Statistical Characterization Using Automatic Learning Gaussian Mixture Models in Diamond M Field, TX David Lubo*, The University of Oklahoma, Simon Bolivar University Vikram Jayaram, The University of Oklahoma Kurt J. Marfurt, The University of Oklahoma

RESEARCH OBJECTIVE  In a situation when we have thousands of wells in a resource play, the propose workflow can determine which wells are alike and which are different. We can also deduce if is there a correlation to those that are alike or different to know where we have good EUR.

OUTLINE  Problem Statement: Unsupervised classification using GMM  Gaussian Mixture Models (GMM)  Independent Component Analysis (ICA)  Geological Setting: Diamond M Field  Statistical Characterization using GMM  Study conclusions

PROBLEM STATEMENT (Unsupervised Classification using GMM) GENERATIVE TOPOGRAPHIC MAPPING (GTM) From Roy,2013

GAUSSIAN MIXTURE MODEL (GMM) where,  Provides greater flexibility and accuracy than traditional unsupervised clustering algorithms. How can we calculate these Gaussian Parameters?  We use an Expectation Maximization Algorithm, which use a convergence function to obtain the model parameters of each mixing component. Also, we use a “dynamic” algorithm to determine the true number of mixing components. This algorithm is capable of adding and removing mixing component WITHOUT any user intervation.

GAUSSIAN MIXTURE MODELS (GMM) ATTRIBUTE2 ATTRIBUTE

INDEPENDENT COMPONENT ANALYSIS (ICA) s=W -1 m (5) Person 1 Person 2

GEOLOGICAL SETTING: DIAMOND M FIELD Modified from Walker,1995  Located in Scurry County, TX at 80 Mi of the Midland Basin.  Is a component of the Permian Basin. (Late Mississippian – Pensyllvanian)  Collision of North America and Tobosa Basin.  Carbonate shelves developed along the western, northern, and eastern margins. Study Targets Horseshoe Atoll Complex and San Andres Formation

GEOLOGICAL SETTING: DIAMOND M FIELD Horseshoe Atoll:  Cisco and Canyon Formation  Late Pennsylvanian to Early Permian  Carbonate buildup composed of rich biomicritic grainstones with some packstone, wackestone and boundstones sequences  High variability of the sea level gives rise to a layering of tight and porous layers and hence significant reservoir heterogeneity Modified from Tinker et al., 2004

GEOLOGICAL SETTING: DIAMOND M FIELD San Andres Formation:  Carbonate prograding stratigraphic unit.  Lithology includes: Dolomite Limestone Salt Siliciclastics Facies  Porosity was probably developed during subaerial exposure  The fact we have many types of lithologies within the reservoir, implies reservoir heterogeneity. Modified from Tinker et al., 2004

STATISTICAL CHARACTERIZATION USING GMM  Producer Wells: Jade, Topaz and M08  Dry Wells: F03, K03A and L02A  An Inversion Cube was used with values from 30,000 to 60,000 ft.gr/s.cm3  Run the Inversion Cube with a 3 by 3 window (taking all the trace), applying ICA, GMM and Bayes Classifier.

STATISTICAL CHARACTERIZATION USING GMM

M08 vs F03

STATISTICAL CHARACTERIZATION USING GMM Jade vs K03A

STATISTICAL CHARACTERIZATION USING GMM Topaz vs L02A

STATISTICAL CHARACTERIZATION USING GMM M08-F03 vs Jade (Producer) Jade-K03A vs M08 (Producer) M08-F03 vs K03A (Dry) Jade-K03A vs F03 (Dry)

STATISTICAL CHARACTERIZATION USING GMM Performance

STATISTICAL CHARACTERIZATION USING GMM M08 F03K03AL02A

STATISTICAL CHARACTERIZATION USING GMM JADE F03K03AL02A

F03K03AL02A STATISTICAL CHARACTERIZATION USING GMM TOPAZ

CONCLUSIONS  We propose a workflow based on independent component analysis and Gaussian mixture models that statistically represent the variability measured between the producers and dry wells. This characterization is derived without any user intervention. For this reason, it is called an “automatic learning” GMM.  The variability in Gaussian Mixture Model (GMM) represents the lateral and vertical changes seen in acoustic impedance within the reservoir. Although making probability maps, using the variability between wells, allow us to identify and quantify possible sweet-spots.  In a situation when we have thousands of wells in a resource play, the propose workflow can determine which wells are alike and which are different. We can also deduce if is there a correlation to those that are alike or different to know where we have good EUR.  The algorithm is really fast, each map can be made in 30 minutes using a personal computer.

ACKNOWLEDGEMENTS We thank to Parallel Petroleum LLC for the use of their data and the Attribute- Assisted Seismic Processing and Interpretation (AASPI) consortium for its financial support. Graphics were made using licenses to Petrel, provided to OU for research and education courtesy of Schlumberger.

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