Summary
A rigorous statistical methodology using survival analysis (SA) was
developed and applied to electrical submersible pump (ESP) system performance
data. The approach extracts unbiased information from performance data and
permits lifetime modeling, with parameter combinations employing all available
data. The analysis explicitly accounts for ESPs that are still operational at
the time of the study, thus removing a historical source of statistical bias.
The analysis uses Kaplan-Meier (KM) (Kaplan and Meier 1958) and Cox
proportional hazards (CPHs) (Cox 1972) modeling to determine statistical
significance of explanatory variables (EVs). Methods developed to facilitate EV
factor collapsing are also discussed (the partitioning of levels of each factor
into nonempty subsets of statistically similar response), so that an acceptable
degree of parsimony is achieved. Essential definitions necessary for
preliminary data structure are also covered.
We demonstrate the practical utility of this methodology on a comprehensive
data set to enable unbiased and conclusive appraisal of ESP performance,
thereby resolving a common concern about comparative-system reckoning. The
paper concludes that SA, suitably applied to properly censored data, is
essentially the only reliable method of evaluating ESP system performance (and
other types of time-to-event data).
Introduction
The critical importance of ESP system performance to field economics and
deliverability has been well documented (Allis and Capps 1984; Upchurch 1990;
Brookbank 1996). What has been missing, however, is agreement as to what
constitutes the most appropriate methodology for analyzing the wealth of
performance data that are collected. The manner in which the available data are
scrutinized, analyzed, qualified, and presented is influential to timely,
economic, and accurate well and field design. This paper shows how we can
extract the full profundity of useful information that inhabits even a
moderately sized data set through application of, what we consider to be, the
only truly appropriate technique for analyzing time-to-event data: SA.
The objective of any SA is to identify variables that influence survival and
to predict survival probabilities. This is achieved by finding a suitable
statistical model that fits the data closely. We then examine variables
included in the model and, finally, make predictions about ESP system
performance for well- and field-planning purposes. The structure of this
article is as follows:
- First, we outline the problems and inconsistencies inherent with existing
(non-SA) analysis approaches to ESP performance analysis.
- Background on SA is then provided, along with an outline of the three main
classes of SA methodology.
- We define terminology; in particular, the terms “system” and
“components.”
- We then present a summary of the extensive data set employed in the
analysis.
- The remainder of the paper presents a detailed and sequential SA for a rich
data set to demonstrate how parameter interaction, factor collapsing, and
appropriate goodness-of-fit measures can be employed to achieve a parsimonious
model of the given data. Note that a parsimonious model, in this context,
refers to one containing the minimum number of significant parameters that
adequately represents the data.
- Finally, we conclude that SA is the only viable and appropriate unbiased
time-to-event methodology for evaluating ESP system performance.
The analytical process we propose represents the given data parsimoniously
and provides performance indicators (with confidence bounds) in response to
specific questions. At the risk of premature presentation of results, Fig. 1
shows just one such SA plot that can be generated. This plot provides unbiased
answers to a specific question: “What is the performance between Cable
Manufacturers A, B, and C when required to last 500 days, when installed with
Motor Series “D” in a well that has sand (abrasion) present?” Also, “What
degree of confidence can we have in these results?”
We see from Fig. 1 that 57% of pumps installed with Cable Manufacturer “A”
are expected to survive to 500 days, while only approximately 33% of pumps with
Cable Manufacturer “B and C” survived to this time (note that B and C are
grouped together, as are Motor Series Types “D, L, and I,” because there is no
statistical difference between them). For Cable Manufacturer A, we are 95%
confident that the interval between 40 and 80% covers the true (unknown)
proportion surviving to 500 days. The equivalent range for Cable Manufacturers
B and C is between 25 and 48%. We conclude, therefore, that for the specific
conditions stated in the question (and everything else being equal),
Manufacturer A performs better than B and C by the margins stated. Associated
validation statistics also conclude that we may draw reliable statistical
inference from these results. We now have a solid platform upon which to base
performance contracts.
By the end of this article, we hope to have demonstrated a rigorous and
unbiased methodology for analyzing ESP system performance data and essentially
any time-to-event data.
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
24 October 2005
- Meeting paper published:
9 October 2005
- Revised manuscript received:
9 March 2006
- Manuscript approved:
10 March 2006
- Version of record:
20 November 2006
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