Twenty Second Annual Meeting 20192020 Multivariate Analysis for

Twenty Second Annual Meeting: 2019/2020 Multivariate Analysis for Response Surface Methodology: Horn River Shale Case Study Chuks Anthony Sunday

Content • Introduction • Objective • Methodology • Data structure • Exploratory data analysis • Data Imputation • Response Surface Methodology (RSM) • Conclusions • References 2

Introduction • Multiple geological rock properties are jointly used for characterizing geologic deposits of formation • Geological and engineering models are constructed from multiple rock properties • Geological models – to assess resources/reserves • Engineering models - for engineering design, study and optimize processes, and for predictions of properties of interest • Multivariate analysis and property modeling are thus very essential in resource management 3

Objectives • Understand the multivariate relationships between the HRS formation properties • Use both parametric and non-parametric response surface methodologies (RSM) to develop response surface production models for the HRS formation. 4

Methodology 5

Geology of the Horn River Shale (HRS) • HRS occupies approx. 12, 000 km 2 within the Horn River Basin in the Northeastern BC and extends into the Northwest Territories. • Comprises of 3 formations: Muskwa, Otter Park and Evie members • Traps approx. 11. 1 TCF of gas (Teklu et al. , 2018). Stratigraphic position of the Horn River Basin (Teklu et al. , 2018) 6 Stratigraphic layout of the HRS (Ferri et al. , 2011)

Geology of the HRS cont. • HRS is divided into 9 stratigraphic units • Muskwa – 2 units; • Otter Park member – 5 units; and • Evie member – 2 units 7

Data Structure • Total number of wells: 150 • Basic reservoir geometry data: top elevation • Well log data: gamma-ray log • Production data from 30 wells: barrels of oil equivalent (BOE) • Three (3) formations: Muskwa, Otter Park, and Evie • NAN – missing value • Objects (ᴏ, �, ⌂, √): sampled values 8

Exploratory Data Analysis (EDA) • Summary statistics • Location map of the wells • Declustering of the data • Normal score transformation of the data – keeps all data in the same range of values. • Bivariate scatter plot • Correlation coefficients outliers • Variography outliers 9

EDA cont. • Summary statistics • Location map of the wells • Declustering of the data • Normal score transformation of the data – keeps all data in the same range of values. • Bivariate scatter plot • Correlation coefficients • Variography 10

EDA cont. • Summary statistics • Location map of the wells • Declustering of the data • Normal score transformation of the data – keeps all data in the same range of values. • Bivariate scatter plot – reveals the relationship between two variables • Correlation coefficients • Variography 11

EDA cont. • Summary statistics • Location map of the wells • Declustering of the data • Normal score transformation of the data – keeps all data in the same range of values. • Bivariate scatter plot • Correlation coefficients • Variography 12

EDA cont. • Summary statistics • Location map of the wells • Declustering of the data • Normal score transformation of the data • Bivariate scatter plot • Variography – spatial variability of the variables. 13

Data Imputation GMM Imputation • Non-parametric method • Fitted Gaussian Mixture Model (GMM) with 3 components. • Use the GMM to generate L realizations of data (sampled + impute), L=100 • Note: sampled values are unchanged and no imputation is done for production data 14

Data Imputation cont. • 15

Response Surface Methodology (RSM) • A method for creating a mathematical relationship between a response variable and some predictor variables. • Goal to is develop, improve, and optimize a prediction or response model • Two techniques considered • Parametric regression method • Non-parametric regression method 16

Response Surface Methodology (RSM) • A method for creating a mathematical relationship between a response variable and some predictor variables. • Goal to is develop, improve, and optimize a prediction or response model • Two techniques considered • Parametric regression method • Non-parametric regression method 17

RSM cont. Parametric Regression Methods • Use a parametric function to fit and develop a direct relationship between a response and some predictors • Could be: • Linear regression method or • Polynomial regression method 18

RSM cont. Parametric Regression Methods 19

RSM cont. Parametric Regression Methods Data Preparation • Training and test data = 30 wells • Training data = 40% • Testing data = 60% • Prediction data = 120 wells • Goal is to develop response surface production models 20 prediction data

RSM cont. Parametric Regression Methods 21

RSM cont. Parametric Regression Methods 22

RSM cont. Non- Parametric Regression Methods 23

RSM cont. Non- Parametric Regression Methods 24

RSM cont. Non- Parametric Regression Methods 25

RSM cont. Model Comparison 26

RSM cont. Model Summary • ACE and ACE Bootstrapping regression methods seem good to model the HRS formation 27

Conclusions • Parametric response surface models are easy to develop for multiple variables but are biased with non-parametric signals. • Non-parametric regression method should be used to model multiple variables with non-linear, non-parametric relationships, such as the HRS dataset. • The ACE bootstrapping regression model would yield reliable predictions since it accounts for uncertainty in the training data and is not overfitted. • Models could be used as decision making tools 28

References • Aydar, A. Y. (2018). Utilization of Response Surface Methodology in Optimization of Extraction of Plant Materials. DOI: 10. 5772/intechopen. 73690, Intechopen, https: //www. intechopen. com/books/statistical-approaches-with-emphasis-on-design-ofexperiments-applied-to-chemical-processes/utilization-of-response-surface-methodology-in-optimization-of-extraction-of-plantmaterials , February 7. • Ferri, F. , Hickin, A. , and Huntley, D. (2011). Besa River Formation, Western Liard Basin, British Columbia (NTS 094 N): Chemistry and Regional Correlations. Geoscience Reports. British Columbia Ministry of Energy, Mines and Natural Gas. • Hmoud, S. and Boisvert, J. (2016). Horn River Shale: Dataset Overview and Spatial Statistics. CCG Paper 2016 -211, Centre for Computational Geostatistics, University of Alberta, Edmonton, Canada. • Lekou, D. J. (2013). Probabilistic Design of Wind Turbine Blades – Advances in Wind Turbine Blade Design and Materials. Science. Direct, https: //www. sciencedirect. com/topics/engineering/response-surface-method • Teklu, T. W. , Park, D. , Jung, H. , and Miskimins, J. L. (2018). Integrated Rock Characterization of a Shale Gas Field in the Horn River Basin, Canada. URTe. C-2880467, presented at the Unconventional Resources Technology Conference held in Houston, Texas, USA, July 23 -25. 29

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