# Electrical Submersible Pump Survival Analysis

Topics: Survival analysis, Proportional hazards models, Weibull distribution Pages: 10 (3168 words) Published: May 21, 2013
ELECTRICAL SUBMERSIBLE PUMP SURVIVAL ANALYSIS
MICHELLE PFLUEGER Petroleum Engineer, Chevron Corp. & Masters Degree Candidate

Advisor Dr. Jianhua Huang With help from PHD Candidate Sophia Chen

Department of Statistics, Texas A&M, College Station

MARCH 2011

ABSTRACT
A common metric in Petroleum Engineering is “Mean Time Between Failures” or “Average Run Life”. It is used to characterize wells and artificial lift types, as a metric to compare production conditions, as well as a measure of the performance of a given surveillance & monitoring program. Although survival curve analysis has been in existence for many years, the more rigorous analyses are relatively new in the area of Petroleum Engineering. This paper describes the basic theory behind survival analysis and the application of those techniques to the particular problem of Electrical Submersible Pump (ESP) Run Life. In addition to the general application of these techniques to an ESP data set, this paper also attempts to answer: Is there a significant difference between the survival curves of an ESP system with and without emulsion present in the well? Of the variables collected, which variables best describe the survival function? Do the variables collected in the dataset capture the variation in the survival function?

Survival Analysis in Petroleum Engineering ................................................................................4 Theory of Survival Analysis .........................................................................................................4 Kaplan Meier (Non-Parametric) ...............................................................................................4 Cox Proportional Hazard (Semi-Parametric) ............................................................................6 Weibull (Parametric) ................................................................................................................7 Stepwise Cox & Weibull Regression ........................................................................................8 Application to an ESP Data Set ...................................................................................................9 Data Description ......................................................................................................................9 Finding the P50 time to failure for a dataset...........................................................................11 Comparing two survival curves differing by a factor ...............................................................12 Choosing the Variables that Characterize a Survival Curve ...................................................13 Conclusions ..............................................................................................................................15 Appendices ...............................................................................................................................16 Appendix A: Important Definitions.........................................................................................16 Appendix B: ESP Schematic ................................................................................................17 Appendix C: Data Description Summary ...............................................................................18 Appendix D: References .......................................................................................................19 Appendix E – H: Output ........................................................................................................20

SURVIVAL ANALYSIS IN PETROLEUM ENGINEERING
A common metric in Petroleum Engineering is “Mean Time Between Failure” or “Average Run Life”. It is used to characterize the average “life span” of wells and artificial lift types, as a metric to compare production conditions (which ones give better run life), as well as a measure of the performance of a given...