G Z Song, Y Lin, S F Lu (2013). Resource evaluation method for shale oil and its application. Earth Sci Front, 20(4): 221–228
28	S Verma, T Zhao, K J Marfurt, D Devegowda (2016). Estimation of total organic carbon and brittleness volume. Interpretation (Tulsa), 4(3): T373–T385 https://doi.org/10.1190/INT-2015-0166.1
29	H J Wang (2017). Prediction of geological dessert in shale gas with pre-stack seismic inversion. Dissertation for the Master’s Degree. Qingdao: China University of Petroleum (East China)
30	L Wu, C H Shen, A Hengel (2017). Deep linear discriminant analysis on fisher networks: a hybrid architecture for person re-identification. Pattern Recognit, 65: 238–250 https://doi.org/10.1016/j.patcog.2016.12.022
31	S Wang, Q Feng, F Javadpour, T Xia, Z Li (2015). Oil adsorption in shale nanopores and its effect on recoverable oil-in-place. Int J Coal Geol, 147–148: 9–24 https://doi.org/10.1016/j.coal.2015.06.002
32	H Wang, S C Yan, D Xu, X O Tang, T Huang (2007). Trace ratio vs. ratio trace for dimensionality reduction. In: Proceedings of the Conference on Computer Vision and Pattern Recognition. Minneapolis, USA: IEEE, 1–8
33	Z Wang, Q Ruan, G An (2016). Facial expression recognition using sparse local Fisher discriminant analysis. Neurocomputing, 174: 756–766 https://doi.org/10.1016/j.neucom.2015.09.083
34	X Y Yin, W Cui, Z Y Zong, X J Liu(2014). Petrophysical property inversion of reservoirs based on elastic impedance. Chinese J Geophys, 57(12): 4132–4140 https://doi.org/10.6038/cjg20141224
35	J Q Yu, Z Q Yu, Z Q Mao, G Gao, K Luo, T Lei, Z Y Zong(2020). Prediction of total organic carbon content in source rock of continental shale oil using pre-stack inversion. Geophys Prospect Petrol, 59(5): 823–830 https://doi.org/10.3969/j.issn.1000-1441.2020.05.016
36	X Y Yin, Z Y Zong, G C Wu (2015). Research on seismic fluid identification driven by rock physics. Sci China Earth Sci, 58(2): 159–171 https://doi.org/10.1007/s11430-014-4992-3
37	X Y Yin, S H Yuan, F C Zhang (2004). Rock elastic parameters calculated from elastic impedance. CPS/SEG Technical Program Expanded Abstracts
38	Z Y Zong, X Y Yin, G C Wu (2013). Elastic impedance parameterization and inversion with Young’s modulus and Poisson’s ratio. Geophysics, 78(6): N35–N42 https://doi.org/10.1190/geo2012-0529.1
39	Z Y Zong, X Y Yin, F, Zhang G C Wu (2012a). Reflection coefficient and pre-stack seismic inversion with Young’s modulus and Poisson’s ratio. Chinese J Geophys, 55(11): 3786–3794 https://doi.org/10.6038/j.issn.0001-5733.2012.11.025
40	Z Y Zong, X Y Yin, G C Wu (2012b). Pre-stack inversion for rock brittleness indicator in gas shale. In: Annual meeting of Chinese Geoscience Union 2012. Beijing, 17: 495

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