Statistical Characterization Using Automatic Learning Gaussian Mixture

Models in Diamond M Field, TXDavid Lubo*, The University of Oklahoma, Simon Bolivar UniversityVikram Jayaram, The University of OklahomaKurt J. Marfurt, The University of Oklahoma

Norman,OK. November , 2014

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) Is a linear sum of M Gaussian probability density functions (PDFs). Multidimensional data aj(t) can be modeled using Gaussian Parameters ().

where,

M

jmmjmjjmj taGtap

1

,),( C

jmjmT

jmj

mJmjmj tatataG

)()(

21

exp)2(

1,),( 1

2/12/C

CC

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

ATTR

IBU

TE1

4 Gaussians= ,= ,= ,= ,

1

34

2

INDEPENDENT COMPONENT ANALYSIS (ICA)

𝑴𝟏=𝒘𝟏𝟏𝒔𝟏+𝒘𝟏𝟐𝒔𝟐(3)

𝑴𝟐=𝒘𝟐𝟏𝒔𝟏+𝒘𝟐𝟐𝒔𝟐(4) s=W-1m (5)

𝒔𝟏

𝒔𝟐

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 FIELDHorseshoe 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 FIELDSan 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

STATISTICAL CHARACTERIZATION USING GMMM08 vs F03

STATISTICAL CHARACTERIZATION USING GMMJade vs K03A

STATISTICAL CHARACTERIZATION USING GMMTopaz vs L02A

STATISTICAL CHARACTERIZATION USING GMMM08-F03 vs Jade (Producer) Jade-K03A vs M08 (Producer)

M08-F03 vs K03A (Dry) Jade-K03A vs F03 (Dry)

STATISTICAL CHARACTERIZATION USING GMMPerformance

STATISTICAL CHARACTERIZATION USING GMMM08

F03 K03A L02A

STATISTICAL CHARACTERIZATION USING GMMJADE

F03 K03A L02A

F03 K03A L02A

STATISTICAL CHARACTERIZATION USING GMMTOPAZ

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.

ACKNOWLEDGEMENTSWe 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.

QUESTIONS